ArticlePDF Available

Seven-Day versus Five-Day Flow-Capacity

Authors:

Abstract and Figures

Studies show that, for emergency presentations, there is a positive correlation between admission at weekends and poorer outcomes as measured by higher mortality. Data from a typical medium sized hospital reveals that the A&E 4-hour breach rates shows a 7-day cycle, as do the emergency admissions and hospital discharges. The combined effect is a rising hospital bed occupancy over the weekend which, if beds are limited, creates an admission bottleneck, admission delays, potential harm for the most vulnerable patients and stress for staff. A stream-aligned discrete event simulation (DES) model was developed and verified using actual data from the hospital. This was then used to predict the impact of switching from a 5-day to a 7-day discharge flow-capacity policy. The effect was a reduction in variation of hospital bed occupancy that released sufficient space-capacity (beds) to eliminate the weekend admission bottleneck. Just smoothing the decision making and discharge flow-capacity across the week provided the necessary flow-resilience to significantly reduce admission delays and 4-hour breaches in A&E. The cost of this policy change is predicted to be neutral. We conclude that developing system-wide flow design capability in the NHS is a potentially high-benefit strategy for improving safety, flow, quality experienced by both patients and staff, and NHS productivity. (207 words).
Content may be subject to copyright.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
1 | Page http://www.journalofimprovementscience.net Version 1.2
Seven-Day versus Five-Day Flow-Capacity.
Author:
Simon Dodds, MA, MS, FRCS.
e: simon.dodds@heartofengland.nhs.uk
Sponsor:
Kate Silvester BSc, MBA, FRCOphth.
e: Kate@katesilvester.co.uk
Abstract
Studies show that, for emergency presentations, there is a positive correlation between admission at
weekends and poorer outcomes as measured by higher mortality. Data from a typical medium sized
hospital reveals that the A&E 4-hour breach rates shows a 7-day cycle, as do the emergency admissions and
hospital discharges. The combined effect is a rising hospital bed occupancy over the weekend which, if
beds are limited, creates an admission bottleneck, admission delays, potential harm for the most
vulnerable patients and stress for staff. A stream-aligned discrete event simulation (DES) model was
developed and verified using actual data from the hospital. This was then used to predict the impact of
switching from a 5-day to a 7-day discharge flow-capacity policy. The effect was a reduction in variation of
hospital bed occupancy that released sufficient space-capacity (beds) to eliminate the weekend admission
bottleneck. Just smoothing the decision making and discharge flow-capacity across the week provided the
necessary flow-resilience to significantly reduce admission delays and 4-hour breaches in A&E. The cost of
this policy change is predicted to be neutral. We conclude that developing system-wide flow design
capability in the NHS is a potentially high-benefit strategy for improving safety, flow, quality experienced by
both patients and staff, and NHS productivity.
(207 words).
Keywords
Healthcare; Safety; Mortality; Flow; Length of Stay; Quality; Productivity; Cost; Seven Day Services; System
Behaviour Charts; System Dynamics; Simulation Model; Vitals Charts;
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
2 | Page http://www.journalofimprovementscience.net Version 1.2
Context
Published evidence shows that patients admitted as emergencies at weekends have a higher mortality than
those admitted on weekdays and that the effect persists after adjusting for other factors [7].
Fig 1. A chart from [7] showing that, taking Monday
as the reference, the risk of mortality of being
admitted at a weekend is about 8% higher and if
admitted on a Thursday is about 4% lower (bars are
95% confidence intervals).
The cause of this statistically significant association is assumed to be multi-factorial. Often suggested as
causal factors are reduction in the availability of junior and senior medical staff and limited access to
diagnostic services at weekends; but robust evidence to support these hypotheses is hard to find.
The conclusion that follows is that, to avoid the excess mortality and to provide a safer service, we would
require more weekend working by staff, particularly along the whole unplanned care pathway. The
consequences are that this change would increase the cost of the whole emergency pathway from
presentation, to referral and attendance at hospital, and through to discharge back home.
This essay examines the hypothesis for a typical medium-sized district general hospital. The largest
emergency flow stream is the medical emergencies including the medical elderly. So we will focus on just
that stream.
It is well known that delay from presentation to diagnosis and treatment is associated with poorer
outcomes for patients presenting with symptoms of heart attacks or strokes, and that designing processes
to be capable of shorter ‘door-to-needle’ times improves outcomes and reduces length of stay (LoS) [4,5].
So it is reasonable to suggest that delay from presentation to definitive treatment for a wider range of
emergency referrals may be associated with a more severe illness, poorer outcomes, longer length of stay,
lower quality of patient experience and higher costs [3].
One frequently reported cause of clinical delay is medical emergencies who are seen and assessed quickly
but then have to wait for many hours for a hospital bed to become available. If that delay leads to a more
serious illness and a longer length of stay, then a self-reinforcing adverse feedback loop is created in which
the longer length of stay increases the bed occupancy and exacerbates the admission bottlenecks and A&E
delays. It may even contribute to a higher mortality in the most vulnerable patients.
This chronic ‘internal pressure’ leads naturally to demands for more beds to ease the congestion, and then
to carving this larger bed-stock into more manageable pieces that are dedicated to specific groups of
patients: A&E majors, GP referrals, medical, surgical, short stay, long stay, frail elderly, and so on. This
fragmentation creates further complexity for staff, impairs efficient communication and effective decision-
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
3 | Page http://www.journalofimprovementscience.net Version 1.2
making and indirectly contributes further to longer length of stay and increased cost. So, in the context of a
limited budget, fragmentation of services is not a wise strategy.
The alternative approach is to reduce bed occupancy by facilitating the flow of emergency admissions
through the hospital including earlier diagnosis, treatment monitoring and discharge. By this means a self-
reinforcing, beneficial feedback loop would be created with shorter length of stay, reduced bed occupancy,
better staff to patient ratios, better outcomes, less severe illness and potentially lower costs.
Challenge
The challenge here is to understand the current system design well enough to identify if there are any
‘sweet spots’ along the emergency pathway where interventions would lead to improved safety, flow, and
quality performance; without increasing the costs.
To do this we need to map, measure and model the current state of the emergency medical pathway in a
real hospital to gain a deeper understanding of the root causes of the system behaviour that we observe.
This is an empirical approach, we are not testing a research hypothesis, we are diagnosing a ‘system design
disease’.
Fig 1. Shows that the complexity of the patient’s pathway through the hospital system compared to the
relative simplicity of the clinical process. Delays at any stage in the clinical process (including monitoring
and reviewing a patients progress) will result in delays and congestion along the pathway. Failing to
address these delays in the clinical process will require more bed capacity and increase the complexity of the
system.
The emergency medical pathway
A&E
Assessment
Unit(s)
Short stay
Specialist ward (s)
diagnostics
Theatres
ITU
pharmacy
Community
Care
Social care
Home
Ambulance
transport
GP
therapies
Hospital
The emergency medical process
Presentation
History &
Examination
& Observations
Diagnostic
tests
Discharge
To self care,
+/- support from GP,
OP, community
social care
Monitor
Response
Compare to
Diagnosis &
prognosis
Diagnosis
Prognosis
Plan
Treatment
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
4 | Page http://www.journalofimprovementscience.net Version 1.2
Current State
In order to examine the flow along the emergency pathway from attendance to admission and discharge,
the activity data from a typical medium-sized district general hospital for emergency medical admissions for
one financial year, April 2011 to April 2012, were extracted from the hospital information system. We shall
call our hospital St. Elsewhere’s® (StE) and it is a real hospital.
The daily counts for the patients attending A&E, emergency admissions from A&E, the emergency patients
discharged from hospital, and the bed occupancy are plotted as a time-series charts in order of date and
then split into rational groups by day of the week to test if there is a weekly cycle within the data.
Fig 2. System behaviour chart of daily StE A&E arrivals for 2011-12. The green line is the average and the red
lines are the limits of natural variation (average +/- 3 sigma). The blue histogram shows the distribution.
Fig 2 shows that there is (1) no sustained change in A&E activity over the year, (2) evidence of a regular
weekly cycle, and (3) only a weak seasonal cycle with higher activity in the summer and lower in the winter.
07/04/2011
14/04/2011
21/04/2011
28/04/2011
05/05/2011
12/05/2011
19/05/2011
26/05/2011
02/06/2011
09/06/2011
16/06/2011
23/06/2011
30/06/2011
07/07/2011
14/07/2011
21/07/2011
28/07/2011
04/08/2011
11/08/2011
18/08/2011
25/08/2011
01/09/2011
08/09/2011
15/09/2011
22/09/2011
29/09/2011
06/10/2011
13/10/2011
20/10/2011
27/10/2011
03/11/2011
10/11/2011
17/11/2011
24/11/2011
01/12/2011
08/12/2011
15/12/2011
22/12/2011
29/12/2011
05/01/2012
12/01/2012
19/01/2012
26/01/2012
02/02/2012
09/02/2012
16/02/2012
23/02/2012
01/03/2012
08/03/2012
15/03/2012
22/03/2012
29/03/2012
Date
0
50
100
150
200
250
300
350
400
450
Patients St. Elsewhere's (R) - Daily A&E Arrivals
BaseLine 1.20.010
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
5 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 3. Shows the same daily A&E arrivals data rationally grouped by day of the week. The green lines are the
averages for each group and the red lines are the limits of natural variation (average +/- 3 sigma). The blue
histogram shows the same bimodal distribution as Fig 2.
Fig 3 confirms that there is indeed a weekly cycle with highest A&E arrivals on Sat, Sun and Mon.
Fig 4. System behaviour chart of the count of daily emergency medical admissions rationally grouped by day
of the week and plotted in time order. Green lines are the average for each group and red lines are the
upper and lower process limits (average +/- 3 sigma). The global mean is 42.2 admissions per day.
Fig 4 shows visually and clearly that the StE system exhibits a 7-day cycle with 20% fewer medical
emergency admissions at weekends, and slightly higher than average admissions on Mondays.
06/06/2011
15/08/2011
24/10/2011
02/01/2012
12/03/2012
24/05/2011
02/08/2011
11/10/2011
20/12/2011
28/02/2012
11/05/2011
20/07/2011
28/09/2011
07/12/2011
15/02/2012
28/04/2011
07/07/2011
15/09/2011
24/11/2011
02/02/2012
08/04/2011
17/06/2011
26/08/2011
04/11/2011
13/01/2012
23/03/2012
28/05/2011
06/08/2011
15/10/2011
24/12/2011
03/03/2012
08/05/2011
17/07/2011
25/09/2011
04/12/2011
12/02/2012
Date
0
10
20
30
40
50
60
70
80
90
100
Patients St Elsewhere's (R) - Medical Admissions
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
16/05/2011
04/07/2011
22/08/2011
10/10/2011
28/11/2011
16/01/2012
05/03/2012
26/04/2011
14/06/2011
02/08/2011
20/09/2011
08/11/2011
27/12/2011
14/02/2012
06/04/2011
25/05/2011
13/07/2011
31/08/2011
19/10/2011
07/12/2011
25/01/2012
14/03/2012
05/05/2011
23/06/2011
11/08/2011
29/09/2011
17/11/2011
05/01/2012
23/02/2012
08/04/2011
27/05/2011
15/07/2011
02/09/2011
21/10/2011
09/12/2011
27/01/2012
16/03/2012
30/04/2011
18/06/2011
06/08/2011
24/09/2011
12/11/2011
31/12/2011
18/02/2012
03/04/2011
22/05/2011
10/07/2011
28/08/2011
16/10/2011
04/12/2011
22/01/2012
11/03/2012
Date
0
50
100
150
200
250
300
350
400
450
Patients St. Elsewhere's (R) - Daily A&E Arrivals
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
6 | Page http://www.journalofimprovementscience.net Version 1.2
So there does not appear to be a direct correlation between the number of attendances at A&E and the
number of medical admissions.
And unless there is a change in the case mix with less ill patients attending A&E at weekends, and/or a
change in the clinical threshold for admission, we need an alternative explanation as to why the admission
rate is lower on Saturdays and Sundays.
Neither does the reported association of higher mortality at weekends make sense as Fig. 4 suggests that
there will be fewer emergency admissions for the weekend teams to manage.
However, new demand is not the only source of weekend workload. The patients already in the hospital
require monitoring, reviewing and ongoing clinical decisions to keep them on the road to recovery and to
discharge.
So to gain a deeper understanding of how this internal queue of patients is varying over time we need to
examine the discharges from hospital as well; because it is the difference between admissions and
discharges that drives the internal queue up and down. This is the work in progress or WIP, the patients
occupying the beds.
Fig 5. System behaviour chart of count of daily discharges for those patients admitted as medical
emergencies. The data is rationally grouped by day of the week and plotted in time order. Green lines are
the average for each group and red lines are the upper and lower process limits (average +/- 3 sigma). The
global mean is 42.2 discharges per day. The obvious bimodal distribution is caused by the much lower
discharge rate at weekends.
Observations:
1. The global average of emergency medical admissions and discharges is the same (42.2 patients per
day). This is expected over a long period of time, even though there may be small differences
between admissions and discharges due to seasonal and other effects over shorter time periods of
days and weeks.
06/06/2011
15/08/2011
24/10/2011
02/01/2012
12/03/2012
24/05/2011
02/08/2011
11/10/2011
20/12/2011
28/02/2012
11/05/2011
20/07/2011
28/09/2011
07/12/2011
15/02/2012
28/04/2011
07/07/2011
15/09/2011
24/11/2011
02/02/2012
08/04/2011
17/06/2011
26/08/2011
04/11/2011
13/01/2012
23/03/2012
28/05/2011
06/08/2011
15/10/2011
24/12/2011
03/03/2012
08/05/2011
17/07/2011
25/09/2011
04/12/2011
12/02/2012
Date
0
10
20
30
40
50
60
70
80
90
100
Patients St Elsewhere's (R) - Medical Discharges
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
7 | Page http://www.journalofimprovementscience.net Version 1.2
2. Compared to Fig. 4 there is a larger amplitude 7-day cycle in the number of daily discharges than
the number of daily admissions over the same period of time with about 40% fewer discharges at
weekends.
The inevitable effect of this cyclical mismatch between admissions and discharges will be a 7-day cycle of
variation in the size of the queue of emergency medical patients within the hospital; patients who are
somewhere along the clinical and administrative process between admission and discharge. Given that a
hospital represents fixed space-capacity in terms of the number of beds available for patients to occupy
then, if the queue of patients increases predictably over the weekend, we might expect to find it becomes
more difficult to admit new medical emergency patients on Sundays and Mondays.
Figures 6 and 7 show the daily bed occupancy at midnight.
Fig 6. System behaviour chart of the number of emergency medical patients in hospital at midnight for the
same period as the admissions and discharges (01/04/2011-31/03/2012).
The pattern in Fig. 6 shows considerable variation with both a slow downward trend between June and
December, and a regular 7-day cyclical pattern. The lowest medical emergency bed occupancy was 198
patients (Xmas 2011) and the highest was 331 patients (Mar 2012). The global mean was 283 patients.
07/04/2011
14/04/2011
21/04/2011
28/04/2011
05/05/2011
12/05/2011
19/05/2011
26/05/2011
02/06/2011
09/06/2011
16/06/2011
23/06/2011
30/06/2011
07/07/2011
14/07/2011
21/07/2011
28/07/2011
04/08/2011
11/08/2011
18/08/2011
25/08/2011
01/09/2011
08/09/2011
15/09/2011
22/09/2011
29/09/2011
06/10/2011
13/10/2011
20/10/2011
27/10/2011
03/11/2011
10/11/2011
17/11/2011
24/11/2011
01/12/2011
08/12/2011
15/12/2011
22/12/2011
29/12/2011
05/01/2012
12/01/2012
19/01/2012
26/01/2012
02/02/2012
09/02/2012
16/02/2012
23/02/2012
01/03/2012
08/03/2012
15/03/2012
22/03/2012
29/03/2012
Date
150
200
250
300
350
400
450
Patients St Elsewhere's (R) - Midnight Occupancy
BaseLine 1.20.010
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
8 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 7. Same data as Fig. 6 plotted in rational groups by day of the week. The blue line is the global mean of
283 patients in hospital. The pattern over time in each group matches the seasonal pattern shown in Fig. 6,
but each group is shifted on the Y-axis with highest average occupancy on Sun, Mon, Tue and Wed, and
lowest on Thu and Fri - illustrating the weekly cycle effect. Note that WIP data is not plotted with process
limits because it is a cusum metric (cumulative sum of the difference between admissions and discharges)
and this invalidates the standard method for estimating sigma.
So having established that the bed occupancy is higher on Sundays, Monday, Tuesdays and Wednesdays,
does the breach rate in A&E show the same pattern, supporting our hypothesis that the poor flow through
the hospital, impacts the flow through A&E?
Fig 8. System behaviour chart of the daily % of 4 hour breaches for the same time period..
Comparing Fig. 8 and Fig. 6 reveals an association between the A&E 4-hour breach rate and the number of
occupied beds at midnight; the higher the occupancy the higher the breach rate.
10/04/2011
20/04/2011
30/04/2011
10/05/2011
20/05/2011
30/05/2011
09/06/2011
19/06/2011
29/06/2011
09/07/2011
19/07/2011
29/07/2011
08/08/2011
18/08/2011
28/08/2011
07/09/2011
17/09/2011
27/09/2011
07/10/2011
17/10/2011
27/10/2011
06/11/2011
16/11/2011
26/11/2011
06/12/2011
16/12/2011
26/12/2011
05/01/2012
15/01/2012
25/01/2012
04/02/2012
14/02/2012
24/02/2012
05/03/2012
15/03/2012
25/03/2012
Date
0
5
10
15
20
25
30
35
40
% 4hr Breach St. Elsewhere's (R) - 4hr A&E Breach Rate
BaseLine 1.20.010
06/06/2011
15/08/2011
24/10/2011
02/01/2012
12/03/2012
24/05/2011
02/08/2011
11/10/2011
20/12/2011
28/02/2012
11/05/2011
20/07/2011
28/09/2011
07/12/2011
15/02/2012
28/04/2011
07/07/2011
15/09/2011
24/11/2011
02/02/2012
08/04/2011
17/06/2011
26/08/2011
04/11/2011
13/01/2012
23/03/2012
28/05/2011
06/08/2011
15/10/2011
24/12/2011
03/03/2012
08/05/2011
17/07/2011
25/09/2011
04/12/2011
12/02/2012
Date
150
200
250
300
350
400
450
Patients St. Elsewhere's (R) - Midnight Bed Occupancy
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
9 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 9. Same data as Fig. 8 plotted in rational groups by day of the week. The pattern within each group
matches the seasonal pattern and the group average shows highest 4-hour A&E breach rates on Mon, Tues
and Weds. Note that the seasonal pattern is ‘amplified’ on the days with higher than average breach rates.
This is called the Forrester Effect after Jay W Forrester who described it in the 1950’s [1] .
We can now see that there is a clear temporal association between the number of discharges at weekends
and the higher bed occupancy on Mondays, Tuesdays and Wednesdays; which in turn is associated with a
higher breach rate in A&E on Mondays, Tuesdays and Wednesdays. We can also see that the range of the
variation in the discharges and bed occupancy is amplified ‘backwards’ up the stream from discharges to
A&E. This non-linear system behaviour was described by Jay W. Forrester in 1950s [1] and goes some way
to explain why the ‘pain’ is felt in A&E but the pathology is downstream where the ‘smaller’ signal is
unrecognised.
Summary of Empirical Evidence
The system behaviour charts of the A&E and Hospital stages of the system show several regular cycles
superimposed on each other and on top of non-cyclical random variation:
1. A moderate weekly cycle of A&E arrivals: lower mid-week (Tuesday to Friday) and slightly higher on
Sunday and Monday.
2. A marked weekly cycle of emergency admissions: higher during the week and lower on Saturdays and
Sundays.
3. A more marked weekly cycle of inpatient discharges: increasing across the week (Monday-Friday) and
much lower at weekends.
4. A cumulative mismatch between the emergency admissions and discharges reflected in the weekly cycle
of bed occupancy and of A&E breaches.
5. A seasonal cycle of bed occupancy and A&E breaches: lower in the summer, and higher in the winter.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
10 | Page http://www.journalofimprovementscience.net Version 1.2
So we need to develop a plausible cause-and-effect model of the current system that explains the observed
behaviour, and we can then test that model by making predictions and looking for evidence to support or
refute them.
Hypotheses
A. The weekend pattern of increased A&E arrivals, lower admissions, much lower discharges, increasing
bed occupancy and increased A&E breaches suggests that it is the lower weekend discharges that is a
significant contributor to high bed occupancy and A&E breaches.
B. The higher A&E demand and lower emergency admissions at weekends is a spill-over effect of reduced
flow-capacity upstream of the hospital, especially for those patients triaged as ‘ less urgent.
C. The lower emergency admissions at weekends could be due to a combination delayed demand, due
reduced flow capacity upstream of the hospital, or back pressure due to high downstream bed occupancy.
The clinicians assessing patients at the ‘front end’ of the clinical pathway may also be raising their threshold
for admission in response to the queue of patients already waiting for a bed.
D. The higher mortality reported for weekend emergency admissions may be due to a combination of:
(1) The sicker patients being delayed by a referral bottleneck upstream of the hospital,
(2) the admission delay that sicker patients experience from higher bed occupancy,
(3) the fact that there are fewer medical staff available at weekends to manage both the new admissions
and the inpatients, which delays some discharges and in-turn delays the medical emergency patients
waiting for a bed,
(4) the higher bed occupancy at weekends puts more workload on the nursing and medical staff, making
their flow capacity less effective which then aggravates the admission and discharge flow bottlenecks,
(5) so in response to the internal queue for a bed, the medical staff are raise the threshold for admission, so
only the sicker patients (those who are more likely to die) are those admitted at weekends.
So the focus of this study is to explore the relationship between discharge flow-capacity, bed occupancy
and admission delays and to test the first hypothesis (A) that lower weekend discharge rates is the primary
cause of delayed emergency admissions.
It is important to remember that causal relationships cannot be inferred from statistical associations so an
experiment is required to observe the temporal effect of a planned system design change. Such an
experiment can only disprove a causal hypothesis because an effect cannot happen before its cause.
This type of causal experiment is neither practical nor ethical to perform in a real system so we shall use a
verified simulation model of the real system instead. As discharge is our primary focus of attention we first
need to build a more detailed model of the discharge process.
The Discharge Process
The process of discharging a patient, who was admitted as a medical emergency, requires a number of
factors to come together at the same time. Exactly what and how will vary from patient to patient. Some
patients just need a medical decision to be discharged; others require a more complicated package of care
including prescribed drugs, transport, and extra support at home or transfer to a different provider such as
an intermediate care facility. If any of those requirements are not available when the patient is medically
fit for discharge (MFFD) then the discharge cannot proceed and is delayed. So, for these delayed patients,
the length of stay (LoS) is longer and the number of beds occupied is higher.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
11 | Page http://www.journalofimprovementscience.net Version 1.2
So if there is a weekend discharge delay for the more complex patients then we would expect to see the
patients who are discharged at the weekend to have a shorter than average LoS; and the delayed patients
being discharged earlier in the week to have a longer than average LoS.
If we take the data for the same period of time (April 2011 to April 2012) and look at:
1. The total number of patients discharged over this period,
2. the total number and % discharged on each day of the week,
3. the overall average LoS for all those patients discharged over this period,
4. and the average LoS for all the patients discharged each day of the week,
then we predict that the smaller % of patients discharged at weekends to have a shorter LoS on average.
Table 1. Breakdown of discharges
and average length of stay (ALOS)
by the day of week of discharge.
The empirical evidence supports our prediction that the weekend discharges have shorter LoS and weekday
discharges have longer LoS. So if delayed weekend discharge of patients with more complex discharge
processes are causing a backlog and higher bed occupancy, then that could impede the flow of new
emergency admissions and we would predict that the 4-hour breach rate in A&E will be higher on
Mondays.
Table 2. Breakdown of the
average A&E 4-hour breach rate,
admissions, bed occupancy and
discharges by day of the week of
admission for the same period.
The upper table shows the
absolute values, the lower table
the normalised values created by
dividing each absolute value by
its group average to make
comparison of temporal patterns
easier to see.
The empirical evidence (Table 2) confirms our prediction that 4-hour breach rates are higher on Mondays
(29% above the average for the week ) and that coincides with a higher WIP (4% above average for the
week). Table 2 shows a complicated temporal relationship between the safety and quality metrics (4-hour
DoW of Di scharge n % of Dis charges Avg LOS % Diff
1-Mon 2381 15.1% 7.7 14%
2-Tue 2644 16.7% 7.0 3%
3-Wed 2575 16.3% 7.5 10%
4-Thu 2691 17.0% 7.3 8%
5-Fri 2873 18.2% 7.3 8%
6-Sat 1454 9.2% 4.3 -36%
7-Sun 1195 7.6% 3.5 -48%
Total 15813 ALOS 6.77
DoW % 4Hr Breach Avg Admits Avg WIP Avg Discharges
1-Mon 9.3 46.2 294 44.7
2-Tue 8.6 43.5 287 49.8
3-Wed 8.1 44.1 283 48.2
4-Thu 6.1 44.6 277 50.8
5-Fri 5.6 45.4 269 53.3
6-Sat 6.2 37.3 279 27.3
7-Sun 6.7 34.5 292 21.9
All 7.23 42.2 283 42.2
DoW % 4Hr Breach Avg Admits Avg WIP Avg Discharges
1-Mon 129% 109% 104% 106%
2-Tue 119% 103% 102% 118%
3-Wed 111% 104% 100% 114%
4-Thu 84% 106% 98% 120%
5-Fri 77% 108% 95% 126%
6-Sat 85% 88% 99% 65%
7-Sun 93% 82% 103% 52%
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
12 | Page http://www.journalofimprovementscience.net Version 1.2
breach) and the flow metrics (admissions, WIP and discharges); a pattern that is consistent with a
significant fall in discharge flow-capacity at weekends. This complicated temporal pattern is easier to see
by plotting these data over time.
Fig 10. Shows the same normalised data as in the lower part of Table 2 in a graphical format.
Fig. 10 shows that when discharges (green) exceed admissions (amber) between Tues and Fri then the WIP
(blue) is falling and 4-hour breaches (red) are also falling. The reverse effect is observed to happen over the
weekend because discharges fall more than admissions and the hospital is filling up.
There is a clear correlation and temporal association between 4-hour breaches and WIP which is preceded
by a fall in discharge flow. This evidence supports the hypothesis that it is the ‘fullness’ of available beds
that is creating the ‘back pressure’ on A&E and causing the admission delays and 4-hour A&E breaches.
The empirical evidence supports our hypothesis that a lack appropriate discharge flow-capacity at
weekends, in particular for the more complex patients, is a significant factor in the admission delays for
new emergencies, and the potential increased risk of harm. In other words there is an safety issue created
by the current planning, scheduling, and co-ordination of discharge flow-capacity.
The opportunity this insight creates is that just by improving the scheduling of discharge flow-capacity we
might see multiple beneficial secondary effects of:
(1) increasing weekend discharge flow,
(2) reducing bed occupancy mean and variation,
(3) increasing space-capacity resilience,
(4) reducing delayed admissions,
(5) reducing 4-hour A&E breaches,
(6) and reducing the risk of harm and potentially the higher weekend mortality.
0%
20%
40%
60%
80%
100%
120%
140%
% 4Hr Breach
Avg Admits
Avg WIP
Avg Discharges
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
13 | Page http://www.journalofimprovementscience.net Version 1.2
However, this retrospective diagnostic analysis does not answer two important questions:
Q1: Is more total discharge flow-capacity needed or can the existing flow-capacity be used more
effectively?
Q2: Would a safer, calmer, higher quality design be more expensive, cost the same or be less expensive
than the current design?
Purpose
The primary purpose of this study is to test the hypothesis that just addressing the admission versus
discharge flow-capacity mismatch could reduce admission delays and 4-hour breach rates. A secondary
purpose of this study is to explore the whole system cost of that single intervention.
Method
It was clearly impractical to explore this hypothesis using a real system so a representative model of the
real system was used. The data from the real system (i.e. the medium sized district general hospital above)
was used to design, build and verify a flow simulation model that is capable of predicting the effect of
changing discharge flow-capacity in isolation.
It was not the purpose of this exercise to model the real hospital exactly, just to build a representative
model based on the observed behaviour of the real system.
Simulation Model Design
The model used was a single stream (emergency medical flow) and a single stock (beds) design (Fig. 11) but
to predict length of stay and breaches accurately it required modelling down to the granularity of individual
patients. So rather than using a stock-and-flow simulation, the model was built using a stream-aligned
discrete event simulator (CPS 1.66, SAASoft Ltd) [2].
Fig 11. illustrates the simple structure of the flow model.
The admissions (amber) will increase the work in progress
(blue) and the discharges (green) will reduce it. The
horizontal line represents the lead time or length of stay
(LoS).
The average flow, WIP and lead time are related by Little’s
Law where: WIP = Lead time * Flow
The simplifying assumptions made in this model were as follows:
1. We assumed that the demand for a bed (i.e. the request for admission) is 42.2 per day.
2. This is the equivalent of a takt time of 34.1 minutes over the 24-hour period (i.e. inflow was assumed to
be constant which is not strictly true in reality).
3. If a request for a bed could not be satisfied within 4-hours that was counted as a ‘breach’.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
14 | Page http://www.journalofimprovementscience.net Version 1.2
4. After admission to a bed all inpatients are reviewed daily and a decision made if they are medically fit
for discharge (MFFD).
5. The real data of the distribution of the LoS for the patients was used to model the LoS.
Fig 12. The histogram shows the length of stay distribution for the real system in terms of midnights in
hospital.
NB. It is important to note that
measuring LoS this way introduces a
bias because admissions and
discharges are not equally distributed
over a 24 hour period: admissions
tend to be earlier in the day and
discharges tend to be later.
The LoS distribution is skewed, with an approximately exponential fall off after 1 midnight in hospital, so
this was approximated to a Poisson process with the probability that a patient would be deemed medically
fit for discharge (MFFD) on any day as the reciprocal of the measured average length of stay:
p(MFFD)=0.152 per patient per day.
6. We assumed that 50% of patients have a more complex discharge requirements so for those patients,
after they are deemed medically fit for discharge, a further request is made for discharge flow-capacity. If
this flow-capacity is not available at weekends then the patient is delayed and this is consistent with the
observed reduction in discharges at weekends and shorter LoS of weekend discharges.
Simulation Model Build
This structurally and functionally simplified flow model only requires three resources:
(1) admission flow-capacity,
(2) bed space-capacity and
(3) discharge flow-capacity.
The admission flow-capacity was set to be available 24x7 and was not a flow bottleneck. All patient
requests for flow-capacity or space-capacity were assumed to be handled as equal priority using first-in-
first-out (FIFO) queues.
So the only sources of variation in the flow model inputs were:
1. The daily, random Y/N medically fit for discharge decision i.e. p(MFFD)=0.152
2. The daily, non-random (i.e. scheduled) availability of discharge flow-capacity.
This discharge-flow capacity was available between 09:00-17:00 and either 5-days (Monday-Friday) or 7-
days a week.
The algorithm used in the CPS simulator is shown below (Figure 13) and illustrates that, in a stream-aligned
discrete event simulation, the process is viewed from the perspective of the patient and not from the
0%
5%
10%
15%
20%
25%
0
1
2
3
4
5
6
7
8
9
10
11
12
13
% of Patients (n=15488)
Midnights in Hospital
Length of Stay Distribution
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
15 | Page http://www.journalofimprovementscience.net Version 1.2
perspective of the provider. This is a fundamentally different approach and has the benefit of dramatically
simplifying the design of the simulation model.
Fig 13. The graphical pathway algorithm illustrating the request and release of resources and the pauses
between the actions. White diamonds are decision points and the yellow boxes are comments. The first
decision determines if the patient has breached the 4-hour target. The ‘sync’ action forces the path to wait
until the next absolute time: 09:00:00 in this case, to simulate the daily morning ward round. The next
decision tests if the patient is medically fit for discharge and the last decision tests if the more complex
discharge flow-capacity is required.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
16 | Page http://www.journalofimprovementscience.net Version 1.2
Simulation Model Verification
Before using a flow model for predictive work it is essential to run verification tests to establish that the
model is a good-enough representation of reality and to explore the relationship between the input
parameters and the observed system behaviour.
So we simulated what the model predicts would happen during periods of:
1. Low flow: 1 patient admitted/24hours for 12 months.
2. Full flow : 42.2 patients admitted/24 hours for 6 months
1. One patient per day for one year (Low Flow)
One patient per day for one year with an expected average length of stay of 8 days and all flow-capacity
and space-capacity available 24x7.
Fig 13. Predicted length of stay shows
the observed skewed distribution seen in
the real data (Fig 12) with an average of
just under 8 days (average = 7.3 days).
Fig 14. The predicted work in progress
from a flow of 1 patient per day with the
LoS distribution above. It shows high
variation (range 1 to 13 patients) and an
average of just under 8 patients
(average = 7.7 patients).
The Low Flow model behaviour is consistent with the model design and passes the Little’s Law verification
test where:
average WIP = average lead time * average flow.
0
7
14
21
28
35
42
01/01/2015
29/01/2015
26/02/2015
26/03/2015
23/04/2015
21/05/2015
18/06/2015
16/07/2015
13/08/2015
10/09/2015
08/10/2015
05/11/2015
03/12/2015
31/12/2015
Days
Lead Time
0
2
4
6
8
10
12
14
01/01/2 015
29/01/2 015
26/02/2 015
26/03/2 015
23/04/2 015
21/05/2 015
18/06/2 015
16/07/2 015
13/08/2 015
10/09/2 015
08/10/2 015
05/11/2 015
03/12/2 015
31/12/2 015
Occupied Beds
Work In Progress
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
17 | Page http://www.journalofimprovementscience.net Version 1.2
What may appear surprising is the high variation in the work in progress in a system with a low flow of only
1 patient/day combined with a relatively long LoS and illustrates that to avoid admission delays we always
need some space-capacity resilience; in this case (13-8) = 5 extra beds. It also illustrates that in a low-flow
high-LoS context, the average space-capacity utilisation may be very low (7.7/13 = 59% in this case).
2. Forty two patients per day for six months (Full Flow)
The flow model was then configured to offer complex discharge flow-capacity for 5 days per week (Monday
to Friday). So that at weekends only 50% of the patients could be discharged. The model was then run with
excess beds so that no breaches would happen for that reason in order to observe the undistorted
behaviour of the system subject to the 5-day complex discharge flow-capacity policy.
The model was run for six months (01/04 to 30/09) which is 183 days and the results were reported for the
last 3 months to allow enough time for the system to achieve flow equilibrium.
The admission and discharge events for the simulated patients were exported and used to generate the
Vitals Charts (demand, activity, work in progress and lead time) for that three month period.
Fig 15. Admissions per day shows the constant rate of demand as configured in the model. This is not
actually realistic and is done deliberately to exclude this source of variation for the purpose of model
verification. Note there are 42 admissions for four days and 43 on the fifth giving an average of 42.2 per
day.
02/07/2011
04/07/2011
06/07/2011
08/07/2011
10/07/2011
12/07/2011
14/07/2011
16/07/2011
18/07/2011
20/07/2011
22/07/2011
24/07/2011
26/07/2011
28/07/2011
30/07/2011
01/08/2011
03/08/2011
05/08/2011
07/08/2011
09/08/2011
11/08/2011
13/08/2011
15/08/2011
17/08/2011
19/08/2011
21/08/2011
23/08/2011
25/08/2011
27/08/2011
29/08/2011
31/08/2011
02/09/2011
04/09/2011
06/09/2011
08/09/2011
10/09/2011
12/09/2011
14/09/2011
16/09/2011
18/09/2011
20/09/2011
22/09/2011
24/09/2011
26/09/2011
28/09/2011
Date
0
10
20
30
40
50
60
70
80
Patients Model Verify (Admissions per day)
BaseLine 1.20.010
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
18 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 16. Discharges per day shows much higher variation because of the combination of (a) the Poisson
process for deciding if a patient is fit for discharge and (b) the non-availability of complex discharge flow-
capacity at weekends. Note that the average is the same as admissions and shows that we have achieved
flow equilibrium.
The demand (admissions) and activity (discharges) charts are consistent with the design of the simulation
model and approximately replicate the discharge pattern behaviour of the real hospital (compare Fig 2 and
Fig 3 with Fig 17 below.)
Fig 17. Predicted daily discharges rationally grouped by day of the week.
There is a 7-day cycle with a lower discharge rate at weekends. The falling discharge rate across the week
is not quite what is observed in reality (see Fig 5) and is the result of approximating using a Poisson process
in which discharge demand is driven only by the current bed occupancy. Fig 5 shows in reality there is a
rise in discharges on Fridays suggesting the real process is slightly more complicated.
02/07/2011
04/07/2011
06/07/2011
08/07/2011
10/07/2011
12/07/2011
14/07/2011
16/07/2011
18/07/2011
20/07/2011
22/07/2011
24/07/2011
26/07/2011
28/07/2011
30/07/2011
01/08/2011
03/08/2011
05/08/2011
07/08/2011
09/08/2011
11/08/2011
13/08/2011
15/08/2011
17/08/2011
19/08/2011
21/08/2011
23/08/2011
25/08/2011
27/08/2011
29/08/2011
31/08/2011
02/09/2011
04/09/2011
06/09/2011
08/09/2011
10/09/2011
12/09/2011
14/09/2011
16/09/2011
18/09/2011
20/09/2011
22/09/2011
24/09/2011
26/09/2011
28/09/2011
30/09/2011
Date
0
10
20
30
40
50
60
70
80
Patients Model Verify (Discharges per day)
BaseLine 1.20.010
11/07/2011
25/07/2011
08/08/2011
22/08/2011
05/09/2011
19/09/2011
05/07/2011
19/07/2011
02/08/2011
16/08/2011
30/08/2011
13/09/2011
27/09/2011
13/07/2011
27/07/2011
10/08/2011
24/08/2011
07/09/2011
21/09/2011
07/07/2011
21/07/2011
04/08/2011
18/08/2011
01/09/2011
15/09/2011
29/09/2011
08/07/2011
22/07/2011
05/08/2011
19/08/2011
02/09/2011
16/09/2011
30/09/2011
09/07/2011
23/07/2011
06/08/2011
20/08/2011
03/09/2011
17/09/2011
03/07/2011
17/07/2011
31/07/2011
14/08/2011
28/08/2011
11/09/2011
25/09/2011
Date
0
10
20
30
40
50
60
70
80
Patients Model Verify (Discharges per day)
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
19 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 18. Predicted midnight bed occupancy rationally grouped by day of the week.
The pattern of the WIP also shows a 7-day cycle with bed occupancy falling during the week and rising at
weekends, which is what we observe in reality (Fig 7).
Fig 19. Predicted midnight bed occupancy (ungrouped).
The 5+2 day ‘saw tooth’, cyclical pattern is clearly visible with 5 days of falling WIP and 2 days of rising WIP
(compare the saw tooth pattern in Fig 19 with that of the real system daily bed occupancy in Fig 6).
11/07/2011
25/07/2011
08/08/2011
22/08/2011
05/09/2011
19/09/2011
05/07/2011
19/07/2011
02/08/2011
16/08/2011
30/08/2011
13/09/2011
27/09/2011
13/07/2011
27/07/2011
10/08/2011
24/08/2011
07/09/2011
21/09/2011
07/07/2011
21/07/2011
04/08/2011
18/08/2011
01/09/2011
15/09/2011
29/09/2011
08/07/2011
22/07/2011
05/08/2011
19/08/2011
02/09/2011
16/09/2011
30/09/2011
09/07/2011
23/07/2011
06/08/2011
20/08/2011
03/09/2011
17/09/2011
01/10/2011
10/07/2011
24/07/2011
07/08/2011
21/08/2011
04/09/2011
18/09/2011
Date
200
220
240
260
280
300
320
340
360
Patients Model Verify (Midnight Occupancy)
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
02/07/2011
04/07/2011
06/07/2011
08/07/2011
10/07/2011
12/07/2011
14/07/2011
16/07/2011
18/07/2011
20/07/2011
22/07/2011
24/07/2011
26/07/2011
28/07/2011
30/07/2011
01/08/2011
03/08/2011
05/08/2011
07/08/2011
09/08/2011
11/08/2011
13/08/2011
15/08/2011
17/08/2011
19/08/2011
21/08/2011
23/08/2011
25/08/2011
27/08/2011
29/08/2011
31/08/2011
02/09/2011
04/09/2011
06/09/2011
08/09/2011
10/09/2011
12/09/2011
14/09/2011
16/09/2011
18/09/2011
20/09/2011
22/09/2011
24/09/2011
26/09/2011
28/09/2011
30/09/2011
Date Signal detected (runs=25)
200
220
240
260
280
300
320
340
360
Patients Model Verify (Midnight Occupancy)
BaseLine 1.20.010
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
20 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 20. Predicted LoS for one month (Aug). The average is 6.7 days and the histogram shows a realistic
skewed distribution.
Using Little’s Law with an average flow of 42.2 per day and an average LOS of 6.7 days will give an average
WIP of 283.
Note: The observed range of bed occupancy in Fig 19 suggests that 330 beds are required to meet the
expected variation in occupied beds which is 47 beds (17%) more than the average of 283.
So having confirmed that the baseline predicted system behaviour of our simplified flow model is
acceptably close to the observed in the real, and much more complicated, medium-sized DGH, we can
move on to use our model to see what happens when we change the system design.
03/08/2011 08:19
05/08/2011 17:09
08/08/2011 01:59
10/08/2011 10:49
12/08/2011 19:39
15/08/2011 04:29
17/08/2011 13:19
19/08/2011 22:09
22/08/2011 06:59
24/08/2011 15:49
27/08/2011 00:39
29/08/2011 09:29
31/08/2011 18:19
Date
0
7
14
21
28
35
42
Days Model Verify (Length of Stay)
BaseLine 1.20.010
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
21 | Page http://www.journalofimprovementscience.net Version 1.2
Simulation Model Prediction
The impact on daily discharges, length of stay, bed occupancy and admission delays over whole year was
predicted by the model.
Fig 21. Shows the predicted WIP chart for the whole period for the pre-change model (5-day complex
discharge flow-capacity and 330 available beds).
Run-in and run-out effects are clearly visible on the chart and are expected with this type of simulation
model as it starts and finished ‘empty’. These end-effects are removed by using smaller reporting window
in the middle of the larger data window (e.g. May-Sep).
The 7-day cycle is clearly visible in the saw tooth pattern with the highest WIP at weekends. There is a
wide range of WIP from about 230 to 330. This variation is generated by the combination of the variable
LoS and the varying discharge flow-capacity and it suggests that if only 300 beds are available then there
will be periods when bed occupancy is 100% and potentially 4-hour breaches as the backlog of waiting
admissions waxes and wanes.
With only 300 beds available (i.e. average occupancy of 283/300=94.3%) we will expect to generate some
admission delays but it is not obvious if this would actually increase 4-hour breaches and by how many.
So this scenario was simulated to confirm our prediction. The pre-change model parameters were set with
a 5-day complex discharge flow-capacity policy and space-capacity set to 300 beds. The model was then run
and the number of delayed admissions of more than 4-hours were counted and presented as a percentage
of daily admissions.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
22 | Page http://www.journalofimprovementscience.net Version 1.2
Fig 22. Predicted percentage of admissions waiting >4 hours from arrival to admission per day, rationally
grouped by day of the week.
The global average is 5% (blue line) but there is wide between-group variation with a 7-day cyclical pattern
of many more breaches on Sunday and Monday. There is also very wide and unpredictable within-group
variation especially in groups with high average breach rates (i.e. Sunday and Monday).
This pattern of 4-hour breaches matches the system behaviour observed in the real data and so supports
the assertion that we have a valid and verified flow model.
Summary of the Model Verification Phase
Model assumptions and simplifications:
1. Demand for beds to hold new emergency medical admissions was set at 42.2 per day. This is the
equivalent to a takt time of 34.1 minutes over the 24-hour period and this was assumed to be constant.
(Note this is not true in real life but is a reasonable simplification as we are looking at longer term
qualitative patterns rather than detailed quantitative predictions).
2. If a request for a bed could not be satisfied within 4-hours that was counted as a ‘breach’. This is a
simplification of reality where breaches relate to A&E arrivals not just emergency admissions.
3. After admission, all inpatients are reviewed daily and a decision is made if they are fit for discharge using
a simple Poisson process using the real data of the distribution of the LoS for the patients. About 50% of
occasions the patients deemed medically fit for discharge (MFFD) require a more complex discharge plan.
4. The more complex discharge flow-capacity is only available 5 out of 7 days.
Results:
This simplified Poisson model shows a falling discharge rate from Monday to Friday that is driven by the
bed occupancy. This is not entirely accurate because in reality we see a rise in discharges on Fridays
compared with earlier in the week. This suggests the real discharge process is a bit more complicated.
06/06/2011
15/08/2011
26/04/2011
05/07/2011
13/09/2011
25/05/2011
03/08/2011
14/04/2011
23/06/2011
01/09/2011
06/05/2011
15/07/2011
23/09/2011
28/05/2011
06/08/2011
17/04/2011
26/06/2011
04/09/2011
Date
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
%Model Verify (Admission 4-hour Breach Rate)
BaseLine 1.20.010
1-Mon
2-Tue
3-Wed
4-Thu
5-Fri
6-Sat
7-Sun
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
23 | Page http://www.journalofimprovementscience.net Version 1.2
Despite the simplifying assumptions, the results show that the structurally and functionally simplified
model exhibits behaviour that is qualitatively and quantitatively comparable to the behaviour of the real
system.
In the context of safety and flow, the pattern of the breaches across the week matches the pattern
observed in the real system with lower breach rates mid-week and rising breach rates at weekends.
So the results verify that the model is suitable for exploring the impact of introducing a 7-day discharge
flow-capacity policy on the breach rate (i.e. risk of delay and harm) generated by the system for a constant
rate of demand.
Using the full-flow (42.2 patients per day) scenario, we can test the effect of synchronising the discharge
flow-capacity with the demand for discharges. In real life this is equivalent to ensuring that there is always
discharge flow-capacity available every time there is a decision to discharge a patient. This does not imply
increasing the total discharge flow-capacity, just smoothing the existing flow-capacity across 7-days.
Test of Change
The post-change model differs only in switching the discharge flow-capacity from a 5-day policy to a 7-day
policy. All the other parameters of the model were unchanged (average demand = 42.2 per day, space-
capacity = 300 beds). The model was run twelve times to explore the run-to-run variation.
Fig 23. Shows the predicted WIP chart for
the whole period post the change to a 7-
day discharge flow capacity.
Compare with Fig 23 with Fig 21 and note
the reduced amplitude of the WIP chart
and no WIP exceeding 300. This implies
that if the maximum number of beds is 300
then there will be no admission breaches
caused by lack of beds.
Fig 24. Impact on breach rate of
moving from the 5-day to 7-day
availably of the discharge flow-
capacity. Before the change the
predicted average breach rate is
nearly 10% and there is a wide
variation. After the change the
predicted average breach rate is
very close to 0% with very low
variation.
2 4 6 8 10 12 14 16 18 20 22 24
Run
0
5
10
15
20
25
30
Avg Breach %
BaseLine 1.20.010
1
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
24 | Page http://www.journalofimprovementscience.net Version 1.2
Summary of Test of Change Results
In this structurally and functionally simplified yet verified whole-system flow model, the effect of moving
from a 5-day to a 7-day policy for discharge flow-capacity is predicted to reduce the WIP variation. This in
turn increases the space-capacity (beds) available, prevents back-pressure on new admissions and so
reduces 4-hour admission breaches caused by the lack of beds. The total amount of discharge flow-
capacity and hospital space-capacity has not changed; only the scheduling of the discharge flow-capacity.
Safety Implications
If we take a delayed admission and 4-hour breach for a new medical emergency as a proxy for a higher risk
of harm then the 7-day policy is safer than the 5-day policy because the number of 4-hour breaches has
fallen significantly (Fig 24).
Cost Implications
Figs 21 and 23 show that with a 5-day discharge flow-capacity policy we need 330 beds to prevent breaches
and if we only have 300 then our design generates breaches and risk of harm (i.e. it is an unsafe design) and
we have created a safety problem. With the same total flow-capacity but a 7-day availability policy we only
need 300 beds to prevent breaches.
So if we already have 300 beds then there is no increase in the cost of the space-capacity required to
achieve the safer design.
The average flow into the hospital has not changed, so the average discharge flow has not changed, so the
total discharge flow-capacity has not changed, so the cost of this discharge flow-capacity has not changed.
All that has changed is that the same total discharge resource capacity has been distributed across 7-days
instead of being concentrated into 5-days.
So the improvement in safety and quality achieved by switching from a 5-day to a 7-day discharge flow-
capacity policy is predicted to be cost neutral.
Learning Points
The use of a verified flow simulation model allows all input parameters to be controlled independently and
their effects explored both individually and in combination. The non-linear behaviour of the system is
clearly visible in the time series charts [1] and challenges the assumption that linear mathematical and
statistical methods are valid tools for exploring realistic time-dependent system behaviour.
The structurally simplified, yet dynamically realistic, flow model of a hospital supports the hypothesis that
when the discharge flow-capacity varies in a predictable and intentional 5-of-7 day cycle, this will increase
the variation in WIP (bed occupancy) so when space-capacity (beds) is limited we will increase the risk of
admission delays, the risk of 4-hour target breaches, and potentially the risk of harm for patients.
Adding a space-capacity buffer (i.e. more beds in an urgent assessment unit) is effective at reducing the 4-
hour breaches but makes no difference to the variation in bed occupancy caused by the uneven discharge
flow-capacity and actually increases the total system cost ... in this case by 10% from 300 beds to 330 beds.
Even with flow-capacity matched to demand we expect some WIP variation caused by the fact that not all
patients follow the same path and have, by the nature of their conditions, a variable length of stay. So
providing some space-capacity buffering will always be required.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
25 | Page http://www.journalofimprovementscience.net Version 1.2
Re-designing the discharge flow-capacity policy so that it matches the discharge demand is a safer, quicker,
more effective, and lower-cost option than only having the same discharge capacity available for only 5 out
of 7 days.
Silvester et al [3] and Jones [6] have both demonstrated in separate real-world studies that by matching
flow-capacity with demand both in amount and timing, we see smoother flow, reduced WIP wobble,
reduced lead time, reduced space-capacity requirement and increased the system resilience.
And all of these benefits come at no additional cost, even though space-capacity utilisation may have fallen.
So striving to drive up bed-utilisation as a proxy for efficiency, cost-effectiveness or productivity is an
illogical, unnecessary and unwise strategy and is dangerous if achieved by reducing the absolute number of
beds in a cost-cutting exercise before understanding and mitigating the reasons for the higher than desired
bed occupancy.
These fundamental flow-design principles are mandated by the Laws of Physics. So even though the
mechanisms by which they work may feel counter-intuitive, they are easily demonstrable, explainable,
teachable, learnable and applicable.
The conclusion we are drawn to is that investing in developing our system-wide flow design capability, both
as NHS commissioners and NHS providers, would appear to be a rational, achievable and affordable option
for improving the safety and affordability of urgent care services.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
26 | Page http://www.journalofimprovementscience.net Version 1.2
References
The convention used in this essay is to list cited references on publication order together with their published
abstracts to make it easier for the reader to assess the supporting evidence.
1. Forrester JW. Industrial Dynamics. 1961. MIT Press. ISBN 0-262-56001.
2. Dodds SR, Silvester KM. The Emergency Pathway Horned Gaussian; Journal of Improvement Science
2012; 1:1-14.
3. Silvester KM, Mohammed MA, Harriman P, et al. Timely care for frail older people referred to hospital
improves efficiency and reduces mortality without the need for extra resources. Age and Ageing 2014; 43:
472477.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
27 | Page http://www.journalofimprovementscience.net Version 1.2
4. Dasari TW, Roe MT, Chen AY, et al. Impact of time of presentation on process performance and
outcomes in ST-segment-elevation myocardial infarction: a report from the American Heart Association:
Mission Lifeline program. Circ Cardiovasc Qual Outcomes 2014;7(5):656-63.
5. Prabhakaran S, Ruff I, Bernstein RA. Acute stroke intervention: a systematic review. JAMA 2015; 313(14):
1451-62.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
28 | Page http://www.journalofimprovementscience.net Version 1.2
6. Jones C. Maintaining the Momentum of Medicines. Journal of Improvement Science 2015; 20: 1-40.
7. Ruiz M, Bottle A, Aylin PP. The Global Comparators project: international comparison of 30-day in-
hospital mortality by day of the week. BMJ Qual Saf. 2015 Aug;24(8):492-504. doi: 10.1136/bmjqs-2014-
003467.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
29 | Page http://www.journalofimprovementscience.net Version 1.2
Acknowledgments
The author would like to thank Dr Peter Ingham for many hours of constructive debate on the issue of
urgent care flows and for valuable feedback on earlier drafts of this essay and to my Sponsor for incisive
critique, wise suggestions and permission to use the St. Elsewhere’s® logo.
Author
Simon Dodds studied medicine and computer science at Cambridge before following a
career in general and then vascular surgery. During his training he researched the problem
of modelling blood flow in networks of diseased arteries and used computer simulations to
develop more accurate non-invasive tests for arterial disease. After appointment as a
consultant surgeon at Good Hope Hospital in North Birmingham he applied his skills as a
software and system designer and a clinician in the redesign of the vascular surgery clinic
and the leg ulcer service. The project was awarded a national innovation award for service improvement
and is documented in the book called Three Wins: Service Improvement Using Value Stream Design. This
experience led directly to the creation of SAASoft which is a global portal for the development and
dissemination of the theory, techniques, tools and training of Improvement Science in Healthcare. His
current role is consultant general surgeon at Heart of England NHS Trust.
Sponsor
Kate Silvester originally trained and practised as an ophthalmologist. In 1991 she
retrained as a manufacturing systems engineer and spent seven years in management
consultancy transferring manufacturing principles to service industries such as banking,
airlines and healthcare. In 1999 she rejoined the UK's National Health Service and
worked on many national programmes improving the flow of patients through the
system; addressing timeliness, cost and quality. Kate's specific area of expertise is in the
management of organisational systems to address the variability in demand and capacity. In November
2007 she joined the EU-Japan World Class Manufacturing Programme to translate the Lean Thinking
approach into Healthcare. She was appointed an Honorary Associate Professor, in the Health Sciences
Research Institute at Warwick Medical School in January 2009. Between 2010 and 2012 she was sponsored
by The Health Foundation to lead an 'Inquiry into Flow, Cost and Quality' with South Warwickshire Hospitals
NHS Trust and Sheffield Teaching Hospitals NHS Foundation Trust. Kate is co-founder of the Journal of
Improvement Science.
Statement of Originality
The author hereby declares that the material presented in this essay is original and that they own the
copyright to it unless explicitly stated in the document. The author(s) hereby grant permission for
Registered Readers of the Journal of Improvement Science free access to use this content for personal use
only. The author(s) do not grant permission for readers to copy, disseminate, or use the material for any
commercial purposes without the prior permission of the copyright holder. This material is present in good-
faith and as-is and neither the Author(s), nor the Sponsor(s) nor the Journal of Improvement Science accept
any responsibility for the outcome of the use of this material.
© Dodds SR. Seven-Day versus Five-Day Flow-Capacity. Journal of Improvement Science 2015; 24: 1-30.
30 | Page http://www.journalofimprovementscience.net Version 1.2
Document Version History
Reference Version Date Document Owner
JOIS_2015_024 1.0 02/10/2015 simon.dodds@heartofengland.nhs.uk
JOIS_2015_024 1.1 03/10/2015 simon.dodds@heartofengland.nhs.uk
JOIS_2015_024 1.2 05/10/2015 simon.dodds@heartofengland.nhs.uk
... In preparation for sprint 3 we investigated whether others had looked at the relationship between bed occupancy, discharges, and admissions. Not surprisingly there is a rather extensive literature on this topic, so we were reassured to be signposted to a similar piece of work published in 2015 [17]. The article helpfully tells the story of the data analysis conducted that helped in the design, build and verification of a discrete event simulation (DES) model of a hospital. ...
... This pattern of events is not a new phenomenon and was described when it was discovered to be happening ten years ago in a different hospital [17]. We have repeated the same analysis and come up with the same results and confirmed that the same patterns are present within our hospital. ...
... In the original work [17], the author built a stream-aligned discrete event simulation (DES) model which allowed him to represent flows down to the individual patient level. Instead, we opted to build our Windkessel model using Microsoft Excel® for three reasons: ...
Article
Full-text available
Abstract Medicines reconciliation (MR) and preparation of To Take Out medicines (TTOs) are two key processes in the medicines pathway for hospital inpatients. The former is completed at the admission stage and the latter at discharge. Early completion of the MR process is vital in highlighting medication related reasons for admission and optimising patient’s treatment earlier, both of which contribute to a reduction in length of stay. The pharmacy team based at Morriston Hospital, Swansea designed an improvement project focusing on these processes in an attempt to improve the timeliness of both with the aim of increasing the quality of service for the patient by reducing their length of stay. At baseline, the current system had significant variation in the length of time between admission and completion of MR. There was a definite five-working-day cycle seen within the data. Time from admission to completion of MR ranged from a few hours up to ninety-six hours after arrival in hospital with a noticeable increase in the time taken to complete the MR process within the patient group admitted on Friday and Saturday. The TTO process cannot be started until the MR process has been completed, as MR is an essential pre-requisite to transfer of accurate information to the GP. Under the current five- working -day cycle the number of TTOs and MRs waiting to be processed builds from Friday afternoon to a peak on Monday morning. At this point demand for MR and TTOs is at its highest across all directorates. A service delivery redesign was undertaken using the A3 problem solving process. The data was analysed to identify areas for improvement and the causes of delay in the discharge process were identified. Following implementation of a Saturday MR team the time delay between admission to completion of MR was halved and the length of stay of patients admitted on a Saturday was reduced from 13.3 to 10.0 days (24.8%). As a result of up skilling members of the discharge team mean total TTO process time was reduced from 90.3 minutes to 59.1 minutes (34.5%). This was achieved by reducing the time delay in informing pharmacy of the need to process the discharge and increasing the efficiency of the dispensing process itself. Redesigning the delivery model for core services can result in substantial efficiency savings within the current staffing establishment. Furthermore, the same service improvement methodology enables you to prove the benefits that will be realised, if further funding is provided to facilitate extending the time that service is available for. It is vital in informing when, where and how a service should be delivered to maximise the benefit that service provides. (440 words). Keywords Pharmacy; Medication; To Take Out (TTO); Discharge; Length Of Stay; Study-Plan-Do (SPD); A3 Problem Solving; Medicines Reconciliation; Five Day Working; Prudent Healthcare; Patient Flow; Improvement Science; Seven Day Working; Service Improvement;
Article
Full-text available
To examine the association of mortality by day of the week for emergency and elective patients. Retrospective observational study using the international dataset from the Global Comparators (GC) project consisting of hospital administrative data. 28 hospitals from England, Australia, USA and the Netherlands during 2009-2012. Emergency and surgical-elective patients. In-hospital deaths within 30 days of emergency admission or of elective surgery. We examined 2 982 570 hospital records; adjusted odds of 30-day death were higher for weekend emergency admissions to 11 hospitals in England (OR 1.08, 95% CI 1.04 to 1.13 on Sunday), 5 hospitals in USA (OR 1.13, 95% CI 1.04 to 1.24 on Sunday) and 6 hospitals in the Netherlands (OR 1.20, 95% CI 1.09 to 1.33 on Saturday). Emergency admissions to the six Australian hospitals showed no daily variation in adjusted 30-day mortality, but showed a weekend effect at 7 days post emergency admission (OR 1.12, 95% CI 1.04 to 1.22 on Saturday). All weekend elective patients showed higher adjusted odds of 30-day postoperative death; we observed a 'Friday effect' for elective patients in the six Dutch hospitals. We show that mortality outcomes for our sample vary within each country and per day of the week in agreement with previous studies of the 'weekend effect'. Due to limitations of administrative datasets, we cannot determine the reasons for these findings; however, the international nature of our database suggests that this is a systematic phenomenon affecting healthcare providers across borders. Further investigation is needed to understand the factors that give rise to the weekend effect. The participating hospitals represent varied models of service delivery, and there is a potential to learn from best practice in different healthcare systems. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.
Article
Full-text available
Acute ischemic stroke is a major cause of mortality and morbidity in the United States. We review the latest data and evidence supporting catheter-directed treatment for proximal artery occlusion as an adjunct to intravenous thrombolysis in patients with acute stroke. To review the pathophysiology of acute brain ischemia and infarction and the evidence supporting various stroke reperfusion treatments. Systematic literature search of MEDLINE databases published between January 1, 1990, and February 11, 2015, was performed to identify studies addressing the role of thrombolysis and mechanical thrombectomy in acute stroke management. Studies included randomized clinical trials, observational studies, guideline statements, and review articles. Sixty-eight articles (N = 108 082 patients) were selected for review. Intravenous thrombolysis is the mainstay of acute ischemic stroke management for any patient with disabling deficits presenting within 4.5 hours from symptom onset. Randomized trials have demonstrated that more patients return to having good function (defined by being independent and having slight disability or less) when treated within 4.5 hours after symptom onset with intravenous recombinant tissue plasminogen activator (IV rtPA) therapy. Mechanical thrombectomy in select patients with acute ischemic stroke and proximal artery occlusions has demonstrated substantial rates of partial or complete arterial recanalization and improved outcomes compared with IV rtPA or best medical treatment alone in multiple randomized clinical trials. Regardless of mode of reperfusion, earlier reperfusion is associated with better clinical outcomes. Intravenous rtPA remains the standard of care for patients with moderate to severe neurological deficits who present within 4.5 hours of symptom onset. Outcomes for some patients with acute ischemic stroke and moderate to severe neurological deficits due to proximal artery occlusion are improved with endovascular reperfusion therapy. Efforts to hasten reperfusion therapy, regardless of the mode, should be undertaken within organized stroke systems of care.
Article
Full-text available
The characteristic bimodal lead time behaviour of A&E systems that are subject to arbitrary performance targets is predicted by a simple, stream-focussed, discrete event simulation model. The model behaviour suggests that quality may in fact be compromised by a performance target-driven approach to improvement of A&E lead time performance. Rational and focussed changes to the design of the process could avoid the problem entirely by creating an A&E system that is both stable and capable of meeting the required performance specification. Investment in process design capability in the NHS is a realistic and pragmatic strategy.
Article
Full-text available
Background: hospitals are under pressure to reduce waiting times and costs. One strategy that may be effective focuses on optimising the flow of emergency patients. Objective: we undertook a patient flow analysis of older emergency patients to identify and address delays in ensuring timely care, without additional resources. Design: prospective systems redesign study over 2 years. Setting: the Geriatric Medicine Directorate in an acute hospital (Sheffield Teaching Hospitals NHS Foundation Trust) with 1920 beds. Subjects: older patients admitted as emergencies. Methods: diagnostic patient flow analysis followed by a series of Plan Do Study Act cycles to test and implement changes by a multidisciplinary team using time series run charts. Results: 60% of patients aged 75+ years arrived in the Emergency Department during office hours, but two-thirds of the admissions to GM wards were outside office hours highlighting a major delay. Three changes were undertaken to address this, Discharge to Assess, Seven Day Working and the establishment of a Frailty Unit. Average bed occupancy fell by 20.4 beds (95% confidence interval (CI) -39.6 to -1.2, P = 0.037) for similar demand. The risk of hospital mortality also fell by 2.25% (before 11.4% (95% CI 10.4-12.4%), after 9.15% (95% CI 7.6-10.7%) which equates to a number needed to treat of 45 and a 19.7% reduction in relative risk of mortality. The risk of re-admission remained unchanged. Conclusion: redesigning the system of care for older emergency patients led to reductions in bed occupancy and mortality without affecting re-admission rates or requiring additional resources.
Article
Background: Prior studies demonstrated that patients with ST-segment-elevation myocardial infarction presenting during off-hours (weeknights, weekends, and holidays) have slower reperfusion times. Recent nationwide initiatives have emphasized 24/7 quality care in ST-segment-elevation myocardial infarction. It remains unclear whether patients presenting off-hours versus on-hours receive similar quality care in contemporary practice. Methods and results: Using Acute Coronary Treatment and Intervention Outcomes Network-Get With The Guidelines (ACTION-GWTG) database, we examined ST-segment-elevation myocardial infarction performance measures in patients presenting off-hours (n=27 270) versus on-hours (n=15 972; January 2007 to September 2010) at 447 US centers. Key quality measures assessed were aspirin use within first 24 hours, door-to-balloon time, door-to-ECG time, and door-to-needle time. In-hospital risk-adjusted all-cause mortality was calculated. Baseline demographic and clinical characteristics were similar. Aspirin use within 24 hours approached 99% in both groups. Among patients undergoing primary percutaneous coronary intervention (n=41 979; 97.1%), median door-to-balloon times were 56 versus 72 minutes (P<0.0001) for on-hours versus off-hours. The proportion of patients achieving door-to-balloon time ≤90 minutes was 87.8% versus 79.2% (P<0.0001), respectively. There were no differences attaining door-to-ECG time ≤10 minutes (73.4% versus 74.3%, P=0.09) and door-to-needle time ≤30 minutes (62.3% versus 58.7%; P=0.44) between on-hours versus off-hours. Although in-hospital all-cause mortality was similar (4.2%) in both groups, the risk-adjusted all-cause mortality was higher for patients presenting off-hours (odds ratio, 1.13; 95% confidence interval, 1.02-1.26). Conclusions: In contemporary community practice, achievement of quality performance measures in patients presenting with ST-segment-elevation myocardial infarction was high, regardless of time of presentation. Door-to-balloon time was, however, slightly delayed (by an average of 16 minutes), and risk-adjusted in-hospital mortality was 13% higher in patients presenting off-hours.