Improving reliability by increasing the level of balancing and by substitution

Abstract

Problems with the current methods for reliability improvement are discussed as well as two generic methods for reliability improvement. The paper argues that reliability improvement is underpinned by common principles that provide key input to the design process. The domain-independent methods change the way engineers and scientists approach reliability improvement. The presented generic methods encourage simple low-cost solutions as opposed to some traditional high-cost solutions based on introducing redundancy, condition monitoring, reinforcement and use of expensive materials. The domain-independent methods allow engineers and scientists in a particular domain to access excellent solutions and practices for eliminating failure modes in other domains. In this way, the constant ‘reinventing of the wheel’ is avoided. As part of the presented approach, a generic method for increasing reliability by increasing the level of balancing and by substitution have been presented. In addition, a new classification of techniques related to increasing the level of balancing has been introduced and discussed for the first time. The paper also proves rigorously that if two components must be selected from n batches containing reliable and faulty components with unknown proportions, the likelihood that both components will be reliable is maximised by selecting the components from a randomly selected batch.

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Proc IMechE Part C:
J Mechanical Engineering Science
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ÓIMechE 2022
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DOI: 10.1177/09544062221132419
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Improving reliability by increasing the
level of balancing and by substitution
Michael Todinov
Abstract
Problems with the current methods for reliability improvement are discussed as well as two generic methods for
reliability improvement. The paper argues that reliability improvement is underpinned by common principles that
provide key input to the design process. The domain-independent methods change the way engineers and scientists
approach reliability improvement. The presented generic methods encourage simple low-cost solutions as opposed to
some traditional high-cost solutions based on introducing redundancy, condition monitoring, reinforcement and use of
expensive materials. The domain-independent methods allow engineers and scientists in a particular domain to access
excellent solutions and practices for eliminating failure modes in other domains. In this way, the constant ‘reinventing
of the wheel’ is avoided. As part of the presented approach, a generic method for increasing reliability by increasing the
level of balancing and by substitution have been presented. In addition, a new classification of techniques related to
increasing the level of balancing has been introduced and discussed for the first time. The paper also proves rigorously
that if two components must be selected from nbatches containing reliable and faulty components with unknown
proportions, the likelihood that both components will be reliable is maximised by selecting the components from a
randomly selected batch.
Keywords
Increasing the level of balancing, improving reliability, reducing risk, generic methods for reliability improvement
Date received: 11 July 2022; accepted: 17 September 2022
Introduction
The problems with current reliability-improvement
methods
For a long time, the reliability and risk literature
1–9
failed to acknowledge that reliability improvement
is underpinned by generic principles and methods.
As a result, practically no relevant discussion about
generic methods for reliability improvement in
design exists in standard textbooks on mechanical
engineering.
10–21
Many industries have almost iden-
tical risk-reduction solutions but prefer to look for
risk-reduction solutions only within their own spe-
cific domain. This approach raises unnecessary bar-
riers between industries and prevents sharing
effective, universally applicable generic solutions.
As a consequence, much time is wasted as engi-
neers and scientists often re-invent the wheel in a par-
ticular domain instead of accessing proven generic
solutions from other domains. In addition, the lack of
education in generic methods for reliability improve-
ment led to numerous missed opportunities for
improving reliability by using cheap and effective
methods.
Domain-independent methods for improving relia-
bility
22,23
take engineers and scientists along highly
profitable exploration paths – along paths they would
not otherwise have travelled. Generic risk-reduction
methods provide a constant reminder about the exist-
ing highly-effective generic concepts for improving
reliability, boosting creativity and help translate the
generic concepts into useful reliability-improvement
ideas and solutions.
The widely popular among many reliability practi-
tioners physics-of-failure approach created the incor-
rect perception that reliability improvement can only
be achieved by developing physics-of-failure models.
According to this approach, deterioration and fail-
ures are the result of underlying failure mechanisms.
Despite that in a number of cases, the physics-of-
failure approach does lead to effective reliability
School of Engineering, Computing and Mathematics, Oxford Brookes
University, Oxford, Wheatley, UK
Corresponding author:
Michael Todinov, School of Engineering, Computing and Mathematics,
Oxford Brookes University, Oxford, Wheatley OX33 1HX, UK.
Email: mtodinov@brookes.ac.uk

improvement, often, the physics-of-failure approach
is not feasible and cannot bring satisfactory solutions.
Indeed, in many cases, the complex mechanisms
causing failure remain unknown or are highly uncer-
tain. Often, failure is the result of many contributing
factors. Identifying the causes of failure usually
requires extensive research which is costly and time
consuming.
The root-cause-analysis approach has a substantial
appetite for data. Thus, obtaining the values of the
constants entering the physics-of-failure models
requires numerous lengthy and expensive experiments
and often remain unknown or highly uncertain.
Gathering data for months and years to be used as a
basis for a realistic reliability model is a time-
consuming and painful approach to improving
reliability.
Finally, physics-of-failure models serve only a nar-
row domain and cannot normally be used to improve
reliability in other domains. For example, a physics-
of-failure model for reducing the consequences from
hydrogen embrittlement in welds cannot be applied in
other unrelated areas.
A distinction must be made between the discussed
generic methods for improving reliability and
TRIZ.
24–27
TRIZ is a general methodology for inven-
tive problem solving which is not necessarily oriented
towards reducing risk, despite that TRIZ includes 40
general inventive principles that, in a number of
cases, can be used to reduce risk. The TRIZ metho-
dology and its popularity in industry is a strong evi-
dence of the power of generic thinking in problem
solving. TRIZ however, cannot be used as a substi-
tute for the generic methods for reliability improve-
ment for the following reasons:
- TRIZ does not employ any mathematical models
and algorithms. In many cases, developing a cor-
rect risk-reduction strategy does require such mod-
els. Reliability improvement in these cases, is done
by building reliability models of the competing
systems and determining which system is more
reliable.
- The TRIZ system of 40 inventive principles does
not cover key reliability improvement techniques.
For example, TRIZ does not include the method
based on improving the level of balancing, the
principle requiring a decrease of the rate with
which damage accumulates and the method based
on using deliberate weaknesses to reduce risk.
- Reliability improvement methods which follow
from the reliability theory such as removing/block-
ing a common cause, k-ot-of-n redundancy and
standby redundancy, are beyond the reach of the
TRIZ methodology.
- TRIZ does not normally cover mechanisms
through that harm develops and techniques that
help to delay or block these mechanisms. In con-
trast, an important part of the proposed generic
methods is the classification of failure mechanisms
and the techniques through which failure modes
resulting from these mechanisms are eliminated.
Domain-independent methods provide a basis for
disciplined thinking towards identifying effective
reliability improving solutions
Improving the reliability of an engineering product or
process effectively consists of eliminating failure
modes. The reliability improvement solution must
preserve the functions of the original product/process
and eliminate critical failure modes.
In addition, the reliability improvement solution
must not introduce new critical failure modes or make
the product/process more complex and expensive.
One of the pillars of the domain-independent
approach to reliability improvement is the similarity
of the reliability improvement problems and their solu-
tions across various domains of human activity.
Thus, a common cause (e.g. incorrect maintenance
procedure) and techniques for removing common causes
are frequently encountered problems in mechanical engi-
neering, electrical engineering, manufacturing, construc-
tion, aerospace engineering, automotive industry,
medicine, environmental sciences, etc.
Another pillar of the domain-independent
approach to reliability improvement is the observa-
tion that while there is practically an infinite number of
reliability improvement problems, the general principles
on which the reliability improvement is based are rela-
tively few.
Indeed, a reliability improvement problem in a
particular domain has often been solved in another
domain by using a similar method. Thus, eliminating
failure modes of a mechanical system by substituting
it with electrical, magnetic or optical system has been
applied in the control of automotive engines, in mea-
suring temperature, in measuring loading stresses, in
controlling manufacturing processes, etc. At the heart
of the reliability improvement in all these domains is
the method of substitution, whose underlying idea is
eliminating failure modes by substituting assemblies
working on a particular physical principle with assem-
blies/systems working on a different physical princi-
ple. This is a common generic method that can be
used for eliminating critical failure modes in various
industries.
Domain-independent methods discipline the think-
ing about reliability improvement and help avoid the
constant ‘reinventing of the wheel’.
2Proc IMechE Part C: J Mechanical Engineering Science 00(0)

It must be stressed that the generic methods for
reliability improvement do not replace the profes-
sional knowledge in the specific domain where they
are employed. Instead, these methods help structure
the problem and suggest likely avenues where efficient
solutions can be deployed.
In what follows, two powerful generic methods for
improving reliability are discussed in detail: the
method based on increasing the level of balancing and
the method of substitution. These methods must be
part of the design tools of every design-engineer.
The presented domain-independent methods:
- do not rely on reliability data.
- are appropriate for new designs, with no failure
history and with insufficiently researched failure
mechanisms.
- are not associated with extra cost.
The presented methods also encourage simple, low-
cost solutions as opposed to some traditional high-cost
solutions based on introducing redundancy, condition
monitoring, reinforcement and use of expensive materials.
Improving reliability by increasing
the level of balancing. Classification
of techniques for increasing the level
of balancing
Despite that in a number of practical solutions, relia-
bility has been effectively improved by increasing the
level of balancing, improving reliability by increasing
the level of balancing has not yet been distilled as a
generic reliability improvement method in engineering
design. No analysis of mechanisms and techniques
through which increasing the level of balancing
improves reliability has ever been presented. The
known applications have not been used to formulate
the method and build appropriate classification of
different techniques related to this method.
Consequently, the outlined gap in the relevant pub-
lished literature determined one of the goals of this
paper: introducing a new generic method for improv-
ing reliability by increasing the level of balancing,
classifying key techniques relevant to this method and
introducing new techniques for improving reliability
by increasing the level of balancing.
Figure 1. Classification of techniques related to improving reliability by increasing the level of balancing.
Todinov 3

The underlying idea of this method is improving
reliability by ensuring increased balance of loads, prop-
erties and reliability-critical parameters over the differ-
ent parts of a system.
In well-balanced systems, load is distributed more
uniformly across components and as a result, the
loading stresses are smaller. Distilling numerous
examples of improving reliability by increasing the
level of balancing and organising the knowledge
yielded the following major techniques (Figure 1):
- Ensuring a more uniform distribution of loads
- Altering the transmission paths of forces
- Ensuring a more uniform distribution of internal
stresses
- Ensuring a more uniform distribution of material
properties
- Improving the systems’ stability
- Reducing the magnitudes of inertia forces
- Capturing a compensating factor
- Reducing variability of reliability-critical parameters
Examples of efficient application of the different
techniques for increasing the level of balancing
Ensuring a more uniform load distribution leads to
significantly reduced contact stresses and wear.
Imbalanced electrical loads, for example, fre-
quently cause excessive heat generation and reduced
reliability of electrical devices. An adequate prescrip-
tion of the parameters of the components in electrical
circuits improves the level of balancing of electrical
loads and reliability. Imbalanced input voltage, for
example, could lead to imbalanced input power of the
modules in electronic circuits which creates a possibil-
ity of exceeding voltage rating of capacitors and sys-
tem failure. This can be prevented by increasing the
level of balancing through a voltage sharing balance
circuit.
28
Imbalanced flow of data in computer networks fre-
quently results in delays and lost packets of informa-
tion. Proper management of the data flow by
employing prioritisation algorithms improves the
level of balancing of the data flows and improves the
quality of service of the network.
Self-balancing of transportation networks involv-
ing autonomous vehicles could make a full use of the
intelligent characteristics of the self-driving vehicles
and improve the utilisation rate of the vehicles in the
system. This improves the distribution of transporta-
tion resources in the road network and the efficiency
of vehicle service.
29
Point loading often causes excessive deflection of
the load-carrying surfaces, excessive stresses and fail-
ure. Unless the load-carrying surface has been specifi-
cally designed to accommodate point loads, the point
load often causes excessive deformation and failure.
Increasing the level of balancing of external loads by
distributing them uniformly over the load-carrying
surface decreases deflections and stresses and reduces
the likelihood of failure. Including deliberate weak-
nesses or extra degrees of freedom, for example, does
not permit the formation of peak stresses and contri-
butes to a more uniform distribution of the internal
stresses. Such is, for example, the case where extra
degrees of freedom are introduced in statically inde-
terminate trusses to turn them into statically deter-
mined structures. The result is a more uniform
distribution of the internal stresses and reduced peak
stress magnitudes.
Altering the transmission paths of forces. Altering the
transmission paths of forces contributes significantly
to increasing the level of balancing and improving the
reliability of assemblies and structures. As a rule,
short and direct transmission paths are associated
with minimum amount of deformation and increased
level of balancing. Avoiding eccentric axial loading of
columns by applying the force through the centroid
of the column cross section avoids bending associated
with eccentric loading and leads to a better stability
of the column.
30
External forces, applied through the centres of
symmetry of sections and through axes of rotation,
are associated with an increased level of balancing
due to absence of moments. An increased level of bal-
ancing is also present if the transmission path of the
external force is within the cone of friction.
Reducing the magnitudes of inertia forces also
increases the level of balancing and is commonly per-
formed on rotating components.
Ensuring a more uniform distribution of the internal
stresses. In designing components, a more uniform
distribution of the internal stresses can be achieved by
avoiding stress concentrators. These lead to elevated
local levels of the stresses that can easily exceed the
strength of materials even at relatively low nominal
internal stresses away from the stress concentrators.
Imbalanced internal stresses in loaded components
however, can be present even in the absence of stress
concentrators. In the design of composite rods, com-
posite beams and composite torsion bars, the limit
state corresponding to the onset of failure (e.g. yield-
ing) in the different materials can occur at signifi-
cantly different levels of the loading force. This leads
to an unbalanced design where components made of
a particular material are overdesigned while compo-
nents made of another material are designed with
insufficient strength. Commonly, unbalanced designs
of composite components are characterised by signifi-
cantly different factors of safety related to the consti-
tuent parts. In many cases, such designs can be
balanced to some extent by altering the geometry of
the constituent parts made of different materials in
4Proc IMechE Part C: J Mechanical Engineering Science 00(0)

such a way that the limit state associated with the dif-
ferent constituent parts occurs at close magnitudes of
the loading force.
Using segmentation and intermediate components to improve
the level of balancing. As a rule, increased segmentation
of external loads increases the level of balancing and
improves the load-carrying capacity of the assembly.
Thus, for high-torque applications, planetary type
of gearbox is often preferred for transmitting torque
because of the increased number of contact points
(three instead of one).
31
This reduces the contact stres-
ses on the gear teeth and enhances durability.
Similarly, transitioning from a key connection in
shaft/hub assembly to a spline connection is beneficial
because torque is transmitted through multiple ele-
ments (instead of a single element) and, as a result,
the contact stresses are reduced.
Often, the contact of two components with high
hardness does not permit a uniform distribution of
the contact stresses. As a result, some zones from the
contacting surfaces are characterised by high contact
stress intensity while for others, the stress intensity is
low. Using elastic components as mediators (e.g. rub-
ber or other appropriate material) improves the distri-
bution of contact stresses and reduces their
magnitude. Increasing the level of balancing through
intermediate components provides protection against
elevated stresses from shock loading.
In what follows, an example will be given related to
improving reliability by increasing the level of balan-
cing through an intermediate component. The exam-
ple is related to concrete piles driven into the ground
27
(Figure 2(a)).
In Figure 2(a), driving the pile 1 into the ground
(3) causes damage to the top end of the pile because
of uneven distribution of the contact pressure from
the hammer 2. Part of the top end of the concrete pile
is overstressed which promotes cracks and damage of
the concrete pile.
Introducing a cheap intermediate component 5
between the hammer 2 and the pile 1 by using the
sleeve 4 (Figure 2(b)) improves the uniformity of the
load distribution over the top end of the pile. This
results in reduced contact stresses and reduced likeli-
hood of damaging the top end of the pile. The inter-
mediate component can simply be sand or other
cheap material.
Increasing the level of balancing by correcting negative distri-
bution of loads resulting from segmentation. As noted,
although segmentation is beneficial in reducing the
stresses in loaded assemblies, it is associated with a
downside. Often, the loads are not distributed uni-
formly across the separate segments. This is a techni-
cal contradiction associated with segmentation and,
to the best of our knowledge, no discussion has been
presented in the literature so far about the negative
effects from segmentation.
Possible ways of resolving this technical contradic-
tion and improving the load distribution over the sep-
arate segments is the alteration of material properties,
geometry or structure.
Here is an example of resolving this contradiction by
an alteration of the material properties. Consider a load
Pacting at the centre of a square platform supported
by four symmetrically arranged load-carrying elements
(legs) made of the same material and with equal cross-
sectional area. Because of the segmentation into four
load-carrying elements (legs), in the ideal scenario, the
load P will be supported by legs each carrying a load
with magnitude P/4.
Suppose that, because of geometrical imperfec-
tions, one of the elements has a height which is by D
shorter than the height of the other three elements.
As a result, the load carrying elements will no lon-
ger carry loads with the same magnitude P/4. Three
of the elements will be loaded with loads P0.P=4
and the shorter element will be loaded with a load
P1\P=4(3P0+P1=P). This has been illustrated
in Figure 3(a) and (b).
The magnitudes P0of the loading forces on
the three supporting legs can be reduced if the level
of balancing is increased by decreasing the stiffness
of the load-carrying legs from kto k1(k1\k) (Figure
3(c) and (d)).
This alteration of the material properties results in
reduced loading forces P0
0on the identical load-
carrying legs and increased loading force P0
1on the
shorter leg (3P0
0+P0
1=P). The magnitude of the
Figure 2. Eliminating the failure mode ‘damaging the top of a
pile driven into the ground’ (a), by increasing the level of
balancing through an intermediate component (b).
27
Todinov 5

largest stress in the load-carrying legs has been
reduced because all loading forces moved closer to
the ideal loading magnitudes equal to P=4.
Anexampleofalterationofgeometrytoimprove
the level of balancing can be given with the use of dif-
ferent pitch values to ensure uniform thread load dis-
tribution in bolted joints.
32
More uniform distribution
of the stresses along the thread of a bolt connection is
also ensured by selecting the material of the nut to be
of smaller stiffness than the material of the bolt.
32
Increasing the level of balancing through continuity and
homogeneity. It is a well-documented fact that fatigue
life depends strongly on the amplitude of the loading
stress. According to the Paris-Erdogan law (Paris and
Erdogan
33
), the rate of fatigue crack propagation
r=da=dN is given by
r=C(DK)m
where DKis the stress intensity factor range while C
and mare constants. The stress intensity factor range
is directly proportional to the stress range Ds.
Avoiding discontinuous operation (start-stop
regimes) of pressure vessels and pipelines reduces the
range of the internal thermal and loading stresses and
greatly enhances fatigue life.
Ensuring continuity in welding and hot rolling
avoids defects associated with the interruption of the
operation and improves the quality of the final prod-
uct. Eliminating transitional regimes in electrical cir-
cuits with large inductors, caused by unnecessary
start-stop regimes eliminates excessive voltages and
the risk of damaging components in the circuit.
Shifting from a linear reversed motion to a rotation
eliminates large inertia forces associated with rever-
sing the motion.
Homogeneity in material properties is an impor-
tant factor in increasing reliability by increasing the
level of balancing. A uniform heating and cooling of
a steel component with non-uniform thermal proper-
ties in the core and at the surface layers causes the
appearance of a significant thermal gradient and ther-
mal stresses. The thermal stresses can be so large that
they often lead to the fracture of components with
large sections. In contrast, uniform properties of heat-
treated component guarantee uniform thermal prop-
erties and a significant reduction of the internal ther-
mal stresses upon heating and cooling.
Furthermore, eliminating the anisotropy of the
microstructure in loaded components eliminates the
anisotropy of strength and creates better conditions
for resisting forces acting in different directions.
Guaranteeing a structure with uniform grain size in
an alloy eliminates excessive variation of the fracture
Figure 3. The differences in the load magnitudes P1 and P0 in (a) and (b) can be reduced as shown in (c) and (d), by reducing the
stiffness of the load-carrying elements.
6Proc IMechE Part C: J Mechanical Engineering Science 00(0)

toughness and creates better resistance to crack pro-
pagation. Uniform stiffness of supporting columns
guarantees uniform elastic deformations and
enhanced reliability.
Increasing the level of balancing by improving system’s
stability. Stability is a property of vital importance to
engineering systems. For a stable system, a bounded
input produces a bounded output and the system
returns in equilibrium state once the external distur-
bances have been removed. The system’s stability can
be improved significantly by ensuring conditions for
self-balancing.
Improving system’s stability by self-balancing. Unwanted
forces create excessive internal stresses in components
and assemblies and require extra material or reinforced
material with increased stiffness to resist them. As a
result, the weight and cost of assemblies are increased.
The extra loads also create extra friction forces, prema-
ture wear, fatigue degradation and failure.
The need for extra material, reinforced material
and heavier construction can be avoided if conditions
for self-balancing are created. As a rule, ensuring con-
ditions for self-balancing in a system improves the sys-
tem reliability.
34,35
Self-balancing can be achieved by (i) full or partial
compensation of forces or negative factors or by (ii)
stabilising the system through open-loop or closed-
loop control.
Self-balancing through symmetrical design can be
used to eliminate undesirable forces. An example of
such symmetrical design
36
can be given with two tur-
bines mounted on a common shaft in such a way that
the axial force on one of the turbines is compensated
by an equal and opposite axial force from the second
turbine. As a result, a trust bearing is no longer
needed; degradation caused by wear of the trust bear-
ing is avoided and the reliability of the assembly is
improved.
Increasing the level of balancing can be done by
counter-balancing mechanisms designed to take the
effort out of moving and supporting heavy loads, and
positioning manipulator arms. The result is reduced
magnitudes of the required forces for maintaining
equilibrium states, improved positioning precision
and reduced stresses. Thus, using counter-weights in
robots avoids the need for powerful actuators to over-
come static loads. For such counter-weight systems,
the required motion can be attained by a low-power
actuator whose energy consumption is necessary only
for overcoming the friction forces.
37
Counterweights in lift carriages increase the
ascending acceleration and decrease the descending
deceleration. As a result, the amount of power
required from the motor is much smaller than the
power needed to lift the weight of the carriage in the
absence of counterweights which extends the reliabil-
ity of the motor and its life.
Improving the system’s stability by active
balancing. Multiple components of the same type,
working simultaneously, often rely on devices/circuits
whose sole purpose is to actively balance the load on
the separate components. In these applications, pas-
sive balancing is not sufficient to guarantee the
required flexibility and resilience and there is a need
for active balancing.
An example of a transition from passive to active
balancing can be found in crane systems where the
counterweight from fixed becomes dynamic, with possi-
bility to be shifted, depending on the operating load.
38
Super-capacitors in particular, because of manu-
facturing variations, are not identical. During charg-
ing super-capacitors in series, at a constant current,
the capacitor that reaches first the rated voltage could
be damaged if charging continues after the capacitor
has reached its rated voltage. Supplemental active cir-
cuits can then be used for monitoring and balancing
the charging process.
39
Active balancing is also very important for battery
cells. The variation in the capacity of battery cells
connected in series, causes the voltage of some cells to
rise into dangerous levels, which results in a faster
degradation of the cells. Active balancing of battery
cells
40
is not only important for improving the perfor-
mance of the battery; it also extends battery life and
enhances safety.
Active balancing can also be done by open-loop or
closed-loop controllers which monitor the controlled
process variables and compare their values with speci-
fied reference levels. A control action is generated that
brings the process variables to match their specified
reference values.
Increasing the level of balancing by a compensating
factor. In this type of balancing, a third factor is used
to provide the balancing response. Capturing a com-
pensating factor is present in cases where disturbances
initiate changes which correct the disturbances. Thus,
seals should be designed in such way that frictional
heat does not cause an increase of the frictional forces
but their reduction. Pahl et al.
15
consider a layout of
taper roller bearings where the thermal expansion of
the shaft creates a compensating effect which does
not allow the load on the bearings to increase. Often,
disturbances initiate two factors acting in opposite
direction that compensate each other and return the
system into a stable state.
Increasing the level of balancing by selecting
components from the same variety
Increasing the level of balancing can also be achieved
if the variability of critical parameters is reduced. The
variability reduction prevents a non-uniform distribu-
tion of loading stresses.
For an assembly built on components logically
arranged in series, the life of the assembly is limited
Todinov 7

to the shortest life of a component in the assembly. A
significant variation in the lives of the components
arranged in series shortens the life of the assembly.
Thus, variation in the fatigue resistance of compo-
nents with identical functions, sharing a common
load and logically arranged in series, means that due
to variation in fatigue resistance, the assembly will
fail significantly before the expected life span in the
absence of such variation. Similarly, the variation in
the properties of seals could cause a seal assembly to
leak long before such leakage appears in an assembly
with small variation of properties.
Reliability-critical parameters vary and this variabil-
ity should be controlled to increase the level of balan-
cing. Broadly, the following techniques for controlling
variability can be distinguished: (i) selecting compo-
nents of the same variety; (ii) control of material, struc-
ture and properties during manufacturing; (iii) control
of geometrical parameters during manufacturing; (iv)
control of load magnitudes; (v) control of operating
environment and (vi) robust design.
Selecting components from the same variety is an
important technique for reducing the negative impact
of the variability of properties. Often, deep uncer-
tainty is present about the fractions of components
from different varieties. Consequently, an important
question is how to maximise the probability of select-
ing components from the same variety.
Most commonly, the available components are of
two varieties: reliable components and faulty compo-
nents. Commonly, the percentage of reliable components
in nseparate batches (or suppliers) is unknown. In this
case, it can be shown that the probability of purchasing
all components from the variety ‘reliable components’ is
maximised if all components are sourced from the same,
randomly selected batch(supplier).
This can be demonstrated with an example featuring
selecting two reliable components from nbatches (e.g.
containing the same type of bearings, seals, electronic
components, etc.) which are subsequently built into a
system. For the system to work, both components
selected must be from the variety ‘reliable components’.
Suppose that the percentage of reliable compo-
nents characterising the nbatches are
r1,r2,.,rn, correspondingly. These are unknown
quantities.
If the two components are purchased from a ran-
domly selected batch with probability (1/n), the prob-
ability that both components will be of the variety
‘reliable components’ is given by p1=1
nP
n
i=1
r2
i.
If the two components are purchased from two dif-
ferent, randomly selected batches, the probability that
both components will be reliable is given by
p2=1
½n(n1)=2X
i\j
rirj=2
n(n1) X
i\j
rirj
It can be shown that p1øp2:
1
nX
n
i=1
r2
iø1
½n(n1)=2X
i\j
rirjð1Þ
Inequality (1) can be obtained from the classical
Muirhead’s inequality.
41
Let fcgbe a non-decreasing sequence of non-
negative real numbers, where c1øc2ø::: øcnand
fdgbe another non-decreasing sequence where
d1ød2ø::: ødn. The sequence fcgmajorises the
sequence fdgif the following is fulfilled:
c1ød1;c1+c2ød1+d2;c1+c2+::: +cn1ø
d1+d2+::: +dn1and c1+c2+::: +cn1+
cn=d1+d2+::: +dn1+dn.
According to the classical Muirhead’s inequality, if
a sequence fcgmajorises the sequence fdgand
r1,r2,:::,rnare non-negative, the Muirhead inequality
states that
X
sym
rc1
1rc2
2:::rcn
nøX
sym
rd1
1rd2
2:::rdn
nð2Þ
where the symmetric sum P
sym
rc1
1rc2
2:::rcn
nis obtained by
adding the terms corresponding to all distinct permu-
tations of the elements of the sequence fcgwhile the
symmetric sum P
sym
rd1
1rd2
2:::rdn
nis obtained by adding
the terms corresponding to all distinct permutations
of the elements of the sequence fdg.
Consider the sequence fcg=½2, 0, :::,0and the
sequence fdg=½1, 1, 0, :::,0. Sequence fcgmajorises
sequence fdgbecause 2 .1, 2 + 0 ø1 + 1 and
2+0+0ø1+1 + 0, ..., 2+0 + 0 + +0ø1+
1+0+::: + 0. Consequently, the Muirhead
inequality
X
sym
r2
1r0
2:::r0
nøX
sym
r1
1r1
2:::r0
nð3Þ
holds. Next, dividing both sides of inequality (3) by n!
gives inequality (1).
For three batches (n= 3), inequality (1) becomes
(1=3)r2
1+(1=3)r2
2+(1=3)r2
3ø(1=3)r1r2+(1=3)r2r3
+(1=3)r3r1
ð4Þ
The difference between the left- and right part of
inequality (4) can be significant. Thus, for r1=0:9,
r2=0:2 and r3=0:65, the probability of selecting
two reliable components from a single, randomly
selected batch is
8Proc IMechE Part C: J Mechanical Engineering Science 00(0)

p1=(1=3)r2
1+(1=3)r2
2+(1=3)r2
3=(1=3)½0:92
+0:22+0:652=0:424
while the probability of selecting two reliable compo-
nents from two randomly selected batches is
p2=(1=3)r1r2+(1=3)r2r3+(1=3)r3r4
=(1=3)½0:930:2+0:230:65 + 0:65 30:9
=0:298
and p1.p2:
It must be pointed out that choosing two products
from the same batch will also maximise the probability
that both selected products will be faulty. It must be
pointed out that selecting two components from a sin-
gle, randomly selected batch will also maximise the
probability that both components will be faulty. This,
however, does not mean that it is more beneficial
to select the components from two different batches.
Despite that selecting from two different batches
decreases the probability that both selected compo-
nents will be faulty, for a faulty system to be present it
is not necessary both selected components to be faulty.
Selecting a single faulty component is sufficient.
Selecting components from two different batches
decreases the probability of having a reliable system
(two reliable components). This conclusion remains
unchanged if the fractions of reliable components are
considered to be fractions of faulty components.
Indeed, if we consider r1=0:9, r2=0:2 and
r3=0:65, to be the fractions of faulty components in
the batches, the probability of selecting two reliable
components from a randomly selected batch is
p1=(1=3)(1 r1)2+(1=3)(1 r2)2+(1=3)(1 r3)2
=(1=3)½0:12+0:82+0:352=0:257
while the probability of selecting two reliable compo-
nents from two randomly selected batches is
p2=(1=3)(1 r1)(1 r2)+(1=3)(1 r2)(1 r3)
+(1=3)(1 r3)(1 r1)=
(1=3)½0:130:8+0:830:35+0:35 30:1=0:132
Again, p1.p2.
No matter what ridenote (percentage of reliable
components or percentage of faulty components) the
probability that both components will be reliable is
always maximised by selecting both components from
the same randomly selected batch. With this, the
probability of safe operation is also maximised.
By using the Muirhead’s inequality (2), the result
related to selecting two components from nbatches
can be generalised to selecting m.2(m4n) compo-
nents from nbatches. This generalisation leads to the
following counter-intuitive result: Irrespective of the
fractions of reliable components characterisng the indi-
vidual suppliers, purchasing all components from a
single, randomly selected supplier, maximises the prob-
ability that all purchased components will be reliable.
Improving reliability by substitution.
Classification of techniques for the
method of substitution
Underlying idea
The underlying idea of the method of substitution is
to remove failure modes of an assembly working on a
particular physical principle by substituting it with an
assembly working on a different physical principle.
The classification of techniques (Figure 4) includes:
- substitution with mechanical assemblies
- substitution with electrical assemblies
- substitution with magnetic assemblies
- substitution with optical assemblies
- substitution with acoustic assemblies
- substitution with software-based systems
Substitution can also be made by using a combina-
tion of the listed basic techniques. Substitution is jus-
tified only if it removes failure modes and does not
introduce more dangerous new failure modes.
Eliminating particular critical failure modes by substi-
tution may cause other critical failure modes. The
design obtained by substitution with electrical or
magnetic assemblies for example, should be checked
carefully for new critical failure modes.
Figure 4. Techniques for improving reliability by substitution.
Todinov 9

Examples of efficient application of the method of
substitution in various domains
The substitution with mechanical assemblies is
sometimes considered for electrical and electronic
devices. Many electronic assemblies depend on the
availability of batteries, on reliable operation of the
power source and are also associated with risk of
overheating and fire. Electronic assemblies also
exhibit increased tendency to failure in environ-
ments with increased temperature, with strong elec-
tromagnetic interference, with increased vibrations
and humidity.
If any of these conditions are present and the risk
of failure is not acceptable, a substitution with
mechanical assembly could be considered. Mechanical
assemblies are less sensitive to strong electromagnetic
radiation, temperature, humidity and vibrations.
A typical example of this type of substitution is the
replacement of a battery-powered radio with mechan-
ical, spring-powered radio in remote places where bat-
teries are not readily available.
Efficient applications of the substitution with elec-
trical/electronic assemblies are: the control of ignition
timing for engines with electronic control module; the
substitution of mechanical relays with electronic
relays; the substitution of mechanical pushbutton
switches with pushbutton switches whose operation is
based on the Hall-effect, etc.
This type of substitution can also be applied with
success for eliminating failure modes associated with
various testing or measurements.
Consider an experimental test for cracks in the
coatings of steel pipe sections working in corrosive
environment. The plastic coating prevents corrosion
of the pipe and it is therefore critical that no through
cracks exist in the coating. Using mechanical test
based on covering the pipe section with fluorescent
paint reveals all the cracks but this mechanical method
is associated with a failure mode. Together with all
through cracks, the fluorescent paint method also
reveals all blind cracks in the coating which do not
provide paths through which the pipe could corrode.
The false indication from the mechanical, fluorescent
paint method can be avoided by substituting the
mechanical testing assembly with an electrical assembly.
The pipe section is submerged in electrolyte. One elec-
trode is attached to the inside surface of the pipe and the
other electrode is placed in the electrolyte which makes a
contact with the outer surface of the pipe section.
If voltage is applied to the electrodes, the presence
of weak current indicates through cracks penetrating
the plastic coating. In the substituting electrical
assembly, blind cracks can no longer distort the
results of the test and cause a false alarm.
The central idea of the substitution with magnetic
assemblies is eliminating failure modes by
substitution with assemblies/systems working on a
magnetic principle.
A typical example is the magnetic stirrer which
eliminates the need for a seal and with this it also
eliminates failure modes related to leakage from seals
and failure modes related to corrosion.
The magnetic worm gear eliminates a number of
failure modes associated with conventional gears:
- No wear is present because the transfer of torque
is frictionless;
- There are no failure modes associated with lubri-
cation because there is no need for lubrication;
- The maintenance is simplified which eliminates fail-
ure modes associated with incorrect maintenance;
- There are no failure modes associated with
misalignment;
- The spread of vibrations is eliminated.
Consider a safety valve on a pipeline carrying
flammable toxic fluid. The valve is maintained in
open position by hydraulic pressure. In case of a loss
of pressure in the hydraulic line, the valve must be
returned in closed position by a mechanical compres-
sion spring. Due to failure caused by fatigue, corro-
sion, or sagging of the spring (caused by stress
relaxation), the spring may fail to return the valve in
closed position and stop the toxic fluid in the pipeline.
This poses significant safety risk which could be elim-
inated if the mechanical spring is replaced by a mag-
netic spring. The substitution of the mechanical
spring with a magnetic spring eliminates all of the
major failure modes of the mechanical spring: fatigue
failure, sagging and corrosion failure without introdu-
cing new failure modes.
Another use of this type of substitution is the sub-
stitution of a mechanical attachment with magnetic
attachment, if a quick release must be made in case of
emergency.
An interesting application of substitution with
magnetic assemblies is the substitution with assem-
blies acting as deliberate weaknesses which discon-
nect/decouple two components when the load exceeds
a certain value. The failure of the deliberate weakness
decouples the components, releases the load and pre-
vents failure. In this case, the advantage of the mag-
netic assembly acting as deliberate weakness
compared to a mechanical type of deliberate weak-
ness (such as a shear pin, rupture disk, etc.) is that it
can be restored quickly, at no cost.
The substitution with optical or acoustic systems/
assemblies simplifies design, eliminates moving parts,
accumulates less damage, reduces wear and fatigue,
increases precision and improves maintainability.
A good example of substitution with optical assem-
blies is the substitution of the electro-mechanical
10 Proc IMechE Part C: J Mechanical Engineering Science 00(0)

mouse (with a rolling ball) with an optical mouse.
Compared to the electro-mechanical mouse, the opti-
cal mouse is characterised by:
- Significantly improved durability;
- No dirt collection;
- Easy maintenance, no need for cleaning;
- Capability to work on any surface;
- Better motion tracking;
- Better precision.
Substitution of electrical wire lines with fibre optic
lines results in:
- Improved performance in harsh environments
(with high humidity, high pressure, high voltage
or high temperature);
- Insensitivity to electromagnetic interference;
- Less amount of accumulated damage.
Substitution with optical assemblies can be applied
with success for eliminating failure modes associated
with various tests or measurements. A typical applica-
tion example is the infrared optical thermometer sub-
stituting the thermocouple. This substitution
eliminates the following failure modes:
- measurement variability caused by the variability
in attaching the thermocouple to the surface
whose temperature is measured;
- disrupted temperature field and errors in the mea-
sured values due to the thermocouple attachment/
insertion;
- high rate of deterioration of the mechanical con-
tact and low durability;
- relatively low measurement speed;
- low reliability in measuring temperatures higher
than 1300°C;
- low reliability of the measured values for high-
voltage surfaces.
Another example of removing failure modes by
substitution with optical assemblies is the substitution
of bonded-type strain gauges with optical strain
gauges. The reading from bonded strain gauges is
very sensitive to the quality of preparation of the sur-
face and the quality of the glue. Therefore, a signifi-
cant measurement variability is present due to the
variability in the quality of strain gauges attachment.
Poor attachment of the strain gauges leads to a dis-
torted measurement. In addition, the measurement
speed is low because the measurement requires careful
preparation of the surface and secure attachment of
the strain gauges.
The optical strain gauges do not require any physi-
cal contact hence avoid failure modes associated with
poor contact. Optical strain gauges also eliminate
errors associated with the preparation of the surface
which causes measurement variability. Finally, optical
strain gauges increase significantly the speed of
measurement.
Reliability can also be improved by a substitution
with software-based systems.
Thus, the complexity needed to guarantee a required
kinematics, for example, can be transferred from very
complex mechanisms to software coupled with simple
servomotors. Software components guarantee flexibility
and do not exhibit deterioration which is a major contri-
buting factor to unreliability. Furthermore, replicating
software does not result in manufacturing variability of
the software component.
Software components can serve as a basis of intelli-
gent equipment that provides guidance and warnings
for the user about its correct operation. This helps to
avoid dangerous actions and prevent injuries and
other failure modes. Software components can also
deliver effective troubleshooting which reduces risk
by reducing the consequences in the case of failure.
The substitution of mechanical assemblies with
electrical and software systems also permits the intro-
duction of sensing capabilities. These make the sys-
tems capable to reset their goals autonomously and
to adapt under changing external environment which
significantly enhances the resilience of the systems.
This also enhances the functionality of mechanical
systems and enables them to meet a broad spectrum
of user requirements. For example, some modern air
conditioning units are capable of sensing both tem-
perature and humidity and adapt their function to the
environment through fuzzy logic reasoning. Another
example is the programmable electronic control units
(ECU) in modern cars. The ECU controls the valve
timing, ignition timing, transient fuelling, air/fuel
ratio, the optimal amount of fuel injected in the
engine at different combinations of engine speed and
throttle position, water temperature correction when
the engine is cold, etc. The programable control
increases reliability, reduces fuel consumption and air
pollution and enhances the life of the engine.
The software components are also major compo-
nents of modern systems with artificial intelligence.
The autonomous car is capable of interpreting the
information coming from sensors, identifying obsta-
cles, lanes, vehicles, pedestrians, taking appropriate
navigation routes and executing necessary actions.
These capabilities help avoid collisions and other
accidents associated with lack of sleep, lack of con-
centration, information overload, insufficient reaction
speed, etc., which are typical for human drivers.
Machine vision, artificial neural networks (ANNs)
and deep neural networks (DNNs) are some of the
software components for visual object recognition.
Todinov 11

Conclusions
1. Despite that a number of solutions for increasing
reliability of components and systems by increas-
ing the level of balancing already exist in engi-
neering, these solutions have not been recognised
as instances of the same domain-independent
method. For this reason, a number of opportuni-
ties for increasing reliability by increasing the
level of balancing can be easily missed in the
design of systems and processes.
2. A domain-independent method and a number of
new techniques have been proposed for increas-
ing reliability by increasing the level of balancing.
In addition, a classification of techniques for
improving reliability by increasing the level of
balancing has been introduced and discussed for
the first time.
3. Central to the proposed classification are the fol-
lowing techniques:
- ensuring a more uniform distribution of
loads;
- altering the transmission paths of forces;
- reducing the magnitudes of inertia forces;
- ensuring a more uniform distribution of the
internal stresses;
- improving the distribution of material
properties;
- improving system’s stability;
- capturing a compensating factor and
- reducing the variability of reliability-critical
parameters.
4. If components must be selected from nbatches
containing reliable and faulty components with
unknown proportions, the probability that all
components will be reliable is maximised by
selecting the components from the same ran-
domly selected batch.
5. Segmentation reduces loads but is also associated
with uneven distribution of the stresses over the
separate segments. A method for re-balancing the
loading stresses in elements supporting a load has
been proposed. The method is based on reducing
the stiffness of the material.
6. Central to the proposed classification of the
method of substitution are the following major
categories: (i) substitution with mechanical
assemblies; (ii) substitution with magnetic assem-
blies; (iii) substitution with electrical assemblies,
(iv) substitution with optical assemblies; (v) sub-
stitution with acoustic assemblies and (vi) substi-
tution with software-based systems.
7. Design for reliability is underlined by common
domain-independent principles that are vital for the
reliability improvement of products and processes
and provide key input to the design process.
8. The generic principles for reliability improvement
allow engineers and scientists in a particular domain
to access excellent solutions and practices for elimi-
nating failure modes in other domains. In this way,
the constant reinventing of the wheel in reliability
improvement and risk reduction is avoided.
9. Generic methods change the way engineers and
scientists approach reliability improvement and
risk reduction. The presented generic methods
encourage simple, low-cost solutions as opposed
to some traditional high-cost solutions based on
introducing redundancy, condition monitoring,
reinforcement and use of expensive materials.
Declaration of conflicting interests
The author declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of
this article.
Funding
The author received no financial support for the research,
authorship, and/or publication of this article.
ORCID iD
Michael Todinov https://orcid.org/0000-0002-3957-7961
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