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manuscript MS-14-01555.R3
Contracting in Medical Equipment Maintenance
Services: An Empirical Investigation
Tian Heong Chan
Goizueta Business School, Emory University, Atlanta, Georgia 30322 tian.chan@emory.edu
Francis de V´ericourt
ESMT European School of Management and Technology, 10178 Berlin, Germany francis.devericourt@esmt.org
Omar Besbes
Graduate School of Business, Columbia University, New York, New York 10027 ob2105@columbia.edu
Maintenance service plans (MSPs) are contracts for the provision of maintenance by a service provider to an
equipment operator. These plans can have different payment structures and risk allocations, which induce
various types of incentives for agents in the service chain. How do such structures affect service performance
and service chain value? We provide an empirical answer to this question by using a unique panel data
covering the sales and service records of more than 700 diagnostic body scanners. We exploit the presence of
a standard warranty period and employ a matching approach to isolate the incentive effects of MSPs from
the confounding effects of endogenous contract selection. We find that moving the equipment operator from
a basic, pay-per-service plan to a fixed-fee, full-protection plan not only reduces reliability but also increases
equipment service costs. Furthermore, that increase is driven by both the operator and the service provider.
Our results indicate that incentive effects arising from MSPs leads to losses in service chain value, and we
provide the first evidence that a basic pay-per-service plan—under which risk of equipment failure is borne
by the operator—can improve performance and reduce costs.
Key words : maintenance repair, contracting, fine balance matching, service value chain, health care
1. Introduction
Operators of capital-intensive equipment often spend a large annual budget on maintenance
so as to ensure high equipment reliability. In the medical imaging equipment industry,
on which our study is based, a top-of-the-line computed tomography (CT) or magnetic
resonance imaging (MRI) device costs nearly a million dollars (US) and requires annual
maintenance expenses amounting to 10% of that price (ECRI Institute 2013). Because
imaging units typically last about ten years, lifetime maintenance costs can easily approach
the original equipment’s purchase price. Hence many leading manufacturers of capital
equipment—including General Electric Co., Siemens AG, and Hewlett-Packard Co.—have
expanded their maintenance service offerings over the last decade (Sawhney et al. 2004).
1
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
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A defining feature of maintenance services is that value is co-produced (Karmarkar and
Roels 2015). That is, achieving desirable outcomes (high equipment reliability and low
service cost) requires operator effort in operational handling as well as service provider
effort in maintenance and repair. Hence, the collaboration between the operator and service
providers is critical for creating good service outcomes (Oliva and Kallenberg 2003). What
governs the effectiveness of this collaboration is the maintenance service plan (MSP)—a
contract that stipulates a payment structure and according to which the responsibility for
equipment failure may shift between the operator and the service provider. One commonly
used MSP is the basic pay-per-service contract. Under this contract, labor and parts are
charged every time repair service is required, and the operator bears the bulk of equipment
failure risk. Another common MSP is the full-protection contract, under which the service
provider covers all maintenance costs over an agreed-upon period of time in exchange for
a fixed fee. In this case, most equipment failure risk is borne by the service provider.
Our paper offers one of the first empirical analyses of how MSPs affect maintenance
service outcomes. We exploit a unique data set supplied by a major medical device man-
ufacturer to disentangle the incentive effects owing to MSPs from endogenous contract
selection. This approach enables us to quantify the (relative) effect of these MSPs on fail-
ure rate, onsite visits, and remote resolutions in addition to costs of labor and replacement
parts. We find that, compared to a basic contract, the full-protection contract leads to more
failures and increased service costs. Because the additional costs must either be absorbed
by the service provider or passed on to the operator in the form of higher fees, our results
establish that the full-protection contract underperforms the basic contract at the service
chain level. We demonstrate also that the service provider’s greater propensity to visit
operators under full-protection plans (rather than to address the issue remotely) explains
the provider’s contribution to the observed cost increase.
Despite the key role played by MSPs in the co-production of maintenance services, hardly
any empirical studies have explored the relative performance of these contracts. There are
good reasons for this lack of empirical research to date. First, there are very few data sets
of MSPs that are amenable to analysis. In addition to confidentiality issues, manufacturers
have only recently begun moving into maintenance services in a significant way (Sawhney
et al. 2004). Second, maintenance contracts can lead to both contract selection and contract
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
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incentive issues, and developing identification strategies that account simultaneously for
these issues is challenging (Abbring et al. 2003, Chiappori and Salani´e 2003).
To overcome these challenges, we use a rich data set covering the monthly service records
of more than 700 medical imaging units (MRI and CT scanners) across 441 hospitals, from
a major medical device manufacturer. Hospitals operate the equipment; the manufacturer
provides maintenance services. The data set records the contract choices made for each
unit and also their service performance and service cost, on a monthly basis, throughout
the standard warranty period and during the subsequent maintenance contract period.
We exploit the structure of this unique data set to account for endogenous contract
selection in our estimation of MSP incentive effects. Specifically, all hospitals have the
same incentive structure during the warranty period, so any observed differences in service
failures and costs among equipment over this period of time can be reasonably attributed
to differences in their innate operating conditions. Adopting this account, we use a state-
of-the-art matching approach to preclude any confounding effects of those innate operating
conditions. Our main specification controls for potential differences in the patterns of
equipment failure and service cost in the warranty period as well as for equipment type,
the operator’s economic importance to the service provider, time patterns, and service
location. Following this procedure enables us to measure differences in service outcomes
that are due to the incentive effects entailed by the type of MSP—that is, the effect on
service outcomes of shifting the risk of equipment failure from one party to the other.
We find that the incentive effects arising from a full-protection plan (as compared with
a basic plan) can increase equipment failure rate by 33%. They can also increase service
costs: onsite visits by 80%, service labor hours by 54%, and spare parts expended by 125%.
We also show that, in response to a reported failure, the service provider makes 55%
more onsite visits to an operator under a full-protection plan than to one under a basic
plan. Yet contingent on the service provider making an on-site visit, its expenditure on
labor and materials seems to be independent of contract type. In other words: the greater
propensity of the service provider visiting operators under full-protection MSPs explains
the increase in per-failure costs for labor and spares that is observed in the data.
Taken together, our results suggest that a full-protection plan induces the service
provider to offer a higher service level (relative to a basic plan) by increasing onsite visits.
It also induces the operator to rely on the service provider for maintenance and may lower
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the operator’s own level of care for the equipment.1These outcomes lead to an unambigu-
ous increase in service costs for the service chain. Given that the average participant in the
US health system orders one (MRI or CT) scan every three years (Smith-Bindman and
Miglioretti 2012), our findings are both statistically and economically significant.
Finally, our results caution against the prevailing view that manufacturers intending
to move into services should either assume more of the equipment failure risk (Oliva and
Kallenberg 2003, Deloitte Research 2006) or take direct responsibility for service perfor-
mance (Guajardo et al. 2012). In our set-up, to the contrary, reliability deteriorates and
costs increase when the service provider assumes more responsibility for equipment failure.
The paper proceeds as follows. In Section 2 we discuss the relevant literature and the-
ory in maintenance service contracting; we then discuss the industrial setting and data in
Section 3. Section 4 offers a graphical representation of the results, which leads to the devel-
opment of our empirical approach in Section 5. We present our main results in Section 6
and a set of additional results and robustness checks in Section 7. Finally, in Section 8 we
conclude and discuss some implications of our findings.
2. Literature Review
In the operations management (OM) literature, most theoretical research that addresses
contracting focuses on the context of physical supply chains and manufacturing systems
(for reviews of work in this area, see e.g. Cachon 2003, Nagarajan and Soˇsi´c 2008). There
is comparatively less theoretical work on service contracting (Zhou and Ren 2011).
In the maintenance service literature, some papers have analyzed maintenance con-
tracting problems within a principal–agent framework, typically where the operator is the
principal and the service provider the agent. In these settings, the operator outsources
maintenance work of equipment to a service provider and is assumed to have no impact on
equipment failures. However, the service provider is susceptible to incentive issues because
its effort in performing repairs directly affects the maintenance outcomes and yet cannot
be observed by the customer. Plambeck and Zenios (2000) studies such a setting with a
dynamic single principal and single agent model. Kim et al. (2007) uses a one-shot sin-
gle principal with multiple agents to study a maintenance setting in which the service
providers can affect maintenance outcomes by altering the inventory level of spare parts.
1Other possibilities explaining the increase in failure rate is an increase in usage rate, or an increased propensity to
report failures. Our analysis using supplementary data sets did not find support for these two alternative explanations
(see Appendix).
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In general, however, services are co-produced in the sense that both the operator and the
service provider contribute to value creation (Fuchs and Leveson 1968), and both parties
may have incentive issues. For situations such as these, identifying simple contract forms
that produce first-best outcomes is difficult (Bhattacharya and Lafontaine 1995, Corbett
et al. 2005, Jain et al. 2013). In this stream of research, the theoretical work of Roels et al.
(2010) is perhaps closest to our paper. Roels et al. compare the service chain value resulting
from a basic, a full-protection, and a performance-based plan when the collaborating parties
could each be susceptible to incentive distortions. Their key finding is that, depending
on the context, each one of these three contract types can dominate the other two. More
specifically, the performance-based plan dominates when both parties are susceptible to
incentive distortions. However, the basic plan (resp., full-protection plan) dominates when
only the equipment operator (resp., service provider) has incentive distortion issues. Our
work provides a first empirical exploration of these theoretical predictions.
If the theoretical literature on maintenance service contracts is scarce, empirical OM
work on the topic is virtually nonexistent—despite the practical importance of these issues
for industry. Nonetheless, scholars have empirically studied a variety of issues in the more
general context of supply chain coordination. For example, empirical papers have examined
the effects of product component sharing (Ramdas and Randall 2008), information sharing
(Terwiesch et al. 2005, Cui et al. 2015), and vertical integration (Novak and Stern 2008,
2009) on collaboration outcomes. These papers all focus on comparing the outcomes of
collaboration and pooling of resources with the outcomes in their absence. In contrast, our
paper focuses on optimizing contractual configurations conditional on collaboration.
To the best of our knowledge, Guajardo et al. (2012) is the only paper that examines
empirically the performance of maintenance service contracts. The setup of our respective
works differs along two dimensions. First, the contracts analyzed are of a different nature.
Guajardo and colleagues focus on performance-based contracts (versus basic plans); such
contracts are common in aerospace and defense industries, where most equipment owners
are large entities. In contrast, we focus on full-protection plans (versus basic plans), which
are much more common in the medical equipment industry and in other industries where
equipment owners are small. Second, these authors focus on estimating the effects of MSPs
on only one metric of service performance: the failure rate. Although we also analyze failure
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rates, in addition we examine service costs (onsite visits, labor hours, spare-part costs) as
well as usage rates and failure severity (the latter two on smaller sets of data).
The conclusions of the two papers are also quite different. Guajardo et al. (2012) find,
for the aircraft engine industry, that performance-based contracts improve reliability over
time-and-materials plans (akin to our basic plan). In other words, they find that basic
plans hamper performance, which they attribute to the service provider expending less
effort on repair and maintenance for operators under basic plans. In our set-up, however,
a basic plan improves both performance and cost (when compared with a full-protection
plan). This result is driven by both the operator’s and the service provider’s behavior.
Finally, the economics literature includes many papers that explore the association
between service contracts and performance. Much as in the OM literature, the number
of empirical papers lag their theoretical counterparts; for a review of the work in this
area, see Chiappori and Salani´e 2003. In particular, papers on service contracts tend to
focus on project-based services. Examples include, among others, IT software development
(Banerjee and Duflo 2000, Gopal et al. 2003, Kalnins and Mayer 2004, Susarla et al. 2010,
Susarla 2012), offshore drilling (Corts and Singh 2004), legal services (Helland 2003), con-
struction (Bajari et al. 2014), motion picture making (Chisholm 1997), and government
services (Levin and Tadelis 2010). We study instead the maintenance industry, in which
the dynamics of repeated interaction introduce different types of incentives.
3. After-Sales Maintenance of Medical Equipment
Both CT scanners and MRI devices help physicians diagnose a range of conditions by
providing cross-sectional views of the body’s interior. Both the equipment operator (i.e.,
the hospital employing radiology technicians) and the service provider play a role in service
outcomes. Maintenance service plans structure payments and so may affect the behavior
of both parties. That is: the basic plan places a greater burden of failures on the operator,
whereas the full-protection plan shifts that burden to the service provider. Shifting the
burden of failure from one agent to the other should, in theory, increase the latter’s incentive
to exert effort toward improving equipment reliability and reducing service costs, while
reducing the former’s incentives on that score. In this case, the overall effect on service
outcomes depends on which of these counteracting forces prevails (Roels et al. 2010).
To study this question, we obtained contract and maintenance service records from a
major medical equipment manufacturer. The data cover sales and service records of MRI
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
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and CT scanners sold by the equipment manufacturer between 2008 and 2012 in a major
OECD country. The data pertain to 712 pieces of equipment, of which 57% are CT scanners.
Each new equipment sale includes a standard warranty period (usually one year); at the
end of that period, the operator chooses one of the three types of MSPs. These types—in
decreasing order of coverage—are: (i) the full-protection plan, which offers the operator
(in return for a fixed annual fee) complete protection against any labor or parts costs
resulting from product failure; (ii) a partial-protection plan, in which the operator pays a
fixed annual fee for all labor plus a variable amount that depends on the parts used for the
repair process; and (iii) the basic plan (a.k.a. a time-and-materials contract), which requires
operators to pay for all labor and parts due to repairs but with a low fixed annual fee. In
addition, all MSPs cover preventive maintenance. Table 1 summarizes the key differences
across these three types of plans. After the warranty period, 74% of the operators select
the full-protection plan, 21% the basic plan, and 5% the intermediate, partial-protection
plan. Given these figures, our analysis focuses on comparing full-protection plans with
basic plans and excludes partial-protection plans.2
Table 1 Summary of MSP Coverage
Plan Type Labor Charges Material Charges
Full-protection Yes Yes
Partial-protection Yes No
Basic No No
Figure 1 sketches the high-level process of how equipment failures are reported and
resolved, which is standard across all operators. This process begins with an equipment
operator calling in to the manufacturer’s service call center to report a failure event. At this
point, an electronic ticket is created to log equipment details and the problem’s description.
The manufacturer has a team of service call engineers, who communicate with the hospitals
to understand the problem. Given remote access to the equipment for diagnosing and
resolving problems, a large fraction of tickets can be resolved at this stage. For problems
that cannot be so resolved, the ticket is assigned to a suitably skilled service engineer who
then visits the operator’s premises. After the problem is resolved, the ticket is closed, with
information on the total repair hours and cost of materials logged into the system.
2The number of scanners under partial-protection is too small to allow reliable statistical statements. Hence our main
analysis addresses the incentive effects of the basic and full-protection plans only.
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Customer reports
failures (Fails)
Problem
resolved
offsite?
Make onsite visits
(Visits)
Close ticket, record
incurred expenses
(Labor & Spares)
Yes
No
Close ticketClose ticket
Figure 1 High-level process of reporting and resolving equipment failures.
We track—monthly—four measures of service performance and operating costs; these
measures capture all the key process elements represented in Figure 1. The first measure
is Fails, a count variable for the number of reported failures. The second measure, Visits ,
counts the number of onsite visits made to the operator’s premises to resolve problems
(some require more than one visit; others can be resolved offsite and so without any visits).
The variables Spares and Labor capture the operating costs of resolving problems: Spares
represents the cost of consumables and spare parts for maintenance and repairs; and Labor
captures the total labor hours spent onsite.3
Table 2 reports summary statistics for the service performance and cost variables
(observed monthly). All four variables—Fails,Visits,Labor, and Spares—are nonnegative
and right-skewed, which is reflected in their large standard deviations relative to the mean.
For example, on average one piece of equipment requires a fairly low 2.8 hours of Labor. Yet
the standard deviation is 8.2 hours and the observed maximum is 219 hours, or 78 times
the average. To tackle this issue, we use an exponential model (i.e., E[F ails] = exp(βX))
to ensure that predictions are in the non-negative domain, and the Poisson regression to
generate estimates that are consistent in the presence of outliers and distributional mis-
specification (Cameron and Trivedi 2009, Wooldridge 2010).
Table 3 provides statistics for measures that are fixed at the equipment level. These
include the plan that the operator selects (our key independent variable), the equipment
type (MRI or CT scanner), the date of the equipment installation, and its physical loca-
tion (one of seven regional areas covered by the service provider). Finally, we use the
number of past MRI and CT scanners that the equipment operator purchased from the
3We scaled both Labor and Spares with a fixed (positive) multiplicative factor to mask the absolute magnitude of
the variables. This transformation does not affect our estimation because we use an exponential setup, which reports
results as percentage changes from a given base.
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Table 2 Summary Statistics for Service Performance and Cost (712 devices; 23,173 monthly observations)
Correlation
Variables Description Mean (S.D.) 1 2 3
1. Fails Number of failures reported per month 1.43 (1.79) 1.00
2. Visits Number of site visits per month 1.00 (2.04) 0.70 1.00
3. Labor Hours consumed per month 2.80 (8.21) 0.54 0.85 1.00
4. Spares Cost of materials consumed per month 1,502 (7,631) 0.28 0.36 0.40
service provider since 1989 (the earliest date covered by our data) to create a CustomerSize
variable that measures the operator’s economic importance to the service provider.4
Table 3 Summary Statistics for 712 Medical Scanning Devices
Correlation
Variables Description Mean (S.D.) 2 3
1. Plan Basic (1), partial-protection (2), or full-protection (3) —
2. Type MRI scanner (0) or CT scanner (1) 0.57 (0.50) 1.00
3. InstallDt Date of installation (months since January 2008) 22.7 (13.9) −0.11 1.00
4. CustomerSize Number of CT or MRI scanners purchased in the past 7.7 (11.6) 0.05 0.13
5. Location Equipment’s service region (1–7) —
4. Visual Representation of Data and Results
Our goal is to identify the effects of the different MSPs on service performance and oper-
ating costs. Table 4 compares the averages of service outcomes across different plan types.
Table 4 Mean Service Measures by Plan Type
Plan Type Fails Visits Labor Spares
Full-protection 1.37 0.94 2.54 1,817
Basic 0.76 0.38 1.04 520
This table indicates that equipment tends to fail more often under full-protection than
under basic plans (failure averages of 1.37 and 0.76, respectively). Equipment covered by
a full-protection plan similarly consumes, on average, more repair resources: it calls for
more onsite visits, more labor, and more spare parts. Table 4 does not indicate whether
4CustomerSize does not change frequently over time and we measure this variable at the installation date.
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these numbers reflect self-selection effects (as when operators know their equipment has a
high failure rate and therefore choose the full-protection plan) or incentive effects (as when
operators and/or service providers are incentivized by the MSP to take actions that end
up increasing the failure rate).
Figure 2 traces the average number of failures (on a quarterly basis) as equipment crosses
the warranty period into the MSP period for the two groups of operators. Thus the figure’s
solid line corresponds to operators that choose the full-protection plan and the dotted line
to those that choose the basic plan. The shaded area represents the period during which
equipment is still under standard warranty.
Figure 2 Average number of monthly failures over time, where the warranty expires at time 0.
Figure 2 highlights three important aspects of the data. First, for data in the warranty
period—say, from month −3 to month −1 (in the shaded area)—the average number of
operator-reported failures is higher for those that selected the full-protection plan (1.60)
than for those that selected the basic plan (1.10). The difference (of 0.50 failures per
month) between the two groups of operators during this period provides visual evidence
of contract selection; that is, operators do not choose MSPs randomly but instead choose
MSPs with more protection if they have higher failure rates.
Second, Figure 2’s dotted line, which marks the equipment failure rates for customers on
the basic plan, exhibits a sharp drop in reported failures as the operators transition from
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the warranty period into the MSP period (from 1.10 failures in months −3 to −1 down
to 0.75 failures in months 1 to 3). This drop is less pronounced for customers that select
the full-protection plan (1.60 versus 1.50). These concurrent changes result in a widening
of the gap—as customers transition from the warranty to the MSP period—between the
line representing customers that select the full-protection plan and the one representing
those that select the basic plan. That widening of the gap (e.g., from 1.60 −1.10 = 0.50 to
1.50 −0.75 = 0.75) reflects the impact of MSPs on service performance that is due to the
service plans’ different incentive structures.
The third important aspect of our data is that the number of failures declines during
the warranty period, and this decline appears faster for customers that select the basic
plan. This declining failure rate is consistent with the so-called bathtub curve, whereby
failures typically first decrease, then flatten out, and finally increase with equipment age
(Nowlan and Heap 1978, Smith and Oren 1980, Aarset 1987, Block and Savits 1997); an
early decrease in the failure rate is usually attributable to the detection and resolution
of (nonrepeating) defects in manufacturing. The difference in trends further suggests that
an equipment under a basic plan may be located on a different part of this curve than
is an equipment under a full protection plan. This possibility constitutes one of our main
estimation challenges, since that difference (in location on the bathtub curve) might itself
at least partly explain the widening gap observed when the warranty expires.
That said, the data in the warranty period allows us to observe innate differences across
equipment that we leverage to identify incentive effects. Specifically, to tackle the issues of
contract selection and failure trends, we match equipment with similar failure trends during
the warranty period (but that ended up on different plans), thereby eliminating systematic
differences during the warranty period across the two groups (details are presented in the
next section). Therefore, any remaining difference after the warranty ends must capture
the MSP effect. Figure 3 presents the equivalent of Figure 2 after the matching procedure.
Here we see that, during the warranty period, the trends are now essentially identical.
Even so, there is once again a sharp divergence in reported failures almost as soon as the
warranty period ends and MSP incentives come into play. In Section 6 we establish that
this incentive effect is statistically significant.
Finally, matching is a natural approach in our set-up. While it is challenging to control for
the differences in trends and curvatures of equipment in a regression framework, matching
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12 Article submitted to Management Science; manuscript no. MS-14-01555.R3
Figure 3 Average number of monthly failures over time for the matched population, where the warranty
expires at time 0.
allows to do this non-parametrically. Identification using the entire sample in standard
regressions would heavily rely on extrapolation (i.e., comparisons using innately dissimilar
units). By contrast, identification under matching relies on the two pools of equipment
where we observe significant overlap (as in Figure 3).
5. Estimation Approach
Our approach consists of three stages. In the first, we rely on data from the warranty
period to estimate parameters for equipment failure patterns. In the second stage, we
match equipment in the full-protection plan against equipment in the basic plan in terms
of those estimated failure patterns and other equipment characteristics. Finally, we use
observations from the post-warranty period to estimate the incentive effect.
5.1. Estimating Parameters of Failure Patterns in the Warranty Period
The main confounds with respect to our data arise because each device may have their
own levels and trends of failures. We use a three-parameter (αi, βi, θi) model to capture
the failure patterns of each piece of equipment i(in the warranty period) conditional on
that unit’s age in months:
E[Fails |i, Age] = exp{αi+βi(Age) + θi(Age2)}.(1)
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
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Note that the right-hand side (RHS) of Equation 1 is enclosed in an exponent so that
predictions will remain in the nonnegative domain. Parameters αi,βi, and θidenote (respec-
tively) the level, trend, and curvature of equipment i’s failures. Equation 1 can be estimated
separately for each equipment, or equivalently in a joint estimation using a single Poisson
regression (with level, trend, and curvature identifiers for each equipment).
In essence, we aggregate the failure patterns of the warranty period into three parame-
ters. Matching directly on the data runs the risk of matching on idiosyncratic month-to-
month failure patterns. Consistent with the literature (Nowlan and Heap 1978, Smith and
Oren 1980, Aarset 1987, Block and Savits 1997), we therefore assume that an underlying
failure curve generates the data (together with other sources of random variations gener-
ating the final monthly failures). Additionally, our quadratic model is sufficiently general
to capture all six patterns of failure curves identified by Nowlan and Heap 1978, including
the bathtub curve. We note that the generality is warranted in this case: the model fit for
a quadratic model is significantly better than the model fit for a linear model.5
Table 5 reports the distributional statistics for the estimated parameters.6The magni-
tudes of the estimation errors (the standard errors of ˆαof 0.44, ˆ
βof 0.12, and ˆ
θof 0.03) are
small compared to the variation of the failure curve parameters across equipment reported
in the table (standard deviation of ˆαof 1.08, ˆ
βof 0.27, and ˆ
θof 0.05). Thus, between-
equipment variation accounts for most of the total variation (86% for α, 84% for β, and
78% for θ)7and the variation in our data is mainly driven by cross-equipment variation
rather than estimation errors. As a result, the imprecision of the failure curve estimates
should not significantly impact the precision of the matching procedure we present next.
We check this further in Section 7 with a bootstrap approach that directly accounts for the
uncertainty in the failure curve estimates. This alternative approach produces very similar
final estimates and all our results remain statistically significant.
5.2. Matching
We follow an optimal matching approach with “fine balance” (Zubizarreta 2012, p.1360)
to create two populations of equipment: one each for the basic and full protection plans.
5The likelihood ratio test produces LR = 837, P (LR > χ2)<0.0001.
6The distribution excludes all equipment on partial-protection plans and includes only equipment with a warranty
period of exactly 13 months (i.e., the modal length), for a total of 465 medical scanning devices.
7using the formula σ2
B
(σ2
B+σ2
W), where σBis between equipment standard deviation, and σWis within standard deviation
arising from estimation errors.
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14 Article submitted to Management Science; manuscript no. MS-14-01555.R3
Table 5 Distribution of ˆα,ˆ
β, and ˆ
θ
Quantiles
Estimates Mean S.D. 5% 25% 50% 75% 95%
ˆα0.119 1.077 −1.80 −0.24 0.34 0.80 1.33
ˆ
β-0.062 0.269 −0.31 −0.11 −0.03 0.03 0.12
ˆ
θ-0.005 0.047 −0.06 −0.02 0.00 0.02 0.05
This approach matches exactly on a one-to-one basis the variables that have a significant
impact on identification (such as the failure curve). Less critical variables are matched on a
population-level, i.e., the matching is done so that the two populations are distributionally
similar. The flexibility of the method allows us to achieve a close match between equipment
without significant loss of data (Rosenbaum et al. 2007, Yang et al. 2012).8
5.2.1. Variables for matching To ensure that the two populations of equipment are
similar, we match them on ten variables as follows. First and foremost, we match the three
estimated failure parameters (ˆα,ˆ
β, and ˆ
θ) to ensure there are no systematic differences in
equipment—with respect to their level of failure or position on the bathtub curve—during
the warranty period.
Second, we ensure the absence of any aggregate differences in service response by match-
ing also on three service cost measures: the average monthly number of site visits made on
account of each device during the warranty period (AvVisits); the average hours of labor
spent (AvLabor), and the average cost expended on spare parts (AvSpares).
Finally, we match on the equipment’s type, customer size, installation date, and loca-
tion (variables that are fixed at the equipment level; see Table 3). Matching on equipment
type controls for potential systematic differences (regarding, e.g., usage or failure patterns)
between MRI and CT scanners. Matching on customer size ensures that we account for the
equipment operator’s economic importance to the service provider. Matching on installa-
tion date (i.e., months elapsed since January 2008) ensures that our observations begin
8To further appreciate this point, consider an alternative close-distance matching approach, that requires identifying
pairs of devices that are close across all covariates. While theoretically ideal, identifying pairs such as these is difficult
with a large number of matching variables, and the approach results in very small and sensitive samples (Stuart
2010). One solution for this issue is to relax how close pairs need to be as in a “coarsened exact matching” (CEM)
approach (Iacus et al. 2011). While using CEM leads to qualitatively similar results (not reported here), the approach
produces a sample that is smaller with matches on the failure curves that are less precise.
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
Article submitted to Management Science; manuscript no. MS-14-01555.R3 15
and end at similar times; in this way, we control for general time trends.9Finally, matching
on location ensures that geographic differences across service regions (e.g., distance from
the service provider) do not affect our estimates.
5.2.2. Optimal matching with fine balance We formulate the matching problem as
a mixed-integer program whose objective is to maximize the number of paired samples
subject to balance constraints (Zubizarreta 2012, Zubizarreta et al. 2014). For the most
critical features—and in particular the failure curve—these constraints reflect an exact
match of equipment. For features that are less critical, the constraints enforce a fine balance
(Rosenbaum et al. 2007, Yang et al. 2012): instead of matching such features exactly, the
constraints guarantee that the distribution of equipment with respect to the considered
features is similar across the two populations. Following this approach allows us to limit
data loss while retaining accurate matches.
We start by identifying the location of 1s in a matching matrix Mwith elements Mbf ,
where bindexes equipment in B(i.e., on the basic plan) and findexes equipment in F(on
the full-protection plan). Note that Mbf = 1 only if equipment bis matched to equipment f
(and otherwise equals 0). The objective of maximizing the number of matches is formally
stated as follows:
max
Mbf ∈{0,1},b∈B,f∈FX
b∈B,f∈F
Mbf .(2)
We now introduce a series of constraints that represent the matching requirements. First,
we implement a one-to-one match; that is, a scanner on the basic plan must be paired with
exactly one scanner on the full-protection plan. Formally, we have
∀f∈F,X
b∈B
Mbf ≤1,
∀b∈B,X
f∈F
Mbf ≤1.
(3)
Next, we match on equipment features. We match exactly on the equipment type and
failure curve. So if Mbf = 1, then we need that Typeb=Typefand that the parameters
ˆαb,ˆ
βb, and ˆ
θbbe (respectively) within εα,εβ, and εθof the parameters ˆαf,ˆ
βf, and ˆ
θf.
We choose εsuch that the distance between the parameter values is less than 0.37 of the
9The effect of this procedure is similar to that of controlling for calendar year-month fixed effects in regressions. We
could instead control for such fixed effects later in the regression, but it is preferable to control for all key variables
up front in the matching process (Imbens 2004).
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interquartile range.10 For instance, εα= 0.37 ×(0.80 −(−0.24)) = 0.38 from the 75th and
25th quartile in Table 5.
The result is the following set of constraints. For all b∈Band f∈F:
Mbf (Typeb−Typef) = 0;
Mbf |αb−αf| ≤ εα,
Mbf |βb−βf| ≤ εβ,
Mbf |θb−θf| ≤ εθ.
(4)
We match the remaining features via the fine-balance approach. Consider the categorical
variable Location, which locates each piece of equipment iinto one of seven distinct service
regions. Our constraint must guarantee that the distribution of equipment over locations
is the same across the two matched populations. Denoting by I(·) the indicator function,
we have the following constraints:
∀j∈ {1,...,7},X
f∈F,b∈B
Mbf I(Locationb=j) = X
f∈F,b∈B
Mbf I(Locationf=j).(5)
The equivalent fine-balance matching for continuous variables consists of matching on
quantiles (Zubizarreta 2012), so we constrain the two distributions to have the same quar-
tiles (median, 25th percentile, and 75th percentile). We employ this technique to match
five different variables: (i) the average monthly number of site visits made to each piece
of equipment during the warranty period (AvVisits); (ii) the average hours of labor spent
(AvLabor); (iii) the average cost of spare parts (AvSpares);11 (iv) CustomerSize; and (v) the
calendar month during which the equipment was installed (InstallDt ). We denote by F−1
v
the inverse cumulative distribution of variable v; hence I(vb≥F−1
v(p)) = 1 if and only if the
variable vfor equipment bis at no less than the pth percentile of the variable’s distribution.
Thus we have the following constraints:
10 0.37 of interquartile range (IQR) is equivalent to 0.5 standard deviation for a normally distributed variable. We
use IQR as a more robust measure of spread. Matching at double the coarseness, i.e., one standard deviation, can
eliminate more than 90% of the bias (Cochran 1968, Imbens 2004). We implement this far more stringent matching
criterion to ensure that the failure curves follow each other as closely as possible.
11 We control for these measures without estimating their trends because much of the service cost (in the warranty
period) is driven by failures. Indeed, if we match on failures then our analysis (not presented here) indicates that,
during the warranty period, the aggregate trends of the service cost measures across matched populations are not
significantly different.
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Article submitted to Management Science; manuscript no. MS-14-01555.R3 17
∀v∈ {AvVisits,AvLabor ,AvSpares,CustomerSize,InstallDt},
∀p∈ {0.25,0.5,0.75},
X
f∈F,b∈B
Mbf I(vb≥F−1
v(p)) = X
f∈F,b∈B
Mbf I(vf≥F−1
v(p)).
(6)
In short, the matching problem amounts to maximizing objective (2) subject to con-
straints (3), (4), (5), and (6). Thus our approach maximizes the number of paired samples
subject to fine, one-to-one constraints on equipment type and the failure curve and subject
to distributional constraints on service cost measures, geographical location, customer size,
and installation date.12
5.2.3. Outcome of matching Using the matching approach just described, we identify
a total of 188 units (94 each under the basic and full-protection plans). Table 6 compares
the statistics of our variables across the two populations. We apply three tests to check the
quality of the match. Two of these tests are discussed here; the more extensive “placebo”
test is presented in Section 7.1.
Table 6 Comparison of Univariate Statistics after Matching (188 scanning devices)
Basic Full-protection Normalized difference
Variables µB(σB)µF(σF) (µF−µB)/σpooled
Type 0.50 (0.50) 0.50 (0.50) 0.00
ˆα0.27 (0.81) 0.29 (0.76) 0.01
ˆ
β−0.05 (0.09) −0.05 (0.10) −0.01
ˆ
θ0.00 (0.02) 0.00 (0.02) 0.00
AvVisits 1.30 (1.07) 1.40 (1.09) 0.10
AvLabor 3.74 (3.40) 4.01 (3.68) 0.08
AvSpares 808 (926) 765 (907) −0.04
CustomerSize 8.77 (12.3) 8.63 (13.2) −0.01
InstallDt 22.5 (11.0) 23.1 (10.3) 0.06
Location — — —
Notes: µBand σB(resp., µFand σF) are the mean and standard deviation for the basic (resp., full) plan.
The divisor σpooled is the pooled standard deviation, which is calculated as σpooled =p0.5(σ2
B+σ2
F).
Statistics are not shown for Location, which is both categorical and perfectly balanced.
The first is a univariate test that checks, for each variable, whether the difference of the
means is less than one fifth of a standard deviation (Cochran 1968, Cohen 1988, Imai et al.
2008). When that is the case, group membership (in either a basic or a full-protection plan)
12 The overall problem has 41,846 decision variables and 292,944 constraints; we solve it using the IBM ILOG CPLEX
Optimization Studio.
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explains less than 1% of each variable’s total variance. We find that all variables satisfy
this strict criterion (i.e., the magnitude of the numbers in the last column of Table 6 should
be less than 1/5).13 The second test checks for whether the variables can jointly predict
which contract an operator chooses after the warranty period (Imbens 2004). Indeed, if
our matches are of good quality then equipment characteristics should have no predictive
power with regards to contract choice. We use a logit regression in which the Plan dummy
variable is set to 1 if the equipment operator chose the full-protection plan (and to 0
otherwise). We run the regression specified in 7 below and find that none of the coefficients
is statistically significant. Of critical importance is that, when we compare this model with
a simpler model that involves just a constant (i.e., logitP[I(Plani= full-protection)] = c),
we find that the model specified in Equation 7 does not fit any better than the simple
model: a likelihood ratio test compares the likelihood of both models and finds no statistical
significance (χ2= 2.29, p= 0.999).
logitP[I(Plani= full-protection)]
=cααi+cββi+cθθi+cvAvVisits +clAvLabor
+csAvSpares +ccCustomerSize +cdInstallDt
+X
j∈{1,...,7}
cjI(Locationi=j) (7)
Figure 3 (in Section 4) illustrates the overall quality of the match and shows that paired
equipment in the full-protection and the basic plan exhibit strongly similar failure rate
curves during the warranty period.
5.3. Estimating Incentive Effects
We now turn to the estimation of incentive effects, which are captured by the difference in
service outcomes during the post-warranty period. (For service failures, this corresponds to
the gap observed in Figure 3 and discussed in Section 4). Equation 8 specifies the regression
setup:
E[Service outcome |MSP] = exp{δI(MSP = full-protection) + c}.(8)
13 For the failure curve variables which are matched on a one-to-one level, we can alternatively analyze the distribution
of pairwise-differences. This procedure also shows that the means of the pairwise differences are small, i.e. less than
.2 standard deviations away from zero.
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Here “Service outcome” may correspond to the number of failures, site visits, labor
hours, or spares consumed. We are most interested in δbecause it represents the incentive
effect arising from shifting an operator from the basic plan to a full-protection plan. The
constant cmodels the baseline aggregate service outcome—that is, when equipment is on
the basic plan. We do not incorporate any control variables since we account for them in
the matching process (Imbens 2004).14
Given that the service outcome measures are nonnegative and right-skewed, we first
enclose the RHS in an exponent to ensure that predictions are in the nonnegative domain.
We also use the Poisson regression to estimate the model (which, as mentioned in Section
3, is unbiased in the presence of outliers and distributional misspecification). All reported
standard errors are clustered by the equipment, so they are robust to the potential presence
of autocorrelation and heteroskedasticity.
6. Results
6.1. Effect of MSP on Service Outcomes
Table 7 presents results for the regressions. Consider first our model in which the dependent
variable (DV) is Fails. The analysis reveals a statistically significant (p < 0.05) and posi-
tive effect of full coverage—as compared with basic coverage—on the number of reported
failures. The mean estimate of the effect δis 0.29, which corresponds to a 33% increase in
the failure rate.15
Table 7 Poisson Regression Estimating the Effect of MSP on Service Performance and Operational Costs
DV: Fails Visits Labor Spares
δ0.29 (0.12)∗0.59 (0.15)∗∗∗ 0.43 (0.21)∗0.81 (0.30)∗∗
Observations 2,085 2,085 2,085 2,085
Log-likelihood −3,257 −2,717 −8,106 −1,828,199
Notes: Standard errors are clustered by equipment.
∗∗∗p < 0.001, ∗∗ p < 0.01, ∗p < 0.05
Consider now the model with dependent variable Visits. The effect of a full-protection
plan on the number of site visits made by the service provider is again statistically signifi-
cant (p < 0.001). Moreover, for a 33% increase in failure rate, the service provider increases
14 All our results are robust to controlling for the matched variables (not reported here).
15 In an exponential model, the translation from a coefficient δto the effect size is given by exp{δ} − 1.
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the number of onsite visits by 80%. These results suggest that, given a reported failure, the
service provider is more likely to visit an operator under Full coverage. (This hypothesis
is tested formally in Section 6.2.)
Similarly, the coefficients δin the Labor and Spares models indicate statistically sig-
nificant increases: in Labor (p < 0.05) and also in Spares (p < 0.01). Specifically, Labor
increases by 54% while Spares increases by 125%.
Altogether these findings establish that MSPs have a large and statistically significant
incentive distortion effect, leading to large increases in costs for servicing equipment under
the full-protection plan as compared with the basic plan. It is certainly possible that both
parties contribute to this cost increase, yet in theory the equipment operator’s contribution
should be more significant because that operator pays a fixed annual cost regardless of the
final repair cost under the full-protection plan.
6.2. Effect of MSP on Service Provider
To explore this incentive distortion effect further, we now examine in greater detail how
the service provider responds to failures. For example, the service provider’s propensity
to make an onsite visit (in response to a reported failure) may vary depending on the
equipment operator’s type of MSP. The service provider could also, in theory, vary its
repair approach—for example, by spending more time on the careful diagnosis of difficult
problems or by deciding to replace not only a failed component but rather all interrelated
components. Such incentive effects would be captured by changes in onsite visit rates (i.e.,
number of visits per reported failure) and in the hours and costs expended per visit.
To explore these possibilities, we create the variables Visits/Fail,Labor/Visit, and
Spares/Visit—dropping months during which we observed no failures or (for the latter
two variables) no visits. We analyze these dependent variables using the same setup as in
Equation 8, and our results are reported in Table 8.
The coefficient δfor Visits/Fail is statistically significant (p < 0.001). Its value of 0.44
indicates a 55% increase in the number of visits per failure. This result is not consistent
with the notion that a service provider would save on repairs when it bears all their costs.
In fact, when the service provider bears these costs, it tends to make more onsite visits.
Finally, the coefficients derived in the regressions on Labor/Visit and Spares/Visit are
not statistically significant. So conditional on the service provider dispatching an engineer,
there are no statistically significant differences in how service engineers repair equipment
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Table 8 Poisson Regression Estimating the Effect of MSP on Failure Response
DV: Visits/Fail Labor/Visit Spares/Visit
δ0.44 (0.07)∗∗∗ −0.06 (0.10) 0.19 (0.19)
Observations 1,143 672 672
Log-likelihood −1,052 −1,428 −386,899
Notes: Standard errors are clustered by equipment.
∗∗∗p < 0.001
due to the MSP chosen by an operator. One possible explanation for this is that the
frequency of site visits is an indication of responsiveness, which allows the service provider
to further signal the added-value of the full-protection MSP. But once on site, the engineer
seems to follow standard procedures.
Figure 4 summarizes our findings. The diagram’s arrows indicate that the full-protection
MSP has two types of effects. First, it drives a 33% increase in reporting of failures by the
operator; second, it induces the service provider to make 55% more onsite visits in response
to reported failures. When combined, these two effects account for the large increases in
labor costs and spare-parts cost (54% and 125%, resp.) described in the main analysis.
Failures Visits
Labor Hour
Spares Cost
MSP
+33% +55%
(+)
(+)
(+)
Figure 4 Effect of full-protection MSP on service outcomes.
7. Robustness and Additional Analysis
7.1. Placebo Tests
We test the validity of our approach by performing a “placebo test” (Angrist and Pischke
2008). The idea is to use data from the warranty period only, then to break that period
into two subperiods, and finally to repeat our analysis while supposing that the warranty
period had ended (and the MSP period had begun) upon completion of the first subperiod.
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If there were selection factors that our main model did not adequately account for, then
the results of these placebo tests should show some statistically significant effect.
We break the standard warranty period into two subperiods as follows: the first subperiod
covers all except the last three months of the warranty period, and the second subperiod
covers those remaining three months. Table 9 depicts the results of this analysis.
Table 9 Poisson Regression Model Assuming Warranty Period Ends Three Months Earlier
DV: Fails Visits Labor Spares
δ0.04 (0.13) 0.22 (0.24) 0.05 (0.32) −0.26 (0.39)
Observations 342 342 342 342
Log-likelihood −595 −552 −1,591 −394,618
Notes: Standard errors are clustered by equipment.
Table 10 shows the result of an alternative setup where the first subperiod covers all
except the last six months. We can see that in none of the models are any of the δcoefficients
statistically significant at the 5% level. Indeed, the mean effect is much smaller than (and
directionally inconsistent with) the effects obtained in our main analysis.
Table 10 Poisson Regression Model Assuming Warranty Period Ends Six Months Earlier
DV: Fails Visits Labor Spares
δ0.10 (0.19) 0.14 (0.30) −0.01 (0.42) 0.01 (0.48)
Observations 276 276 276 276
Log-likelihood −496 −469 −1,339 −336,961
Notes: Standard errors are clustered by equipment.
In other words, the two groups that are matched up to the end of the first subperiod
continue to have parallel trends from that time onward until the warranty period ends.
This finding confirms that our observed effects in the post-warranty period stem from the
contract type, and are not due to inadequately controlling for selection factors (e.g., the
bathtub curve).
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7.2. Errors Arising from Matching on Estimates
To further understand the robustness of our findings to the errors in the failure curve
parameter estimates, we compare our final estimates with the ones obtained by bootstrap-
ping. Using the joint distribution of ˆα,ˆ
β,ˆ
θestablished in Section 5.1, we first create 500
bootstrapped samples (each sample consists of 465 sets of failure curve parameter esti-
mates, i.e., one set of ˆα,ˆ
β,ˆ
θfor each equipment). We then proceed with matching and
estimating the incentive effects based on these bootstrapped samples. Table 11 compares
the results using bootstrapping against our main model. As shown in the table, the boot-
strapping method produces estimates that are very close to the original ones, and all effects
remain statistically significant.
Table 11 Comparison of Poisson Regression Estimates based on our Main Model vs. Bootstrapping Failure
Curves
DV: Fails Visits Labor Spares
Main Model 0.29 (0.12)∗0.59 (0.15)∗∗∗ 0.43 (0.21)∗0.81 (0.30)∗∗
Bootstrap Model 0.30 (0.12)∗0.60 (0.16)∗∗∗ 0.46 (0.23)∗0.87 (0.32)∗∗
Notes: Standard errors clustered on equipment.
∗p < 0.05, ∗∗p < 0.01, ∗∗∗ p < 0.001
7.3. Interactions
In this section, we extend the main analysis by considering possible interactions. More
specifically, we test whether our results differ across customer size, equipment type, or
time. To limit the model’s complexity, we test for these effects separately. In none of these
cases do we detect any significant interaction effects.
Customer size may interact with contractual incentives if the service provider offers
special treatment to only those operators that are large and on the full-protection plan.
We can test for this possibility by interacting δwith CustomerSize, thereby creating the
variable δ×CustomerSize, and then including this term—along with CustomerSize—in
the main regression.16 Table 12 reports the results from this estimation. Note that the
coefficient for δ×CustomerSize is not significant, indicating that the incentive effect does
not seem to increase with larger customers.
16 We de-mean CustomerSize in the regression, so that the coefficient for δcan be interpreted as the incentive effect
on an operator at the mean CustomerSize.
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Table 12 Poisson Regression Model Including Interaction with Customer Size
DV: Fails Visits Labor Spares
δ0.28 (0.11)∗0.59 (0.15)∗∗∗ 0.41 (0.21)∗0.83 (0.30)∗∗
CustomerSize 0.00 (0.01) 0.00 (0.01) −0.00 (0.01) −0.02 (0.01)
δ×CustomerSize −0.00 (0.01) −0.01 (0.01) −0.01 (0.01) 0.01 (0.02)
Observations 2,085 2,085 2,085 2,085
Log-likelihood −3,255 −2,714 −8,073 −1,816,573
Notes: Standard errors are clustered by equipment.
∗∗∗p < 0.001, ∗∗ p < 0.01, ∗p < 0.05
In the same vein, we also test for differences in the incentive effects across scanner type:
MRI versus CT. Here we interact δ×I(Type = MRI) and include the term I(Type = MRI).
Table 13 reports the results. We see that, as compared with CT scanners, MRI scanners
(on average) have higher failure rates and incur greater service costs. Nonetheless, the
coefficients for the interaction terms are again not statistically significant.
Table 13 Poisson Regression Model Including Interaction with Equipment Type
DV: Fails Visits Labor Spares
δ0.48 (0.19)∗0.80 (0.23)∗∗∗ 0.69 (0.20)∗1.41 (0.37)∗∗∗
I(Type = MRI) 0.81 (0.18)∗∗∗ 0.73 (0.24)∗∗ 0.70 (0.34)∗1.18 (0.42)∗∗
δ×I(Type = MRI) −0.34 (0.22) −0.37 (0.29) −0.46 (0.40) −0.97 (0.55)
Observations 2,085 2,085 2,085 2,085
Log-likelihood −3,149 −2,674 −8,012 −1,797,356
Notes: Standard errors are clustered by equipment.
∗∗∗p < 0.001, ∗∗ p < 0.01, ∗p < 0.05
Finally, there may be variation in effects across time if, for example, the operator and
service provider learn how to cooperate better. We implement a test of this possibility by
interacting δwith Age (i.e., δ×Age) and then including this term, together with Age, in
the regression.17 Results are given in Table 14. We see no evidence—over a one-year time
frame—of any changes in incentives.
17 We de-mean Age so that we can interpret the coefficient of δas the incentive effect at the mean (as described for
CustomerSize in note 16).
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Table 14 Poisson Regression Model Including Interaction with Age
DV: Fails Visits Labor Spares
δ0.29 (0.12)∗0.59 (0.15)∗∗∗ 0.48 (0.20)∗0.81 (0.29)∗∗
Age −0.00 (0.01) −0.01 (0.03) −0.01 (0.01) −0.02 (0.05)
δ×Age −0.01 (0.01) 0.01 (0.03) 0.05 (0.05) 0.02 (0.07)
Observations 2,085 2,085 2,085 2,085
Log-likelihood −3,257 −2,717 −8,057 −1,827,697
Notes: Standard errors are clustered by equipment.
∗∗∗p < 0.001, ∗∗ p < 0.01, ∗p < 0.05
8. Discussion and Conclusion
We have established that—in the context of medical equipment maintenance—a fixed-fee,
full-protection plan leads to more failures and higher service costs than does a basic, time-
and-materials plan. For this reason, service providers should be wary of assuming more
responsibility for equipment failure outcomes (as they do when absolving operators under
the full-protection plan of repair costs). Indeed, Roels et al. (2010) have theorized that this
may be a possible scenario, and our work provides the first supporting empirical evidence.
The analysis presented here also establishes that both the equipment operator and the
service provider contribute to increased service costs. Operators on full-protection plans
apparently reduce the level of their own care of the equipment.18 In contrast, the service
provider expends more resources—in terms of a higher onsite response rate—to equipment
under a full-protection plan.19
It is noteworthy that, according to the documents available to us, neither the contract
terms nor the maintenance process itself dictates that more onsite visits (or any other
special treatment) be given to operators under a full-protection plan. Furthermore, account
managers—who could have an incentive to affect the quality of service afforded certain
operators—are not actually involved in the maintenance process. The increase in onsite
visits may therefore result from the intrinsic motivation of the service provider and/or
18 The observed increase in failure counts can arise due to three different reasons: first, operators on full-protection
plans increase their usage levels; second, they tend to report more failures; and finally, they reduce the level of
equipment care. Using data on equipment usage and failure severity (which we use as a proxy for mis-reporting), we
show in the Appendix that the first two factors do not vary significantly across contract types.
19 Because we do not observe significant variation in failure severity across contract types (see previous footnote), the
higher onsite response rate is not driven by systematic variations in problem complexity but rather incentive effects.
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26 Article submitted to Management Science; manuscript no. MS-14-01555.R3
broader organization-level culture (see e.g. Kreps 1997). This, in turn, leads to additional
and perhaps unnecessary costs.
Thus our study documents the presence of significant frictions that result in a decrease
in service chain value relative to the ideal, first-best outcome. In other words, a central-
ized decision maker who managed both the service provider and the equipment operator
could generate higher profits (by reducing equipment maintenance costs) than the sum
of their currently achieved individual profits. In this sense our study reveals that there
are costly inefficiencies in the medical equipment industry and that these inefficiencies are
significant—especially considering the size of the industry.
This research makes clear the need for better coordination mechanisms between service
provider and equipment operator. It may be that alternative contracts could result in
Pareto improvements over the outcomes of existing contracts. Coordination might also
be improved by alternative business models in which, for instance, the service provider
directly operates the equipment at the hospital.
One limitation of our work is the absence of data on preventive maintenance. That
being said, the “reactive” maintenance events we study constitute most of all interventions
(preventive and reactive) in our setup. We therefore do not expect that accounting for
preventive maintenance activities would significantly alter our findings. Yet if such an effect
does exist, then in theory it should be in the same direction as our main result. Hence the
increase in cost and failures observed in the data would be even greater.
Finally, we are limited by the lack of revenue data (owing to commercial sensitivity)
and are prevented from discussing the implications of our results for either the service
provider’s or the equipment operator’s profits. An interesting avenue for future research,
therefore, is to determine if the loss of value we characterize in this paper is actually priced
in, or if the service provider absorbs the cost.
Acknowledgments
We are grateful for the support of Siemens Healthcare Customer Services. In particular, we thank Alfred
Fahringer, Rajneesh Moudgil, and Marc Muehlen (all at Siemens Regional Headquarters Asia–Australia) for
helpful discussions and input.
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Article submitted to Management Science; manuscript no. MS-14-01555.R3 27
Appendix A: Analyses with Supplementary Data
In this appendix we detail analyses that use supplementary data sets. We use these data sets to show that
contracts have negligible effects on equipment usage and failure severity.
A.1. Equipment Use
Here we use scanning data from a small sample of 471 observed months (covering 22 pieces of equipment) to
investigate directly whether plans affect usage. The use data (measured as number of scans per month, but
masked by a multiplication factor) were made available through a trial program whereby the equipment’s
status is tracked remotely in real time. Figure 5 plots use data over time for a sample of six pieces of
equipment.
0
5
10
15
20
25
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
Age in Months
Average Number of Scans per Month
Full
Partial
Basic
MSP Period
Warranty Period
Figure 5 Number of scans across time.
Observe that the number of scans differs considerably from one equipment operator to the next. For a
given operator, however, the number of scans is quite stable over time. More crucially, the post-warranty
change in contract type does not result in visually detectable changes in the number of scans.
We use fixed effects in formally testing the relation between MSP type and equipment usage. As compared
with the matching approach deployed in the main text, a fixed-effects approach differs in two ways. First, it
leverages all the data for inference (and hence is more “data efficient” for small data sets). Second, whereas
matching removes any pre-existing differences with regard to the warranty period, inference based on fixed
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
28 Article submitted to Management Science; manuscript no. MS-14-01555.R3
effects relies on difference in differences (i.e., whether the aggregate gap in usage between those under a
full-protection plan versus a basic plan changes after the warranty period; see Angrist and Pischke 2008).
The specification is given in Equation 9, where (as in our main specification) δcaptures the incentive effects
of the full-protection plan (relative to the basic plan). Once again, we use a Poisson regression to estimate
the model:
E[Scans |Equipment i, Month m]
= exp{ci+δwI(Contractim = Warranty) + δI(Contractim = full-protection)}.(9)
The results are reported in Table 15; note that the δcoefficient is not statistically significant. So in line
with Ning et al. (2014), who studies incentive effects on usage in pay-per-print services, we find that contracts
have a negligible incentive effect on equipment usage.
Table 15 Effect of Plan on Use (Poisson with fixed effects)
DV: Scans
δw(Warranty) −0.09 (0.05)
δ0.01 (0.07)
Equipment fixed effects Yes
Observations 441
Log-likelihood −764
Notes: Standard errors are clustered by equipment.
A.2. Failure Severity
Our main analysis focuses on failure counts, but failures are heterogeneous and the incentive effects we have
uncovered could similarly affect failure severity. Here we test if there are variations in failure severity due to
MSP changes. This provides a direct test of whether the increase in onsite visits is driven by variations in
failure severity. It also indirectly tests whether contracts affect reporting behavior.
Given the very nature of reporting behavior, direct data on it will (almost) never be available. Nonetheless,
failure severity is a natural indirect measure. Indeed, severe failures correspond to those that shut down a
piece of equipment because they cannot be fixed by the operator; thus they can hardly go unreported. In
contrast, the operator may be able to fix a nonsevere failure or at least to continue using the equipment
despite the problem. It follows that any changes in the level of reporting would be detectable through changes
in the mix of severity of reported failures.
To help disentangle this issue, we obtained data covering the severity of each failure over a six-month
period (about 4,000 failure occurrences). Failures can either involve a loss of functionality (e.g., equipment
won’t power up, cooler not working, table not feeding; coded by the service provider as 1) or involve only
minor issues (abnormal noises, minor software issues, etc.; coded as 0). Nearly a quarter of all failure events
are severe.
We test the relationship between failure severity and reporting tendencies by using a fixed-effects setup
similar to that used in Section A.1 (but with conditional logit since the dependent variable now takes binary
Chan, de V´ericourt, and Besbes: Maintenance Service Contracting
Article submitted to Management Science; manuscript no. MS-14-01555.R3 29
values). The results of this analysis are reported in Table 16. Observe that, once again, the δcoefficient is
not statistically significant. Thus we find no statistical evidence that MSPs have an effect on the severity of
equipment failures.
Table 16 Effect of MSP on Failure Severity (conditional logit)
DV: Severity
δw(Warranty) 0.01 (0.43)
δ0.06 (0.48)
Equipment fixed effects Yes
Observations 3,678
Log-likelihood −1,649
Notes: Standard errors are clustered by equipment.
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