*Corresponding author. Tel.:#31-40-247-5944; fax: #31-40-246-7497.
E-mail address:[email protected] (V.T. Petkova).
The use of quality metrics in service centres
Valia T. Petkova*, Peter C. Sander, Aarnout C. Brombacher
Eindhoven University of Technology, Faculty of Technology Management/Section Product and Process Quality, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract
In industry it is not well realised that a service centre is potentially one of the major contributors to quality improvement. Service is able to collect vital information about the "eld behaviour of products in interaction with customers. If this information is well analysed and communicated, the recurrence of old problems in new products will drastically be reduced and so will the expenses on recalls, repairs, warranties, and liabilities. In this paper we discuss the kind of information a service centre has to collect and some quality-related metrics that organisations use, like the"eld call rate, or should use, like the hazard function. ( 2000 Elsevier Science B.V. All rights reserved.
Keywords: Reliability; Service centre; Quality improvement; Quality metrics; Maturity index on reliability (MIR)
1. Introduction
For high-volume consumer products there is a"erce and world-wide competition, in which the four most important business drivers are:
f Functionality:As a result of a fast technological
development, the functionality of products in-creases sharply. For example, any 10-year-old photo camera is as to functionality far behind a recent one in the same price category.
f Time to market: The technological development
is so fast that products are outdated in months instead of in years. This has as a consequence that the time to market has to be very short, otherwise a product is already obsolete by the time it reaches the market. Desktop computers are a clear example.
f Quality and reliability: Customers expect
excel-lent quality even for relatively inexpensive prod-ucts. In line with this the warranty period is extended from half a year to sometimes three years, or even longer. A short time to market and excellent quality are con#icting requirements. For example, a serious test programme needs time, and if the tests show that improvement actions are necessary, then that takes even more time.
f Proxtability:The fact that products are obsolete
in months, has as a consequence that there is a fast price erosion. One of the most striking examples is probably the price of desktop com-puters in relation to their functionality. Because of this price erosion, the necessary investments, and the heavy competition, it is not easy to make a pro"t on consumer products.
In order to survive as a company producing con-sumer products, it is vital to be best in class on one or more business drivers. This means that there
Fig. 1. Feedback control loop.
must be a coherent and company wide approach, in which every department knows its role and under-stands that it is not the pro"tability of the indi-vidual department that counts; what counts is the pro"tability of the company as a whole. This means that departments must be judged by their contribu-tion to the company wide vital business processes. Functionality, time-to-market, quality and pro" t-ability are all the result of business processes, and these processes must constantly be improved and kept in line with the changing environment in order to become or stay best in class and consequently survive as a company.
The availability of feedback control loops is im-portant for the improvement of business processes. In principle a feedback control loop has a simple structure. There is a process and the output of the process has to ful"l certain criteria. In order to check whether the output is in accordance with the speci"cations, some measurements are done. If the measurements make clear that there is a di!erence between the output and the criteria, some action is necessary (cf. Fig. 1). For an overview about dealing with instability of business processes we refer to [1] in this issue. The control of processes is complic-ated by the fact that normally there are all kinds of disturbances, in particular in the input, in the pro-cess, in the measurements and even in the action.
In an organisation feedback control loops are necessary on all levels. On a low level they are used in production, examples are automatic control mechanisms and statistical process control. On a high-level feedback loops have to be used in order to make sure that departments keep in line with the overall company goal.
In a previous paper [2], we demonstrated that service centres are an essential element in the control loop aimed at quality improvement. In the present paper we discuss some metrics that
presently are used in service centres and that at best have some value for logistic purposes, but are not related to the business drivers. Subsequently, some metrics are discussed that focus on the quality of the products.
The structure of the paper is as follows. In Sec-tion 2 the new role for service centres is shortly described, namely the contribution of service centres to quality improvement. In Section 3 the information #ow is presented that facilitates the new role of the service centre. This information#ow is structured by the maturity index on reliability (cf. [3,4]). In Section 4 it is discussed what metrics are valuable in the process of enhancing the quality and reliability of consumer products. We consider two metrics that are currently used in industry, and we propose two metrics that are much more tailored to quality improvement. The conclusions are presented in Section 5.
2. Role of service centres in quality improvement
Up to about 10 years ago companies could see product quality as something&nice to have'. Now-adays it is a must, a boundary condition. Without it there is no reason to enter the market. A unique characteristic of a service centre is that there the customer and the manufacturer have their"rst con-tact when there is a quality problem. That is, when there is a mis"t between what the customer expects and what he gets. This mis"t is the"nal result of the product creation process (PCP). We de"ne the PCP in a wide sense, i.e. it includes all business processes that directly a!ect the "nal product; in particular the business processes in marketing, development, production and service, including the suppliers.
Fig. 2. Observed categories of reliability problems [6].
expectations. The only contact between a customer and the manufacturer is in a service centre when a customer has a complaint. In particular when the complaint is covered by the warranty, the service centre will try to repair the product as fast as possible and with minimum costs. Service centres will try to reduce local costs by skipping expensive and locally non-contributing activities. If a service centre is not assessed on its contribution to quality improvement, it has no motive to spend time on
"nding the root cause of the customer's problem and to communicate this to the other parties in the PCP. Consequently, there is no information #ow from service centres to the other parties. The only information exchange between designers and ser-vice centres concerns the serser-viceability of the prod-ucts. As far as service is concerned, replacing the failed modules or the whole product solves the problem.
Apart from the general remarks in the forgoing about the possible contribution of service centres to quality improvement, there are some special cir-cumstances why just now a di!erent role for service is most advantages. In our opinion the most impor-tant ones are the following:
1. Nowadays the"eld problems service centres are confronted which are of a di!erent nature than in the past. With the increasing reliability of the components and the also increasing complexity of the functionality, component-related reliabil-ity problems have become a minorreliabil-ity of current
"eld complaints (cf. Fig. 2). As service centres are close to the customer, they are in a good position to examine the root cause for all fault categories. This requires a new approach, because, as men-tioned before, up till today a service centre just replaces components or modules by spare-parts without looking for the root cause. Actually, a service centre today is usually not capable of
"nding the root cause, because it has no substan-tial knowledge about design and production.
The best way forward is, in our view, to inten-sify the collaboration between service centres and development and production by exchange of information and exchange of people (cf. [2]). 2. Especially in high-volume consumer products there is a high degree of innovation. The more
innovative new products are, the more di$cult it is to predict the way customers will use them. Therefore, companies must anticipate unan-ticipated hidden quality problems and latent defects shortly after market introduction. As a consequence, it is of most importance that especially in this phase there is a detailed and fast communication between Development, Pro-duction, Quality and Reliability, and Service about all four business drivers. Again, the "rst contact with the customer is in the service centre, so that is a perfect place to start.
The conclusion is that on a company level it is essential to see Service as a department that is crucial in the control loop over the product cre-ation process. Service is able to collect vital in-formation about the"eld behaviour of products in interaction with customers. If this information is well analysed and communicated, the recurrence of old problems in new products will drastically be reduced and so will the expenses on recalls, repairs, warranties, and liabilities.
Now we will focus our attention on the informa-tion #ow that is essential for the quality control loop.
3. Information6ow
This paper concentrates on the contribution of Service to quality improvement. Therefore, in this section we will mainly focus on the information
the Maturity Index on Reliability (cf. [3] and [4]) as this index structures the information#ow.
The overall aim of this section is to prepare for the discussion on the metrics in the following section.
3.1. Informationyow leaving a service centre
As has been mentioned before, service centres are in a unique position to collect"eld failure data and data about customer use, and to analyse the rela-tion between them. This informarela-tion is very helpful in several phases of the PCP:
f "eld failure data determines the critical parts of
a design in relation to customer use,
f "eld failure data demonstrates problem areas in
production,
f information about customer use is vital for the
determination of the test programme. In particu-lar, tests are necessary to "nd out whether the
"eld failures as collected by Service have e! ec-tively been anticipated in design and production.
f After release of a new product,"eld failures must
be communicated to development and produc-tion as soon as possible. Serious quality prob-lems could lead to a disaster like a recall of a whole generation of products.
3.2. Maturity index on reliability
The basic idea behind the maturity index on reliability (MIR) is that the quality improvement loop over the PCP requires a full exchange of information between all parties. As this is exactly the conclusion of Section 2, it makes sense to see how the MIR principle can be used in order to utilise the unique position a service centre poten-tially has in the quality improvement loop.
We only give a short description of the"ve MIR levels, for a more extensive discussion we refer to [3,4]. The MIR levels are structured in such a way that a higher level includes a lower level.
MIR level 0: no quantitative information available
about the,eld behaviour
The manufacturer has no quantitative evidence of the"eld behaviour of the products and, conse-quently, there is no feedback system from Service to Development and Production.
MIR level 1: quantitative information available
about the number of failures
There is a basic feedback system that gives quantitative information indicating
f the performance during production, f the performance in the"eld.
This information must be in the form of metrics that objectively describe the performance of the process between production and the"eld (see Sec-tion 4).
MIR level 2: quantitative information available
about the origin of the problems
The feedback system contains information about the origin of the problems. There is quantitative information about:
f primary causes: design, material, production
process, customer use,
f secondary location of failure, i.e. the location
within the primary cause.
MIR level3:detailed information available on root
-cause level
There is detailed information on root-cause level for all dominant failures, such that causes of failures in previous products and processes can be trans-lated into risks in future products and processes.
MIR level 4:continuous improvement via an adaptive
system
The system is adaptive. Techniques and tools are in place in the organisation to anticipate risks for new products and processes and to eliminate these risks where necessary. Local optimisation is re-placed by global optimisation.
In this paper we concentrate on the role of ser-vice centres in the information#ow that is needed in order to reach MIR level 1. It is quite clear that service centres are invaluable for the other MIR levels as well. Information for MIR levels 2, 3 and 4, for example, can be collected by a service centre that has the right knowledge about design and production. This will be the topic of forthcoming papers.
If all information is collected and e!ectively used, a company is able to reach MIR level 4. It is then a learning organisation where continuous improve-ment is a matter of course. For MIR level 1, how-ever, it su$ces to have useful metrics that describe the product quality performance in production and in the"eld. This is the subject of the next section.
4. Metrics
In this section we will"rst (in Section 4.1) analyse the type of information that is needed for MIR level 1. In Section 4.2 we will discuss some metrics that are presently used in industry. Finally, in Section 4.3, we will come up with operational de"nitions of two metrics that are based on Section 4.1 and that in our opinion are very informative.
4.1. Quality information for MIR level 1
On MIR level 1 there is a basic feedback system that gives quantitative information indicating the number of problems during production and the number of"eld failures. In order to be informative, these numbers must be seen in proportion to the number of products actually produced, respective-ly, in use. The metrics must do more than just describe the situation, they must also be able to detect changes over time. In production it is rela-tively easy to collect the indispensable information. It is much harder to get useful quantitative in-formation about "eld failures.
Before we go into the problem of collecting quantitative information about failures, in Section 4.1.1 we "rst summarise two important reliability concepts. In the Sections 4.1.2 and 4.1.3 we concen-trate on information about problems in production and in the "eld, respectively. Finally, in Section
4.1.4 we give a list of criteria that give insight in the costs of (non-)quality. For MIR level 1 companies must translate the quantitative information about fall-o!in production and about "eld failures into costs.
4.1.1. Reliability concepts
As high-volume consumer products are seldom repaired more than once, we will only mention two reliability concepts that are based on the time to ("rst) failure. This means that we do not discuss reliability models for repairable systems.
4.1.1.1. Reliability. Product reliability is, for
example according to [7] de"ned as the probability
R(t) that a product starting at time zero will survive a given timet:
R(t)"P(¹*t)"
P
= tf(q) dq,
where¹is a suitable continuous random variable representing time to failure with failure probability density functionf(t).
In applications the probability density function
f(t) is usually not known. If an estimate of f(t) is available, then this estimate gives an estimate of
R(t). If there is no estimate off(t) available and if all products are taken into use at the same time, say
t"0, then one of the common non-parametric
estimators ofR(t) can be used (cf. [7]). In this paper we will use
RI(t)" N(t)
N#1,
whereN(t) is the number of unfailed products on the market at timet, andN,N(0).
In the more realistic situation that &identical'
products are taken into use at di!erent time points during a period of, say, half a year, the estimation procedure is more complex; we come back to this in Section 4.3.
4.1.1.2. Hazard function. If a product is still
the conditional probability to survive ¹#tgiven that the product already survived¹. The concept of hazard function (also called hazard rate, failure rate or force of mortality, see [8]), covers this idea. The hazard function j(t) represents the instantaneous failure probability and is de"ned in the following way:
j(t),f(t) R(t)"!
1
R(t)
dR(t) dt .
If all products are taken into use at the same time
t"0, the hazard function can be estimated viajI(t) in the following way. First we notice that the de" ni-tion of the hazard funcni-tion shows that
j(t)" 1
R(t)lim
t?0
R(t)!R(t#*t)
*t .
Next we divide the relevant interval (0,¹) in
ksubintervals with length *q, such that¹"k*q. Now letq
i"i*q, then on the interval (qi,qi#*q)
the hazard functionj(t) can be estimated by
jI(qi,qi#*t),RI(qi)!RI (qi#*q) *qRI(q
i)
or, withM(t) being number of failures on the inter-val (0,t),N(t) the number of products on the market at timet; this leads to
jI(qi,qi#*t)"M(qi#*t)!M(qi) *qN(q
i)
.
The de"nition of the time tneeds some attention. As f(t) is the probability density function of the failure time,tis the timesince the beginning of the
failure behaviour. For consumer products the
inter-pretation: t"time since sales, seems reasonable, even though sometimes the product will not be bought by the end user.
If all products are sold at time zero, then M(t) denotes the number of failures at timetin the class of all products (all sold at time zero). If the products are sold at di!erent times, as is normally the case, then the estimation of the hazard function is more complicated. We come back to this in Section 4.3. For a more thorough discussion of estimators of the hazard function we refer to [9,10].
4.1.2. Information about production problems
In production all kinds of product-related prob-lems can occur. Concentrating on quality and relia-bility it is important to collect data that demonstrates whether particular production pro-cesses need improvement. Therefore, it is important to record the following characteristics as a function of time (per process step and on component, mod-ule and product level):
f the fraction of scrap, f the fraction of rework, f the productivity.
If the performance on these characteristics is a!ected by particular circumstances, these circum-stances must be recorded as well. Common relevant circumstances are the following:
f the time of production, f characteristics of the batch, f the production speed, f the operator and/or shift.
As it is in principle simple to collect all this information and it is also quite clear how this information must be analysed, in the rest of this section we concentrate on metrics that are based on
"eld information.
4.1.3. Information aboutxeld problems
Relevant quantitative information about the
"eld behaviour of products/subsystems/modules/ components is given by the following character-istics (see also [11]):
f the fraction of customer complaints within the
warranty period, or, more general,
f the fraction of customer complaints within a
par-ticular time-interval,
f the fraction of zero-hour failures
(dead-on-arri-val)
f the hazard function,
f the segmentation of customer complaints over
the categories: design problem, production prob-lem, component probprob-lem, product level probprob-lem, customer use, no fault found.
Just as in the case of production problems, also the
characteristics. The most important ones are the following:
f the time of production,
f the date the product is put into use,
f the quantity of use (amount of time, number of
cycles, etc.),
f the way of use (whether or not according to the
user speci"cations),
f the environment in which the product has been
used (for example warm and humid or cold and dry).
The main di!erence between the information about problems in production and problems in the"eld is the in#uence of the factor time. The fall-o!in pro-duction concerns instantaneous failures and in principle the performance of production is well known at any moment. A quantitative analysis of the number of"eld failures is much more complic-ated, because at timetonly the number of failures that occurred before timetis known. This does not a!ect the estimation of, for example, the fraction of zero-hour failures, but it does a!ect, the estimation of the reliability and the hazard function (see Sec-tion 4.3).
The estimation of some characteristics is also complicated by the fact that it is far from easy, even during the warranty period, to determine the total number of sold products, the total number of prod-ucts still in use, and the total number of customer complaints.
4.1.4. Costs of(non-)quality
Information about the performance on quality is not complete without a full view on the costs that are related with making quality, or, better, making non-quality. Some metrics for these costs are:
f costs of the design process itself, f costs of design changes,
f costs of process changes, f warranty costs,
f costs of service activities, f product liability costs,
f image costs and costs of losing customers, f extra costs for the customer.
In this paper we will not go into this in more detail, we will concentrate on reliability metrics.
4.2. Current metrics
Some of the metrics that are presently used in industry will be presented below and their advant-ages and disadvantadvant-ages will be explained. In Sec-tion 4.2.1 the classical "eld call rate will be presented and in Section 4.2.2 the warranty call rate. We will only discuss"eld data, because col-lecting and analysing data about fall-o!in produc-tion is not a serious problem.
A service centre is, of course, the primary source for quantitative information about"eld problems. This does not mean that it is easy to get quantitat-ive information about the "eld performance on product level. For example, it is hardly possible to collect quantitative information about "eld prob-lems expressed as the percentage of products that fail within a one-year warranty period. The reason is, of course, that service centres normally see, even within the warranty period, only part of all prod-ucts that fail.
4.2.1. Classicalxeld call rate
The classical"eld call rate is used to monitor the number of"eld failures of a given product and was developed for logistic purposes. As the hazard func-tion depends on the age of the product it has, in those cases where not all products are sold simulta-neously, little to do with the number of repairs that are expected in a certain time interval.
The de"nition of the classical "eld call rate FCR
#-!44*#!- is very close to the de"nition of the
natural estimatorjI(q,q#*q) of the hazard func-tion (see Secfunc-tion 4.1.1). On the interval (q
i,qi#*q) the number of products on the market at timet.
The di!erence is in the meaning of the timet. In
jI(q,q#*t) timetis measured from the moment the failure behaviour starts. For consumer products this will usually be close to the time since sales. In the estimator of FCR
#-!44*#!-, however,tis the time
since market introductionof the product. It is
account the age of a product at the moment of failure, it just uses the total number of failures. Furthermore, it is important to realise that not all products are sold at timet"0 and this reduces the value of the estimator of the classical"eld call rate, just as it in#uences the meaning of the estimator of the hazard function.
Another disadvantage of the classical "eld call rate is the fact that in the early phases of the life of a product and in the last phases, the number of products actually in use on the market, N(t), has a high level of uncertainty.
The FCR is used to monitor the number of"eld failures of a given product and was developed for logistic purposes, like the estimation of the number of spare parts that will be necessary at a given moment in time and at a given location. As the hazard function usually is a function of the age of the product, the FCR has, in those cases where not all products are sold simultaneously, little to do with the number of repairs that are expected in a certain time interval.
4.2.2. Warrantee call rate
A di!erent method uses the so-called warrantee package method. The warrantee package method is used especially for "nancial purposes. The de" ni-tion of the warrantee call rate WCR
8!33!/5%%
cal-culated according to the warrantee package method is very close to the de"nition of FCR
#-!44*#!-.
products within warrantee on the market at timet. As the name of the model indicates, the main focus in this model is on warrantee aspects of prod-ucts: what fraction of the products fails during the warrantee period. Therefore, although the formula is mathematically close to the formula for the clas-sical"eld call rate, this metric uses a kind of moving time-window and therefore will lead to concep-tually di!erent results. And, again, the expression does not take into account the age of a product at the moment of failure.
From the foregoing it will be clear that the"eld call rate and the warrantee call rate are not very informative. Furthermore, as products are normal-ly taken into use at di!erent time points, a more sophisticated estimator of the hazard function is necessary than the one given in Section 4.1.1. This is the subject of Section 4.3.
4.3. New metrics
In Section 4.3.1 we present an estimator of the reliability and in Section 4.3.2 an estimator of the hazard function. Both estimators make full use of all available data.
4.3.1. Reliability
After market introduction the number of products on the market increases (for some time) and with it the number of defects. If the hazard function is esti-mated at timet, the data are censored on the right, i.e. some products have not yet failed, and their failure times are known only to be beyond their present running time. This type of data is known in the literature as type I multiply censored data. Instead of the estimatorjI(q,q#*t) given in Section 4.1.1, it is much better to use the product-limit estimator of the reliability function, as developed by Kaplan}Meier [12]. The product-limit estimator is usually given for the situation that all&products'start at the same time
t"0 and that the censoring at the right is not the
same for all products. In our situation the products are put into use at di!erent moments and all products are censored at the same moment. Of course, it is possible to transform the failure time data by shifting all starting points to q"0. However, in order to come up with expressions that are relatively easy to use in industry, we prefer not to do this, but to use the data as they are. This leads to the following derivation of the reliability.
We divide the time axes in intervals of, say, one month. Letqi denote the endpoint of theith inter-val I
i with q0"0 (see Fig. 3). To keep things
simple, we act as if sales only take place at the time pointsq0,q1,q22. Furthermore, we suppose that
all products are functioning at the time of sales, but they can fail a split second afterwards.
De"nen
jias the number of products functioning
at q
Fig. 3. Time axis with intervals.
hKj(iunits)"total number of products that failed immediately after survivingitime units
total number of products that surviveditime units
"d0,i`1#d1,i`2#2#dj~i~1,j n
0,i#n1,i`1#2#nj~i~1,j~1
withi)j!1.
p
ji,1!
total number of products sold at or beforeqj~1that failed in the first month after sales total number of products sold at or beforeqj~1
"1! d01#d12#2#dj~1,j n
00#n11#2#nj~1,j~1
. products failing in intervalI
i of all products sold at
q
j,This implies that a product that is sold at¹the age of a product at the time of failing.q j
sur-vivesitime units if for that product holds:¹*q j`i.
The Kaplan}Meier estimator of the reliability of a product to surviveitime units, sayR(iunits), is given by
R(iunits)"P(¹*iunitsD¹*i!1 units)P(¹*i !1 unitsD¹*i!2 units)) ) )P(¹*2 unitsD¹*1
unit)P(¹*1 units).
For a product that is sold at timeqjthe probabil-ityP(¹*1 units) can be estimated by
PKj(¹*1 unit)"PKj(¹*q j`1)
"1!dj,j`1 n
j,j
andP(¹*iunitsD¹*i!1 units), withi*2, can be estimated by
PKj(¹*iunitsD¹*i!1 units)
"PKj(¹*q
j`1D¹*qj`i~1)
"1! dj,j`1 n
j,j`i~1
.
Atqj we estimate P(¹*i!1 unit) by combining all data for products sold at q0,q1,2,qj~1. This
gives the following estimatorp
j1 ofP(¹*1 unit):
Analogously, at qj we estimate P(¹*iunitsD¹* i!1 units), withj*i*2, by
p
ji,1!
+j~1
k/0dk,1`k
+j~1
k/0nk,i`k~1
.
Therefore, at timeq
j the following estimator of the
reliability is available:
RKj(iunits)"<j i/1
p
ji withi)j.
4.3.2. Hazard function
Leth(iunits) be the hazard function of a product at i time units after it has been sold. From the analysis in the foregoing section it follows that this hazard function at time qj can be estimated by combining all available information. That means that at timeqjthe instantaneous failure probability after survivingitime units,j(iunits) is estimated by
If this estimator is plotted as a function ofi, it is possible to compare the graph with the roller-coaster curve. In this way additional information about the failure mechanisms can be collected (see [27]). In a next paper we will give a practical example of this estimator in high-volume consumer products. Of course, in this way it is also possible to predict the fraction of failures under warranty that can be expected, and this estimate is far superior to the warrantee call rate.
5. Conclusion
f In mass production the "rst contact between
a customer and the manufacturer is in a service centre, therefore service centres are most suitable for collecting information about the behaviour of products in real operating conditions.
f Service centres are focused on logistic and not on
their contribution to quality improvement. As a consequence valuable information is not col-lected.
f Service centres only communicate with the other
departments, like production and development, about serviceability.
f In industry some metrics, like the classical"eld
call rate and the warrantee call rate, are used that hardly give any sensible information. In particu-lar these metrics do not give any information about the quality of the products and processes.
f There are simple metrics based on the
Ka-plan}Meier estimator of the reliability and the hazard function that give information that is useful for logistics purposes as well as for quality improvement.
It will be clear that service centres have to be prepared for their new assignment. This holds even stronger when the contribution from service centres to the MIR levels 2, 3 and 4 is analysed, because then a thorough knowledge of design and produc-tion is indispensable. But this is the subject of ongoing research.
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![Fig. 2. Observed categories of reliability problems [6].](https://thumb-ap.123doks.com/thumbv2/123dok/3115970.1378526/3.544.285.465.49.158/fig-observed-categories-of-reliability-problems.webp)
