Computers and Industrial Engineering Vol. 25, Nos 1--4, pp. 469--472, 1993 0360-8352/9356.00+0.00 Printed in Great Britain. All fights reserved Copyright © 1993 Pergamon Press Ltd

PERFORILqNCE - RELIABILITY - MODELS and QUALITY MANAGEHENT

Klaue Fischer

T e c h n i c a l U n i v e r s i t y o f D r e s d e n , F a c u l t y T r a n s p o r t S c i e n c e D - 0 - 8 0 2 7 D r e s d e n , M o m m s e n s t r . 13, G e r m a n y

1. I n t r o d u c t i o n

Quality is an absolute necessity and guarantees success on a competitive market. Therefore it is easy to understand that the importance of product quality and especially, recently, service quality are permanently increasing. In other words SERVICE QUALITY is great a CHALLENGE of today and the biggest CHANCE for the service companies in the future. The European norm EN 29000 ... 29004 sets standards and gives guidelines for quality management systems (QMS) in service sector (see figure I). The customer is in the centre of interest, hence it follows that all efforts must really be concentrated on customers and their satisfaction - this should not only be a slogan but an absolute necessity!

2. Customer-oriented quality strategy

Quality of service is the number one for deciding whether to buy or not to buy. Therefore the service company needs a customer-oriented strategy for service quality.The development and improvement of service quality are urgent need of support (see figure I and 2) with respect to

1. Knowledge concerning the customers (expectations, reactions of the customers) 2. Scientific tools (for the decision-makers and the "service designers")

Service quality must strongly be developed because, as a rule, the customer itself is involved in the service process and so he experiences the beginning, the design and the realization of this process directly. At the same time this is the reason why quality control of services is nearly always too late as far as the customer's satisfaction is concerned. At this tlme the customer did already experience an excellent or poor quality. Rectification are scarcely possible. Therefore it is not sufficient to compute the number of customers served but we need the knowledge with respect to the number of well served (satisfied) as well as poorly served or even rejected (dissatisfied) customers. That literally means SERVICE QUALITY needs a powerful and effective support by OPERATIONS RESEARCH and SYSTEM ENGINEERING. This paper intends to make a contribution to this aim.

S. Mathematical models 3.1. General remarks

P r o d u c t i o n a s w e l l a s s e r v i c e s y s t e m s a r e i n m o s t c a s e s l a r g e / c o m p l i c a t e d s y s t e m s . The c o n s i d e r a t i o n a n d e v a l u a t i o n o f t h e e f f e c t i v e n e s s o f a l a r g e s y s t e m i s n o t p o s s i b l e w i t h t h e w e l l - k n o w n t w o - s t a t e m o d e l s b e c a u s e t h e e f f e c t i v e n e s s o r p e r f o r m a b i l i t y e v a l u a t i o n s m u s t c o n s i d e r t h e v a r i a b i l i t y o f m a i n p e r f o r m a n c e c a p a b i l i t y p a r a m e t e r b e t w e e n i t s maximum v a l u e ( s y s t e m f u l l y e f f e c t i v e ) a n d i t s m in im u m v a l u e ( s y s t e m t o t a l l y n o n - e f f e c t i v e ) . I n t h i s c a s e we n e e d m u l t i - s t a t e models for the system modelling. Statements made for instance on system effectiveness and system reliability standing separately side by side are not helpful and can scarcely contribute to understanding and application of scientific tools in the field of management systems. To overcome these unsatisfactory drawbacks we have felt the necessity to develop mathematical models which permit the calculation of RELIABILITY-RELATED SYSTEM PERFORMANCE CAPABILITY MEASURES. And so the development of PERFORMANCE- RELIABILITY-MODELS (PRM) was a first step to support the progress of QMS by scientific tools. We started out from different foundations and had different a i m s . The maximum system effectiveness y,,, depends on the functionality of the system elements and the system structure El~d a large system can take different states with different levels of system performance capability Yi' where 0 i Yi i Ytu"

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470 Proceedings of the 15th Annual Conference on Computers and Industrial Engineering

3.2. Performance-rellability models

The performance-reliability/dependability-models are mostly a combination of queueing and dependability models. That means one and the same mathematical model includes performance capability as well as dependability parameters. The common aim of the mathematical models consists in computing a reliability- related system effectiveness. On this occasion we have to make clear if we want a calculation which is independent of the system load (then we receive e.g. as a result EY - achievable system effectiveness) or which does depend on system load (then we ~eceive e.g. as result EY r - real system effectiveness). As shown later on the exclusive use of expectation values EY. and EY is not sufficient if the QMS is to operate effectively. It is necessar9 to co~pute also the distribution functions of the important quality characteristics. The result of such a calculation can be seen in figure 3. We distinguish the following types of Performance-Reliability-Models: 1. Markovian-dependability model extended by performance capability charac-

teristics for computing of system performance capability measures independent of system load. Figure 5 shows an example with some simplifications.

2. Boolean-dependability model extended by performance capability characteristics for computing of mainly networks with complicated structures and measures independent of system load.

3. Queueing-models extended by dependability characteristics for computing of system performance capability measures depending on system load.

In all cases we have to take into account the different conditions which are strongly connected with the different typs of models.

4. Aims and Results 4.1. Aims

If service companies want to develop and design their quality they have to look for methods to compute the quality criteria which can be achieved by the company and offered to the customers. And now if the result of the calculation shows that the degree of customer satisfaction will not be high enough they can change/improve the system design (see also figure 2). The PRM can help us to realize a first step in this direction. Therefore in the following some results achieved are briefly described but always with respect to the support given to decision-makers. That means, firstly, we should have a look at some of the most interesting quality characteristics with respect to their dependence on system design and their influence on customer satisfaction.The following quality characteristics are selected for this reason because they play a particular role over and over again. • Quality criterion TIME which appears in manifold shapes (e.g. waiting time,

delay time, delivery time, repair time). • Quality criterion "IN-TIME DELIVERY" of orders taken. The fulfilment of orders

taken can be impossible if the performance capability level of the system is by chance reduced as a result of failures within the system.

• Quality criterion "QUALITY of the EMPLOYEES" of the service system (e.g. behaviour, ability, educational and training level, competence).

4.2. Results

Firstly let us have a look at the quality criterion "waiting time". The customer's waiting time for a service rendered by the service company can easily be computed if we know the arrival rate (of customers) and the service rate (of employees by taking into account the number of service channels)• As a result we obtain for example approximately one time unit if the system load is given with p = 0.7. We know of course that it is rather clear that customer satisfaction decreases with increasing of waiting times and vice versa. That means we can use the expectation value of the waiting time as a measure for customer satisfaction if we only want to compare it with the competitors or if we want to recognize the tendency within the own company. But we know that the waiting time increases if a failure occurs (e.g. system elements out of order, employees absent). That means we should deal with the waiting time problems more intensively. Therefore let us have a look at figure S which shows the distribution function of the waiting times in the case of p - 0.7. There we must recognize that a Io% of customers actually has an essentially longer waiting time than the expectation value of the waiting time. Besides we know that there is a coherence between waiting time and dissatisfaction of customers which is not a linear. Figure 6 shows the "calculated" customer dissatisfaction depending on the "different types of" waiting times• One can recognize that the dissatisfaction of the customers actually is a higher one than the dissatisfaction computed by applying the expectation value of the waiting time. Hence it follows that the service company should mainly try to reduce the longer waiting time in order to improve the customer satisfaction. That is only possible if the company is able to develop a high degree of flexibility• In other words - if the company is actually willing to replace rigid methods by flexible ones. Such a solution is not only a dream. In the supermarkets of Hoogvliet the

FISCHER: Performance-Reliability Models 471

f o l l o w i n g r u l e s a r e a p p l i e d : e a c h c u s t o m e r who i s t h e t h i r d i n t h e q u e u e i n f r o n t o f t h e c a s h c a n l e a v e t h e s u p e r m a r k e t w i t h o u t p a y m e n t . And w h a t i s i m p o r t a n t t o remark is the fact that the profit of the supermarkets have increased about 5...10~. Hoogvlie% has developed a strategy of high flexibility which allows an increase of their service quality and above all of the customer satisfaction. And so "service quality is making profit" becomes true.

Let us have a look at a second example. The highest level of customer satisfaction can be achieved if all orders taken can be fulfilled by the company in time and good quality. At first sight this seems an easy task if the company takes orders/demands which can be fulfilled with the existing capacity. Where are the difficulties? It can happen that some of the system elements fail, that means the performance capability level Yi decreases. In other words the value of Yi depends on the dependability characteristics of the system elements and the system structure which can be calculated by using the model shown in figure 5. However, we have seen in connection with the waiting time, that there are essential differences whether we use an expectation value or the momentary value of y.. The value of Yi can change between 0 i Yl i y... and the probability of y, mustlhe described and computed by the distribution f~Lction of ~. Hence it follows that the service company can reallze the order~ taken only with a certain probability. A high probability of fulfilment of the demands leads to a high customer satisfaction. Unfortunately this probability increases by a reduction of the orders taken and for the demands met. That means that the level of capacity utilization is lower than the achievable system effectiveness calculated but that means losses for the company. Now the service company has to decide what is more expensive • a lower use to capacity or • a lost customer In other words the loss of a customer must be quantified and must then be compared with the loss caused by unused capacities. Some results are shown in figure 4. From these results the following strategies can be derived: • the capacity utilizazation concerning the orders taken should be maximum if the

rejected/dissatisfled customer is of no importance to the service company (see figure 4, curve with 0~).

• the capacity utilization concerning the orders taken should be reduced as a function of the importance/loss of profit due to lost/dissatisfied customers (see figure 4j curves with 50...400~).

But the customer satisfaction must be estlmated/determined in advance in order to avoid undesirable developments. The described PRM can make a contribution to the determination of the (probable) customer satisfaction. Based on this result the management can develop strategies and make decisions in order to improve the customer satisfaction and above all to increase the profit of the company. Progress needs a greater variety of information which is going in more detail. Please compare the results by applying the expectation values and the distribution function of the quality characteristics. The only way to success is a high degree of flexibility of the companies. This is important finding and it means to replace rigid strategies (which are so convenient to apply) by flexible ones. That is a great challenge to the company and the employees, too.

5. Summary

QMS are a necessity for success of service companies today and in the future. Customer satisfaction is the magic formula because the customer and only the customer decides to buy or not to buy. The great problem consists in getting sufficient and meaningful information about the customers' evaluation of services and behaviour and the influence on customers by quality. Mathematical models - for example the PRM - can help to investigate the influence of the strategy of the company with regard to customers. The results computed can be used to compare the probable customer satisfaction of yesterday and today to see the tendency of change and to compare it with other competitors. An essential statement was that we have to compute RELIABILITY/QUALITY-RELATED SYSTEM PERFORMANCE CAPABILITY MEASURES by applying of expectation values and above all distribution functions of the quality characteristics. That's why each of the customers has its own individual expectations and as a rule we don't meet the "avarage customer". OPERATIONS RESEARCH and SYSTEM ENGINEERING are required to develop (simple) models which can be used to support QMS as well as TQM by finding out the right lines for the development. The aim of this paper was to point out management possibilities by showing a few results which can be achieved by mathematical models. It was not the aim to derive and explain the relevant mathematical equations.

472 Proceedings of the 15th Annual Conference on Computers and Industrial Engineering

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