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IntroductionOnly by maintaining high reliability of the computer integrated manufacturing system (CIMS), can the production line be operated steadily for a long time. One of the problems in CIMS is real-time constraints which must be satisfied. The inability of the system to meet real-time constraints is caused by failures and repairs of the system during the production process. The important measure characterizing the quality of the system under real-time conditions is processing time, which consists of operating time (required processing time under ideal conditions without failures) and downtimes during repairs. Under repair we understand all fault-compensation actions after which the system is as good as new. We will consider a manufacturing system with the human operator [1]. The human operator monitors the system to check whether everything is going as planned [2]. If a failure of the system occurs, the human operator interrupts the manufacturing process and determines what should be done to deal with the situation. In order to repair the system, the human operator needs a certain amount of time to analyse system damage.The considered system is extremely simple and has been studied in the probability context under the condition that all system characteristics, such as time to failure and time for repair, are random. However, most of the models considered have been governed by exponential distributions. This restricts their actual application. Moreover, an analysis of the probability behaviour of a system makes sense in practice if three conditions have to be satisfied[3]: an event is defined precisely; a large number of statistical samples are available; and probabilistic repetitiveness is embedded in the collected samples. This implies that the probabilistic assumption may be unreasonable in a wide variety of cases (software reliability [4], and behaviour of the human-machine systems [5]). In these cases, use of the possibility measure has been proposed in place of the probability measure [3,5].