University of Calicut

17 November 2018

Evaluation of System Performance Measures of Multi State Degraded System with Minimal Repair

In binary reliability models the system or its components is assumed to be either in a perfectly functioning state or in a completely failed state. But in most of the real life situations this assumption may not be adequate. There are intermediate states between perfectly functioning state and completely failed state. So we make use of the Multi State system (MSS) reliability model in which the system may rather have more than two states of performance between working perfectly and total failure. The basic concept and further developments of binary system reliability theory were dealt in [2 , 3]. The basic concepts of MSS, tools for MSS reliability assessment and optimization and application problems were discussed in [8]. Multi state with degrading components and concerned with the application of reliability functions to the reliability evaluation of large systems emphasis in [4]. A comprehensive introduction to system reliability theory along with failure models, qualitative system analysis and reliability importance were discussed in [10]. The joint importance measures for multi state reliability systems have been discussed in [13] and[14]. According to [1] Repairable system is a system which after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by a method other than replacement of the entire system. The UGF was first introduced by Ushakov [11] for MSS. The mathematical basics of this technique were available in [12]. An updated version of the UGF with many application was presented in [5, 8]. The combined method using random process and UGF was suggested in [8] and further extended in [6 , 7]. In [9], a new approach was used to evaluate the dynamic reliability of MSS with redundancy.


In this article description of models with assumptions has been presented in section 2. In section 3 the combined stochastic process and UGF technique approach is applied for multi state degraded system for avoiding dimension damnation problem of the stochastic process approach. A new approach of decomposing a system in to two or more sub systems (each sub system consists of the same type of components) has been proposed. Steady state probabilities and system performance characteristics are calculated for subsystems using the random process method and at last reliability indices of the entire system in steady state situation are evaluated using UGF technique. A more realistic system has been taken to validate the applicability of this approach.A power station with two sub systems (each sub system with three generators ) has been illustrated in section 4 of this article. Reliability indices of this power station are evaluated in this paper.

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