Reliability Measures Analysis of an Industrial System under Standby Modes and Catastrophic Failure

Reliability Measures Analysis of an Industrial System under Standby Modes and Catastrophic Failure

Mangey Ram (Department of Mathematics, Graphic Era (Deemed to be University), India) and Monika Manglik (Department of Mathematics, Graphic Era University, Dehradun, India)
DOI: 10.4018/IJORIS.2016070103
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The objective of this research paper is, to present the reliability measures of a model by representing an industrial system having three subsystems. Two of the subsystems have standby unit while the third one has n units in parallel configuration. The entire system can fail due to a failure in subsystems or due to the catastrophic failure. The system failure and the repair rates are assumed to be constant. Markov and supplementary variable methodologies have been used to achieve the mathematical analysis of this model. Generalized expressions of state probabilities, system availability, reliability, mean time to failure, mean time to repair, cost analysis and sensitivity analysis are developed. Graphs for the resulting expressions have been shown.
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The theory and the methods of reliability analysis have been developed significantly during the last forty years and have also been acknowledged in a number of publications (Nakagawa and Osaki, 1975; Bobbio et al., 1980; Singh and Srinivasu, 1987; Gupta and Bansal, 1991; Vilkomir et al., 2006; Zhang and Li, 2010). It is well known that the reliability is the probability of a system which operates without interruption during an interval of interest under specified conditions. Reliability is also an essential measure and an important component of all engineering systems planning and of the operating procedures. Reliability for functional zones of various engineering systems is determined using either analytical probability technique or stochastic simulation methods (Verma et al., 2010; Ram, 2013; Sauma, 2013).

The reliability of a system can be increased by using a redundancy technique without changing the individual unit that forms a system. One of the commonly used forms of redundancy is a cold standby system, which often finds applications in various industrial or other types of setups. Liebowitz (1966) and Minc et al. (1968) while studying the redundant system have assumed that a unit, immediately after the failure, enters repair. Nakagawa and Osaki (1975) discussed a two-unit priority standby redundant system with repairable non-priority unit. Stochastic behaviour, the distribution of time to the system failure, the expected number of visits to the system failure during a finite interval, and the pointwise availability of the system has been obtained. The authors also derived the distribution of the busy period of a repairman and distribution of time for the system recovery. Trivedi (1982) contended that failure/repair behaviour of such systems is commonly modelled separately using techniques classified under reliability/ availability modelling. Gupta et al. (1983) and Pandey et al. (2008) have assumed that the repair times of the failed units are independently distributed. The traditional reliability models predict system performance under the assumptions that all service facilities provide failure free service. It must however be acknowledged that service facilities do experience failures and they can get repaired.

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