Reliability assessment of a discrete time cold standby repairable system
- PDF / 1,261,575 Bytes
- 16 Pages / 439.37 x 666.142 pts Page_size
- 79 Downloads / 226 Views
Reliability assessment of a discrete time cold standby repairable system Cihangir Kan1 · Serkan Eryilmaz2 Received: 2 May 2020 / Accepted: 26 October 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract This paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system’s lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system’s lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system’s lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated. Keywords Hazard rate · Phase-type distribution · Reliability · Repairable system Mathematics Subject Classification Primary: 62N05 · Secondary: 62E15
1 Introduction In reliability theory, most of the assessments are based on modeling of a system’s lifetime as a continuous random variable. Comparatively, much less attention has been given to discrete lifetime modeling. However, there is a need for discrete lifetime modeling if a unit or system operates in cycles. In this case, the lifetime of the system is defined as the number of cycles until failure. For example, the lifetimes of car tires are measured in terms of the number of kilometers or the number of days; the lifetime of the switch is measured by the number of on/off.
* Serkan Eryilmaz [email protected] 1
Xi’an Jiaotong-Liverpool University, Suzhou, China
2
Department of Industrial Engineering, Atilim University, Ankara, Turkey
13
Vol.:(0123456789)
C. Kan, S. Eryilmaz
Discrete time reliability modeling has been considered in various problem setups in the literature. Nakagawa and Osaki (1977) studied discrete time age replacement policies. Gupta et al. (1997) investigated monotonicity of hazard rate of discrete lifetime distributions. Castro and Alfa (2004) defined a replacement policy in discrete time for a single unit system. Gómez-Déniz (2010) studied a generalization of the geometric distribution which can be used as a discrete lifetime model. Various discrete distributions have been proposed by discretizing continuous random variables (see, e.g. Jazi et al. (2010), Bebbington et al. (2012)). Davies and Dembinska (2019) obtained results on the number of failed components in a k-out-of-n system upon system failure when the lifetimes of the components are discretely distributed. Hu and Peng (2019) studied a discrete time multi-state system with random and dependent transition probabilities. Dembinska and Goroncy (2020) presented methods of obtaining single moments of order statistics arising from possibly dependent and non-identically distributed discrete random
Data Loading...
