Reliability assessment of a discrete time cold standby repairable system

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.

[1]  Toshio Nakagawa,et al.  Discrete Time Age Replacement Policies , 1977 .

[2]  Rui Peng,et al.  Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities , 2019 .

[3]  Inmaculada Torres Castro,et al.  Lifetime replacement policy in discrete time for a single unit system , 2004, Reliab. Eng. Syst. Saf..

[4]  Ram C. Tripathi,et al.  On the monotonic properties of discrete failure rates , 1997 .

[5]  Chin-Diew Lai,et al.  The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data , 2012, Reliab. Eng. Syst. Saf..

[6]  S. Eryilmaz.  Discrete time cold standby repairable system: Combinatorial analysis , 2016 .

[7]  J. Navarro.  Stochastic comparisons of generalized mixtures and coherent systems , 2016 .

[8]  Chin-Diew Lai,et al.  A discrete inverse Weibull distribution and estimation of its parameters , 2010 .

[9]  C. O'Cinneide.  Characterization of phase-type distributions , 1990 .

[10]  Ammar M. Sarhan,et al.  Parameter estimations of 1-out-of-2: G repairable system , 2003, Appl. Math. Comput..

[11]  A. Dharmadhikari,et al.  Estimation of parameters of 1-out-of-2:g repairable system , 1983 .

[12]  Avinash Dharmadhikari,et al.  Nonparametric methods for 1-out-of-2: G repairable systems , 1996 .

[13]  D. Sherwin.  On the Availability of 1-out-of-2 Standby Systems , 1984, IEEE Transactions on Reliability.

[14]  Attahiru Sule Alfa,et al.  Discrete time queues and matrix-analytic methods , 2002 .

[15]  Juan Eloy Ruiz-Castro,et al.  Modelling a reliability system governed by discrete phase-type distributions , 2008, Reliab. Eng. Syst. Saf..

[16]  Anna Dembi'nska,et al.  Moments of order statistics from DNID discrete random variables with application in reliability , 2019, J. Comput. Appl. Math..

[17]  Lirong Cui,et al.  Extended Phase-type models for multistate competing risk systems , 2019, Reliab. Eng. Syst. Saf..

[18]  Joby K. Jose,et al.  Estimation of stress-strength reliability using discrete phase type distribution , 2020, Communications in Statistics - Theory and Methods.

[19]  A. Dharmadhikari,et al.  Maximization of availability of 1-out-of-2:G repairable dependent system , 1989, Advances in Applied Probability.

[20]  Karl-Theodor Eisele,et al.  Recursions for Compound Phase Distributions , 2005 .

[21]  Yinghui Tang,et al.  Optimal replacement policy based on maximum repair time for a random shock and wear model , 2017 .

[22]  Qi-Ming He,et al.  Fundamentals of Matrix-Analytic Methods , 2013, Springer New York.

[23]  Serkan Eryilmaz.  Statistical inference for a class of startup demonstration tests , 2019 .

[24]  Anna Dembinska,et al.  On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed , 2019, Reliab. Eng. Syst. Saf..

[25]  Robert S. Maier.  The Algebraic Construction of Phase-Type Distributions , 1991 .

[26]  E. Gómez-Déniz,et al.  Another generalization of the geometric distribution , 2010 .