Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
-
M. Drisya
und
Joby K. Jose
Abstract
The estimation of stress-strength reliability in a time-dependent context deals with either the stress or strength or both dynamic. The repeated occurrence of stress in random intervals of time induces a change in the distribution of strength over time. In this paper, we study the stress-strength reliability of a system whose strength reduces by a constant over each run and the stress is considered as either fixed over time or as increasing by a constant over each run. The number of runs in any interval of time is assumed to be random. The stress-strength reliability of the system is obtained, assuming continuous phase-type distribution for the duration of time taken for completion of each run in any interval of time and Weibull or gamma distribution for initial stress and strength. We obtain matrix-based expressions for the stress-strength reliability and numerical illustrations are also discussed.
References
[1] S. Asmussen, O. Nerman and M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Statist. 23 (1996), no. 4, 419–441. Suche in Google Scholar
[2] M. Bladt, L. J. R. Esparza and B. F. Nielsen, Fisher information and statistical inference for phase-type distributions, J. Appl. Probab. 48A (2011), 277–293. 10.1239/jap/1318940471Suche in Google Scholar
[3] S. Eryilmaz, On stress-strength reliability with a time dependent strength, J. Qual. Reliab. Eng. 2013 (2013), Article ID 417818. 10.1155/2013/417818Suche in Google Scholar
[4] M. N. Gopalan and P. Venkateswarlu, Reliability analysis of time-dependent cascade system with deterministic cycle times, Microelectr. Reliab. 22 (1982), 841–872. 10.1016/S0026-2714(82)80198-4Suche in Google Scholar
[5] M. N. Gopalan and P. Venkateswarlu, Reliability analysis of time-dependent cascade system with random cycle times, Microelectr. Reliab. 23 (1983), no. 2, 355–366. 10.1016/0026-2714(83)90346-3Suche in Google Scholar
[6] J. K. Jose and M. Drisya, Time-dependent stress-strength reliability models based on phase type distribution, Comput. Statist. 35 (2020), no. 3, 1345–1371. 10.1007/s00180-020-00991-3Suche in Google Scholar
[7] M. F. Neuts, Renewal processes of phase type, Naval Res. Logist. Quart. 25 (1978), no. 3, 445–454. 10.1002/nav.3800250307Suche in Google Scholar
[8] K. C. Siju and M. Kumar, Reliability analysis of time dependent stress-strength model with random cycle times, Perspect. Sci. 8 (2016), 654–657. 10.1016/j.pisc.2016.06.049Suche in Google Scholar
[9] K. C. Siju and M. Kumar, Reliability computation of a dynamic stress-strength model with random cycle times, Int. J. Pure Appl. Math. 117 (2017), 309–316. Suche in Google Scholar
[10] R. P. S. Yadav, A reliability model for stress strength problem, Microelectr. Reliab. 12 (1973), no. 2, 119–123. 10.1016/0026-2714(73)90456-3Suche in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
Artikel in diesem Heft
- Frontmatter
- A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics
- Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method
- The Reflected-Shifted-Truncated Lindley Distribution with Applications
- The Marshall–Olkin Transmuted-G Family of Distributions
- Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times
