×

Stochastic outlook of two non-identical unit parallel system with priority in repair. (English) Zbl 1426.90092

Summary: The crux of the study is to investigate a two non-identical unit parallel system where priority is given to first unit. The system consists of two non-identical units arranged in parallel configuration. System failure occurs when both the units stop Working. Weibull failure and repair time distributions of each unit are taken. Several measures of system effectiveness, such as reliability, MTSF, steady state availability, expected profit etc., useful to system managers are obtained by using regenerative point technique. Further, recognizing the fact that the life testing experiments are very time consuming, the parameters representing the reliability characteristics of the system/unit are assumed to be random variables. Both informative and non-informative prior are used for the Bayesian analysis. Therefore, a simulation study is also conducted for analysing the considered system model both in classical and Bayesian setups.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
62F15 Bayesian inference
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chaturvedi, A.; Pati, M.; Tomer, S. K., Robust Bayesian analysis of Weibull failure model, Metron, 72, 1, 77-95 (2014) · Zbl 1308.62044
[2] Chopra, G.; Ram, M., Stochastic analysis of two non-identical unit parallel system incorporating waiting time, International Journal of Quality & Reliability Management, 34, 6 (2017) · doi:10.1108/IJQRM-06-2016-007
[3] Dey, S.; Alzaatreh, A.; Zhang, C.; Kumar, D., A new extension of generalized exponential distribution with application to Ozone data, Ozone: Science & Engineering, 39, 4, 273-285 (2017)
[4] Dhillon, B. S.; Anuda, O. C., Common cause failure analysis of a non- identical unit parallel system with arbitrarily distributed repair times, Microelectronics Reliability, 33, 1, 87-103 (1993) · doi:10.1016/0026-2714(93)90048-4
[5] Dhillon, B. S.; Anuda, O. C., Common cause failure analysis of a parallel system with warm standby, Microelectronics Reliability, 33, 9, 1321-1342 (1993) · doi:10.1016/0026-2714(93)90133-J
[6] El-Sherbeny, M. S., Stochastic behavior of a two-unit cold standby redundant system under poisson shocks, Arabian Journal of Science and Engineering., 42, 3043-3053 (2017) · Zbl 1390.90274 · doi:10.1007/s13369-017-2515-1
[7] Ghasemi, A.; Yacout, S.; Ouali, M. S., Evaluating the reliability function and the mean residual life for equipment with unobservable states, IEEE Transactions on Reliability, 59, 1, 45-54 (2010) · doi:10.1109/TR.2009.2034947
[8] Gupta, P. P.; Agarwal, S. C., A parallel redundant complex system with two types of failure under preemptive-repeat repair discipline, Microelectronics Reliability, 24, 3, 395-399 (1984) · doi:10.1016/0026-2714(84)90462-1
[9] Gupta, P. P.; Sharma, M. K., Reliability and MTTF evaluation of a two duplex unitstandby system with two types of repair, Microelectronics Reliability, 33, 3, 291-295 (1993) · doi:10.1016/0026-2714(93)90014-P
[10] Gupta, P. K.; Singh, A. K., Classical and Bayesian estimation of Weibull distribution in presence of outliers, Cogent Mathematics, 4, 1300975 (2017) · Zbl 1426.62083
[11] Kumar, P.; Bharti, A.; Gupta, A., Reliability analysis of a two non-identical unit system with repair and replacement having correlated failures and repairs, Journal of informatics & Mathematical Sciences, 4, 3, 339-350 (2012)
[12] Lieblein, J.; Zelen, M., Statistical investigation of the fatigue life of deep groove ball bearings, Journal of Research of the National Bureau of Standards, 57, 273-315 (1956) · doi:10.6028/jres.057.033
[13] Malik, S. C.; Bhardwaj, R. K.; Grewal, A. S., Probabilistic analysis of a system of two non-identical parallel units with priority to repair subject to inspection, Journal of Reliability and Statistical Studies, 3, 1, 1-11 (2010) · Zbl 1247.90135
[14] Mann, N., Results on statistical estimation and hypotheses testing with application to the Weibull and extreme value distribution (1968), Dayton, OH: Aerospace Research Laboratories Wright-Patterson Air Force Base, Dayton, OH
[15] Mishra, R. C., Reliability and maintenance engineering (2006), New Delhi: New Age International, New Delhi
[16] Rehmert, I.; Nachlas, J., Availability analysis for the quasi-renewal process Systems, IEEE Transactions on Man and Cybernetics Part A Systems and Humans, 39, 1, 272-280 (2009) · doi:10.1109/TSMCA.2008.2007945
[17] Singh, B.; Rathi, S.; Kumar, S., Inferential statistics on the dynamic system model with time-dependent failure rate, Journal of Statistical Computation and Simulation., 83, 1, 1-24 (2013) · Zbl 1348.62085 · doi:10.1080/00949655.2011.599327
[18] Sridharan, V.; Mohanavadivu, P., Reliability and availability analysis for two non-identical unit parallel system with conman cause failures and human errors, Microelectronics Reliability, 37, 5, 747-752 (1997) · doi:10.1016/S0026-2714(96)00090-X
[19] Weibull, W., A statistical distribution function of wide applicability, Journal of Applied Mechanics, 18, 293-297 (1951) · Zbl 0042.37903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.