On Reliability Analysis of <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> -Out-of-<inline-formula> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula>:<inline-formula> <tex-math notation="LaTeX">$F$</tex-math> </inline-formula> Systems Equipped With a Single Cold Standby Component Under Degradation Performance

Abstract

A $k$ -out-of- $n$ : $F$ system is considered, and its reliability is studied under degradation performance. The effect of the presence of a cold standby component is investigated on likelihood and reliability functions. A Gamma process is assumed for degradation of active and standby components, and the effect of varying the shape and scale parameters is studied on system reliability. The maximum likelihood estimator and also the asymptotic confidence interval for reliability of the system are investigated. Finally, the results are illustrated via a real degradation dataset.