Estimation of multicomponent stress–strength reliability based on unit Burr XII distribution: an application to dam occupancy rate of Istanbul, Turkey

ABSTRACT

In this paper, we consider the estimation of a multicomponent stress–strength reliability when stress and strength variables follow unit Bur XII distribution. In estimation procedure, the maximum likelihood and Bayesian methods are used. The maximum likelihood estimator is obtained via iterative methods. The asymptotic confidence interval is constructed using asymptotic properties of the corresponding estimator. In addition, two bootstrap confidence intervals are constructed. Bayesian estimator is obtained using three different approximation methods: Lindley’s approximation, Tierney–Kadane approximation and Markov Chain Monte Carlo method. The interval estimation based on Bayesian method is studied. The simulation study is conducted to investigate and compare the performance of the considered methods. Finally, an original data set, general dam occupancy rate of Istanbul, Turkey obtained from Istanbul Statistic Office, is analysed in the concept of multicomponent stress–strength reliability.

KEYWORDS:

• Unit Burr XII distribution
• Bayesian estimation
• maximum likelihood estimation
• multicomponent stress-strength reliability

Disclosure statement

No potential conflict of interest was reported by the author(s).