Reliability Estimation of a Consecutive K-Out System for Non-Identical Strength Components with Applications to Wind Speed Data

Abstract

In the stress-strength reliability literature, although identical components assumption may not be realistic due to the structure of a system, independent and identically distributed components have been commonly used. In this study, we aim to contribute to the literature by studying of non-identical distributed components in a consecutive $$k$$k-out of-$$n$$n system when both stress and strength components follow the proportional hazard rate models. Estimation methods for the stress-strength reliability of this system are investigated from frequentist and Bayesian perspectives. Maximum likelihood and uniformly minimum variance unbiased estimations are obtained in the frequentist approach. Based on the suitability of the structure, approximate Bayes estimates methods: Lindley's approximation, Markov Chain Monte Carlo through Metropolis-Hastings or Gibbs sampling algorithms and exact Bayes estimates are derived. Asymptotic confidence and highest posterior density credible intervals are also constructed for all cases. We provide comprehensive simulation experiments for investigating the performances of the considered estimates. Wind speed data from NASA's satellite data source project are used in the application of the considered model and methods. We present the comparison of wind energy potentials of two districts on the Aegean coast of Turkey using our model structure after determining their wind speed distributions.