Bayesian Estimation of Change Point in Inverse Weibull Sequence

Abstract

A sequence of independent lifetimes X ₁,…, X _m , X _m+1,…, X _n were observed from inverse Weibull distribution with mean stress θ₁ and reliability R ₁(t ₀) at time t ₀ but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X _m by change in mean stress θ₁ and in reliability R ₂(t ₀) at time t ₀. The Bayes estimators of m, R ₁(t ₀) and R ₂(t ₀) are derived when a poor and a more detailed prior information is introduced into the inferential procedure. The effects of correct and wrong prior information on the Bayes estimators are studied.

Keywords:

• Bayes estimates
• Change point
• Inverse Weibull distribution

Mathematics Subject Classification:

• Bayesian estimation

Acknowledgment

The authors would like to thank both of the referees for their valuable comments, interest, and suggestions which helped shape this article.