Bayes estimation of shift point in left truncated exponential sequence

Abstract

A sequence of independent lifetimes X1,…,Xm,Xm+1,... Xnwere observed from left truncated exponential populations with reliability R1T at time T and minimum life length of v 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 by change in reliability R2ρ at time ρ. The Bayes estimates of m, R1ρ and R2ρ are derived. Asymmetric loss functions are used to reflect that in most situations of interest, over estimation of a parameter does not produce the same economic consequence than under estimation. Both the non-informative prior and an informative prior on the reliability level at a prefixed time value are considered.