Designing efficient Bayesian sampling plans for two-parameter exponential distribution with censored data
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This article studies a method about how to design Bayesian sampling plans for two-parameter exponential distributions <i>E</i>(<i>μ</i>, <i>λ</i>) based on Type-II censored samples. With a linear loss of the expected life time θ=μ+1/λ, a conventional Bayesian sampling plan (BSP) (nA,rA,δA) is derived. We then study the monotonicity associated with the Bayes decision function <i>δ</i><sub><i>A</i></sub>. According to this monotonicity, an explicit expression of <i>δ</i><sub><i>A</i></sub> is presented. Based on this explicit expression, a curtailed decision function <i>δ</i><sub><i>C</i></sub> is constructed, and an efficient Bayesian sampling plan (EBSP) (nC,rC,δC) is developed. The curtailed decision function <i>δ</i><sub><i>C</i></sub> has the property that <i>δ</i><sub><i>C</i></sub> = <i>δ</i><sub><i>A</i></sub> for all Type-II censoring samples. Furthermore, the Bayes risk of EBSP (nC,rC,δC) is less than or equal to the Bayes risk of the conventional BSP (nA,rA,δA). A simulation is carried out to study the performance of (nC,rC,δC) and (nA,rA,δA). The simulated numerical results indicate that in term of Bayes risks, (nC,rC,δC) outperforms (nA,rA,δA) significantly. Finally, the rationality of some existing BSPs for two-parameter exponential distributions is addressed.
