Optimal Bayesian sampling plan for censored competing risks data

There is a substantial amount of literature in the area of acceptance sampling plan with censored lifetime data. However, the optimality of a Bayesian sampling plan in the presence of competing risks has not been considered so far. In this paper, first, the Bayesian sampling plans (BSP) for Type-II and Type-I hybrid censoring schemes are discussed in presence of competing risks when the lifetime distribution is exponential. The closed-form expression of the Bayes decision function is obtained analytically for a linear loss function. Then we consider the Weibull distribution with an unknown shape parameter under Type-I hybrid censoring scheme in presence of competing risks to obtain the BSP. However, the Bayes decision function cannot be obtained in closed-form for a general loss function, and in such cases, a numerical algorithm is proposed. As an illustration, in the exponential case, a quadratic loss function, and in Weibull case, a non-polynomial loss function, are considered for the application of the proposed numerical approach to obtain the optimum BSPs using the Bayes decision function.