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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.

Optimal Bayesian sampling plan for censored competing risks data