Bayesian optimal life‐testing plan under the balanced two sample type‐II progressive censoring scheme

Abstract

Joint progressive censoring schemes are quite useful to conduct comparative life‐testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Commun Stat‐Theory Methods; 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progressive censoring (BJPC) scheme. Optimal planning of such progressive censoring scheme is an important issue to the experimenter. This article considers optimal life‐testing plan under the BJPC scheme using the Bayesian precision and D‐optimality criteria, assuming that the lifetimes follow Weibull distribution. In order to obtain the optimal BJPC life‐testing plans, one needs to carry out an exhaustive search within the set of all admissible plans under the BJPC scheme. However, for large sample size, determination of the optimal life‐testing plan is difficult by exhaustive search technique. A metaheuristic algorithm based on the variable neighborhood search method is employed for computation of the optimal life‐testing plan. Optimal plans are provided under different scenarios. The optimal plans depend upon the values of the hyperparameters of the prior distribution. The effect of different prior information on optimal scheme is studied.

Exact likelihood ratio and Wald tests for the balanced joint progressive censoring scheme

“…In this work, we apply the VNS algorithm as suggested in Mondal et al. 10 The algorithm works on the strategies that the neighborhood are connected, local optimal solution found in one neighborhood may not be same for other connected neighborhood and global optimal solution is the best solution among those local optimal solutions found by the algorithm. Therefore, it is essential to construct the connected neighborhood in this current set-ups.…”

“…In the literature, applications of VNS algorithm in the context of finding out the optimal censoring scheme, are found in References 17‐19. Mondal et al 10 exploited the VNS algorithm to find out the optimal BJPC scheme based on certain Bayesian criteria. In this work, we apply the VNS algorithm as suggested in Mondal et al 10 …”

“…Mondal et al 10 exploited the VNS algorithm to find out the optimal BJPC scheme based on certain Bayesian criteria. In this work, we apply the VNS algorithm as suggested in Mondal et al 10 …”

“…) denote the number of observed failure from Sam-2. A significant amount of work has been done on different aspects of a BJPC scheme, see for example Mondal and Kundu, 8,9 Mondal et al, 10 Prajapati et al, 11 Goel and Krishna, 12 Alfaer et al, 13 and see the references cited therein.…”

“…Let $$$ {K}_1=\sum \limits_{i=1}^k{Z}_i $$$ denote the number of observed failure from Sam‐1 and $$$ {K}_2=\sum \limits_{i=1}^k\left(1-{Z}_i\right) $$$ denote the number of observed failure from Sam‐2. A significant amount of work has been done on different aspects of a BJPC scheme, see for example Mondal and Kundu, 8,9 Mondal et al, 10 Prajapati et al, 11 Goel and Krishna, 12 Alfaer et al, 13 and see the references cited therein.…”