Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

Abstract

In statistical quality control, decision‐theoretic approach draws a significant amount of attention due to its economic considerations. In reliability life testing, decision‐theoretic approach has been used quite extensively under different censoring schemes. All these implementations are based on single sample of products coming from a particular source. In this work we study decision‐theoretic approach on two sample of products coming from two different sources under a joint censoring scheme when the life times are exponentially distributed. The major advantage of such implementation is to take decision on the acceptance or rejection of one or both the batches in a single life testing experiment. Decision making is performed based on minimizing the Bayes risk with respect to a given loss function. It is observed that under certain set‐ups, the joint censoring scheme is preferable over the two separate single sample censoring schemes in decision making.

Optimal design of reliability acceptance sampling plan based on constant‐stress accelerated life testing considering the uncertainty of accelerated factor

“…The assumed prior distributions of AF can be updated as the posterior distributions from the test data, based on which the acceptance probability was constructed by the Bayesian posterior risk criteria. Meanwhile, Prajapati et al 19 . supposed that the prior distribution of AF can be deduced by the prior density of model parameters, and used a decision‐theoretic approach to obtain the Bayesian sampling plan.…”

“…The assumed prior distributions of AF can be updated as the posterior distributions from the test data, based on which the acceptance probability was constructed by the Bayesian posterior risk criteria. Meanwhile, Prajapati et al 19 supposed that the prior distribution of AF can be deduced by the prior density of model parameters, and used a decision-theoretic approach to obtain the Bayesian sampling plan. Furthermore, Li and Li 20 chose a uniform distribution as the prior distribution of the AF to depict the uncertainty of AF, it means the value of AF is taken with equal possibility, which is not correspond to the engineering practice.…”

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

“…) 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.…”

Acceptance reliability sampling plan for items from heterogeneous populations

“…Balakrishnan et al 17 considered acceptance sampling plans from truncated life tests based on the generalised Birnbaum-Saunders distribution. Prajapati et al 18 investigated optimal decision-theoretic sampling plan for two exponential distributions under joint censoring scheme. Aslam et al 19 studied various repetitive sampling plans using process capability index of multiple quality characteristics.…”