On optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm

Abstract

In determination of optimum Type-II progressive censoring scheme, the experimenter needs to carry out an exhaustive search within the set of all admissible censoring schemes. The existing recommendations are only applicable for small sample sizes. The implementation of exhaustive search techniques for large sample sizes is not feasible in practice. In this article, a meta-heuristic algorithm based on variable neighborhood search approach is proposed for large sample sizes. It is found that the algorithm gives exactly the same solution for small sample sizes as the solution obtained in an exhaustive search; however, for large sample sizes, it gives near-optimum solution. We have proposed a cost function-based optimum criterion, which is scale invariant for location-scale and log-location-scale families of distribution. A sensitivity analysis is also considered to study the effect of misspecification of parameter values or cost coefficients on the optimum solution.

Statistical Inference for Lognormal Distribution with Type-I Progressive Hybrid Censored Data

“…Observe that for a given value of n and m, a total of ð nÀ1 mÀ1 Þ choices are available to select a scheme R ¼ ðR 1 ; RÀ2; :::; R m Þ such that P m i¼1 R i ¼ ðnÀmÞ. Thus, searching an optimal scheme among all possible schemes may be computationally inconvenient for higher values of n and m. Recently, Bhattacharya et al (2016) proposed a meta heuristic based variable neighborhood search (VNS) algorithm which is quite useful in constructing optimal plans for moderate to large values of n and m. The main advantage of using VNS algorithm is that it provides near optimal solution with relatively less computation time. Construction of optimal plans under hybrid censoring is equivalent to selecting the values of m and T based on a given optimal criterion, and one may refer to Dube et al (2011) for optimal hybrid censoring plans for a lognormal distribution.…”

A MCMC-type simple probabilistic approach for determining optimal progressive censoring schemes

“…Kundu (2009, 2013) proposed criterion based on asymptotic variance of estimated pth quantile of the underlying lifetime distribution and obtained the optimal censoring schemes for generalized exponential and Birnbaum-Saunders distributions. Bhattacharya et al (2016) introduced a meta-heuristic algorithm, called variable neighborhood search (VNS), for the determination of optimal censoring schemes. They showed that the VNS algorithm performs sufficiently well for moderate to large values of n and m. Recently, Bhattacharya (2020) introduced the notion of compound optimal design strategy under progressive censoring in a multi-criteria setup.…”

Optimal design of a simple step‐stress accelerated life test under progressive type I censoring with nonuniform durations for exponential lifetimes

“…For concise reviews and resources on planning, modeling, and analyzing the step‐stress ALT, readers are referred to Nelson, Meeker and Escobar, Bagdonavicius and Nikulin, Collins et al, and Limon et al Furthermore, due to time and resource constraints, censored sampling is usually necessary in practice, and in particular, a generalized censoring scheme known as progressive type I censoring allows functional test units to be withdrawn successively from the experiment at some prefixed nonterminal time points. Those withdrawn unfailed units can be used in other tests in the same or at a different facility; see, for instance, Cohen, Lawless, and Balakrishnan et al Despite its flexibility and efficient utilization of the available resources compared with the conventional sampling methods, progressively censored sampling has not gained much popularity in ALT, partly due to its complicated likelihood function rendering its statistical analysis rather difficult or mathematically intractable; see Balakrishnan, Pradhan and Kundu, Cramer and Iliopoulos, and Bhattacharya et al …”