Balanced Joint Progressively Hybrid Type‐I Censoring Samples in Estimating the Lifetime Lomax Distributions

Abstract

The comparative life testing for products from different production lines under joint censoring schemes has received some attention over the past few years. Mondal and Kundu recently used the balanced joint progressive type-II censoring scheme to discuss the comparative exponential and Weibull populations. This paper implements the balanced censoring scheme with a hybrid progressive type-I censoring scheme known as a balanced joint progressive hybrid type-I censoring scheme (BJPHCS). The life Lomax products’ model formulation from two different lines of production with BJPHCS is discussed. The model parameters are estimated under maximum likelihood estimation for point and the corresponding asymptotic confidence intervals. Under independent gamma priors, the Bayes estimators and associated credible intervals are obtained with the help of MCMC technique. The validity of the theoretical results developed in this paper for estimation problems is discussed through numerical example and Monte Carlo simulation study, which report the estimators’ quality. Finally, we give a brief comment describing the numerical results.

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.…”