Abstract
In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters. Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators. Numerical examples using real data set are presented to illustrate the methods of inference developed here. Finally, the maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo simulation study.
Highlights
In life testing and reliability studies, the experimenter may not always obtain complete information on failure times for all experimental units
In this paper, based on a new type of censoring scheme called an adaptive Type-II progressive censoring scheme introduce by Ng, et al [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters
A properly planned adaptive progressively censored life testing experiment can save both the total test time and the cost induced by failure of the units and increase the efficiency of statistical analysis
Summary
In life testing and reliability studies, the experimenter may not always obtain complete information on failure times for all experimental units Data obtained from such experiments are called censored data. The conventional Type-I and Type-II censoring schemes do not have the flexibility of allowing removal of units at points other than the terminal point of the experiment Because of this lack of flexibility, a more general censoring scheme called progressive Type-II right censoring has been introduced. Which are the observed progressively Type-II right censored sample. This distribution is known as Pareto distribution of type II or Lomax distribution This distribution has been shown to be useful for modeling and analizing the life time data in medical and biological sciences, engineering, etc.
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