Abstract
This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.
Highlights
There are many scenarios in life-testing and reliability experiments whose units are lost or removed from experimentation before failure
This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009)
The maximum likelihood and Bayes methods are used for estimating parameters, reliability function and hazard rate function of the CRD based on a new censoring scheme, called a progressive first-failure censoring scheme
Summary
There are many scenarios in life-testing and reliability experiments whose units are lost or removed from experimentation before failure. If an experimenter desires to remove surviving units at points other than the final termination point of the life test, these two traditional censoring schemes will not be of use to the experimenter. If an experimenter desires to remove some sets of test units before observing the first failures in these sets this life test plan is called a progressive first-failure-censoring scheme which recently introduced by [21]. The main aim of this article is to focus on the designing problem of a progressive first-failure censoring life test with a compound Rayleigh failure time distribution.
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