Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring

Abstract

The present paper has developed the preliminary test estimators (PTEs) of the model parameter raised to certain power, σp, and the two measures of reliability, namely, the reliability function, R(t ) and the reliability of an item or a system, P of an exponentiated distribution, under Type- II censoring, based on their uniformly minimum variance unbiased estimators (UMVUEs) and maximum likelihood estimators (MLEs). The preliminary test confidence intervals (PTCIs) are also developed for σ, R(t ) and P based on their UMVUEs and MLEs. Further, the paper has derived expression for coverage probability of the PTCI of the model parameter, σ. Merits of the proposed PTEs are also established through analysis of simulated numerical data.

Keywords

• exponentiated distributions
• preliminary test estimator
• type-ii censoring
• uniformly minimum variance unbiased estimator
• maximum likelihood estimator