Reliability estimation in Maxwell distribution with progressively Type-II censored data

Abstract

Abstract There may be situations in which either the reliability data do not fit to popular lifetime models or the estimation of the parameters is not easy, while there may be other distributions which are not popular but either they provide better goodness-of-fit or have a smaller number of parameters to be estimated, or they have both the advantages. This paper proposes the Maxwell distribution as a lifetime model and supports its usefulness in the reliability theory through real data examples. Important distributional properties and reliability characteristics of this model are elucidated. Estimation procedures for the parameter, mean life, reliability and failure-rate functions are developed. In view of cost constraints and convenience of intermediate removals, the progressively Type-II censored sample information is used in the estimation. The efficiencies of the estimates are studied through simulation. Apart from researchers and practitioners in the reliability theory, the study is also useful for scientists in physics and chemistry, where the Maxwell distribution is widely used. Keywords: Maxwell distributionreliability functionhazard rateprogressively Type-II censored samplemaximum-likelihood estimationBayes estimationsquared error loss functionMonte Carlo simulation Mathematics Subject Classification:: Primary: 62N0162N05Secondary: 62F1062F15 Acknowledgements The authors are grateful to the editor and the learned referee for making useful comments which resulted in much improvement in the paper. The second author is also grateful to the Council of Scientific and Industrial Research, India for providing financial assistance.