Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal

In this paper, we propose maximum likelihood estimators (MLEs) and Bayes esti- mators of parameters of the step-stress partially accelerated life testing of Rayleigh distribution in presence of progressive type-II censoring with binomial removal scheme under Square error loss function, General entropy loss function and Linear exponential loss function . The MLEs and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from Rayleigh distribution. Also, we present to analyze two sets of real data to show its applicability. Keywords Step-stress partially accelerated test · MLEs · Bayes estimators · PT-II CBRs · SELF · GELF · LINEX 1 Introduction The Reilygh distribution is widely used in reliability engineering, survival time anal- ysis in medical and the exchange of goods and services, for different scales. It is also used in other fields like economic, political, social, cultural and technological systems. The origin and properties of the Rayleigh distribution has been originated by Siddiqui [24]. Also this distribution has introduced by Rayleigh [20]. Sinha and Howlader [26], Lalitha and Mishra [15] and Abd Elfattah et al. [1] have proposed various methods in order to obtain the inferences of their parameter under different types of censoring schemes. But in life testing problems, it is not easy to collect information about life- times on highly reliable products, items with long lifetimes, because less number of event or items no failures may occur within a specified testing time under normal con- B Manoj Kumar manustats@gmail.com Department of Statistics, Central University of Haryana, Mahendergarh, Haryana, India Department of Statistics, Central University of Rajasthan, Kishangarh, Rajasthan, India 123 118 Annals of Data Science (2019) 6(1):117–152 ditions. Thus, accelerated life tests (ALTs) or partially accelerated life tests (PALTs) are one of the most...