Assessing the Lifetime Performance Index of Exponential Products Based on the Bayesian Testing Procedure

Hong CW and Wu JW

Published on: 2019-11-29

Abstract

Process capability analysis is an effective means to measure the performance and potential capabilities of a process. In this paper, we construct Bayesian estimators of lifetime performance index (or larger-the-better type process capability index) under the exponential distribution with the upper record values. The Bayesian estimations based on general entropy loss function, linear exponential loss function and squared-error loss function, respectively. Further, the Bayesian estimators of lifetime performance index are utilized to construct the testing procedure for lifetime performance index based on a credible interval with known L. In addition, we also propose another Bayesian test to determine whether the lifetime performance of products adheres to the required level. Finally, we give a practical example and the Monte Carlo simulation to assess the behavior of the lifetime performance index

Keywords

Lifetime performance index; Upper record values; Exponential distribution; Credible interval; Bayesian test; Loss function

Introduction

No one can resist being interested in record values. Record values often arise in industrial stress testing, meteorological analysis, hydrology, seismology, lifetime testing and other similar situations. Record values are very important in management and engineering. For example, the record value of industrial stress testing is used to determine the limit stability of a given system or entity. The record value estimation of rainfall and earthquake can reduce the death of people and the loss of property in meteorological analysis, hydrology and seismology. The record value of products lifetime is used to assess the quality of product in lifetime testing. According to the model of Chandler [1], there are some situations in lifetime testing experiments where the failure time of a product is recorded if it exceeds all preceding failure times. These recorded failure times are the upper record value sequence.