Classical and Bayesian Inferences in Step-Stress Partially Accelerated Life Tests for Inverse Weibull Distribution Under
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CLASSICAL AND BAYESIAN INFERENCES IN STEP-STRESS PARTIALLY ACCELERATED LIFE TESTS FOR INVERSE WEIBULL DISTRIBUTION UNDER TYPE-I CENSORING F. G. Akgul,a,1 K. Yu,b,2 and B. Senoglu
UDC 539.4
c,3
This paper deals with the classical and Bayesian estimations of step-stress partially accelerated life test model under type-I censoring for the inverse Weibull lifetime distribution. In classical estimation, the maximum likelihood estimates of the distribution parameters and the acceleration factor were obtained. In addition, approximate confidence intervals of the parameters were constructed based on the asymptotic distribution of the maximum likelihood estimators. Under Bayesian inference, besides the Lindley and Tierney–Kadane approximation posterior expectation methods, which yielded point estimates of the distribution parameters and the acceleration factors under square error loss function, we also applied the Gibbs sampling method, in order to construct credible intervals of these parameters together with their point estimates. Finally, Monte Carlo simulations were conducted to compare the performances of the above estimation methods. Keywords: step-stress partially accelerated life test, inverse Weibull distribution, type-I censoring, maximum likelihood estimation, Bayesian estimation, Gibbs sampling. Introduction. The high-reliability devices have become an integral part of our lives with technological and industrial improvements. Therefore, the pressure on the manufacturer to produce high-quality products has increased day by day. It is crucial for manufacturers to test the lifetime of their products before launch to the market. However, testing the products under their normal-use conditions can be very costly and take a long time. For this reason, accelerated life tests (ALT) are preferred to obtain enough failure data in a short period [1]. In ALT, the products are tested under stresses, such as temperature, pressure, vibration amplitude, cycling rate, load, etc. The underlying assumption of ALT is that the mathematical model related to the lifetime of the unit and the stress are known. Nevertheless, life-stress relations are not always known, and ALT is not available [2, 3]. In this case, a partially accelerated life test (PALT) is used, in which items are firstly tested under normal conditions until the prefixed time. Then, the survived ones are subjected to accelerated test/stress conditions [4]. According to Nelson [5], stress application can be reduced to step-stress and constant-stress schemes. In step-stress PALT (SSPALT), firstly, the tested item is run under normal conditions. If it does not fail for a specified time, then it is run under accelerated condition until the test terminates. However, in constant-stress PALT (CSPALT), each unit is run at constant stress level until the test is terminated. The objective of these methods is to collect more failure data in a limited time without applying high stresses to all test units [6]. It should be noted that both SSPALT and CSPALT are used to shorten the
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