Parameters estimation for the Burr XII distribution in partially accelerated life tests with multiple censored data

• Main Authors: Yung-Fu Cheng, 鄭永福
• Other Authors: Fu-Kwun Wang
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/70011668693322023984

博士 === 國立臺灣科技大學 === 工業管理系 === 98 === In many life testing and reliability studies, complete information on the failure times of all the experimental units may not be obtained for various reasons. Hence, censoring is very common in life testing experiments. Sometimes the experiments could not be under control completely because units may break accidentally. However, type I and type II censoring schemes do not allow for units to be removed from the test during the life testing duration. Multiple censoring schemes will be a good choice in this situation. The lifetime of products under normal conditions endures a long period of time because of high reliability of products. So it is difficult to obtain information about the lifetime of products under normal conditions. In order to assure rapid failure and then to shorten the testing period, accelerated life test (ALT) is commonly used to obtain information about the lifetime of products quickly and economically under more severe operation conditions. In ALT, items are run only at stress conditions and the acceleration factor is assumed as a known value. However, sometimes the acceleration factor cannot be assumed as a known value especially when new products are on the testing. In this situation, partially accelerated life test (PALT) will be a good candidate to perform the life tests because the major assumption in PALT is that the stress is not known and cannot be assumed. PALT can be carried out by various stress schemes, such as constant-stress PALT (CS-PALT), step-stress PALT (SS-PALT), or progressive-stress PALT (PS-PALT). In this study, CS-PALT and SS-PALT are considered. We consider the testing SS-PALT and CS-PALT for the Burr XII distribution. This dissertation considered two maximum likelihood estimation methods. One of the methods was based on observed-data likelihood function. The maximum likelihood estimates were obtained by using BFGS algorithm. The other was based on complete-data likelihood function. The maximum likelihood estimates were derived by using EM algorithm. Asymptotic variance and covariance matrix of the estimators were derived, and confidence intervals of the estimators were also obtained. Simulation results show that the maximum likelihood estimation perform well in most cases in terms of relative absolute bias, mean bias and root mean square error. The maximum likelihood estimation with BFGS algorithm performs better than EM algorithm in most combinations of simulation conditions in CS-PALT. However, simulation results also show that the maximum likelihood estimation with the EM algorithm outperforms the BFGS algorithm in most cases in SS-PALT.