The Optimum Plan and Accurate Inference for Accelerated Life Test under Inverse Gaussian Distribution

• Main Authors: Meng-Hsien Kuo, 郭孟憲
• Other Authors: Shuen-Lin Jeng
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/59059847175303260743

碩士 === 東海大學 === 統計學系 === 89 === Industry develops very quickly in recent years. High quality products are requested with high reliability. So how to use methods in short time to estimate the life of object is interested. Accelerated life test is a practical method, which place product into a test in some special (accelerated) state by characters, for example, with high temperature and voltage. We obtain information in accelerated conditions and estimate exact life time in the normal operating conditions. This method does not only save time but also save cash. Here we consider the optimum accelerated plan that employs the minimization of standard deviation for estimation to find the proper low and high stress for testing. The best compromise plan is a design that minimize the standard deviation of the target estimator with three stress in equal space and with same allocation of observations on the stress. We derive the Fisher information and employ the large sample theory to obtain the standard deviation of $\widehat{t_{p}}$ (p-th quantile of the distribution). The method based on the normal approximation theory to obtain the stress and allocation of the plan may not result in the real optimum state when sample size is less than 1000. So we propose to find the optimum stress and allocation by simulation. In this thesis, we overcome some predicament in generating Inverse Gaussian random variables. For the most common procedure, one uses uniform random variable and solve the inverse of CDF to obtain the required random variable. This is quite time consuming, so we use the method provided by Michael (1976) based on Chi-square distribution with degree of freedom 1. It is known that the bias problem could be serious when censoring is presented. We use the bias correction by applying bootstrap procedure to correct the estimate of $\widehat{t_{p}}$.