Predicting Type II Censored Data from Repetitious Experiments Using Approximate Maximum Likelihood Method and Optimizing the Response of the Repetitious Experiments with Type II Censored Data

• Main Authors: Chien-Hui Yang, 楊千慧
• Other Authors: Lee-Ing Tong
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/55693295591418924397

博士 === 國立交通大學 === 工業工程與管理系所 === 94 === Design of experiments and Taguchi methods are widely employed in industry to develop new product or enhance product quality and reliability. Because the high technology products are often required to have high reliability, the lifetime or reliability of the high technology products is often considered as a response variable in the reliability experiments. Such experiments are usually time-consuming. In order to shorten the time for bringing the new product to the market, the experiments must be terminated before all the experiment runs are completed. In these situations, the incomplete data are called censored data. When the censored data are arisen in the experimental data, the orthogonality of the statistical models no longer exists and the usual analysis of variance methods of analyzing experimental data cannot be used to determine the optimal factor–level combinations. Many studies proposed various methods to analyze the censored data; especially for type I censored data. However, these methods are either computationally complex or have little practical use. Besides, the time of terminating the experiments to obtain type I censored data cannot be determined easily. If the time of terminating the experiments is too short, the number of uncensored data may be too few; if the time of terminating the experiments is too long, the number of uncensored data may be too many, and consequently, the experimental cost increases. Since the population mean and variance of experimental data are usually unknown in practice, this study proposes four approximate maximum likelihood predictors (AMLPs) to predict the type II censored data under the assumption that process data followed a normal distribution with unknown mean variance. This study utilizes two types of likelihood function to derive AMLPs. Both of two types of likelihood functions involve hazard functions. The first alternative is to replace the hazard functions by their expected values in the first type of likelihood function and then derive the predictor (which is designated as Model I AMLP). The second alternative is to replace the hazard functions by their expected values in the second type of likelihood function and then derive the predictor (which is designated as Model II AMLP). The third alternative is to use the Taylor series expressions of hazard functions to approximate the hazard functions to obtain the predictor (which is designated as Model III AMLP). The fourth alternative is to use the Taylor series expressions of hazard functions to approximate the hazard functions to obtain the predictor (which is designated as Model IV AMLP). Monte Carlo simulation and analysis of variance (ANOVA) method are used to compare the bias and effectiveness of these AMLPs. The results indicate that Model II AMLP and Model IV AMLP are more effective. Finally, the algorithms of optimizing the response from repetitious experiments are developed. Two cases are also given to demonstrate the effectiveness of the proposed optimization algorithms.