Applying MLE Method to Estimate the Low Percentile and Construct a Bootstrap Control Chart for the Low Percentile of a Start-up Weibull Process

• Main Authors: Yu, Ya-Ting, 游雅婷
• Other Authors: Tong, Lee-Ing
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/g34xv4

碩士 === 國立交通大學 === 工業工程與管理系所 === 106 === With the globalization of manufacturing industry, life cycle of a product is constantly shortening, while customer expectations and failure cost are continuously rising.The Reliability of a product is more important than before. In the reliability and failure analysis, we often focus on the low percentile or minimum lifetime of a product.The reliability model is constructed with the Weibull distribution. Therefore, the main objective of this study is to utilize the maximum likelihood estimation (MLE) to derive the percentile estimator of a Weibull distribution, and then uses Bootstrap simulation method and Bootstrap confidence intervals to construct a percentile control chart that can effectively monitors the low percentile of a start-up Weibull process. The sensitivity analysis is utilized to demonstrate the effectiveness of the proposed method. The results of the sensitivity analysis shows that, in most cases, the average run length(ARL0) of PB method has larger values than that of BCa method and the Shewhart control chart. With the increase of shape parameters and the increase of the sample size(n), the detective ability of the PB low-percentile control chart performs better than that of BCa method. The percentile Bootstrap confidence interval method proposed in this study can also be used to solve the problem of insufficient samples of monitoring a new process.