Developing the Tukey’s Control Chart for Monitoring the Percentile of a Start-up Weibull Process

• Main Authors: Su, Chih-Hsuan, 蘇致萱
• Other Authors: Tong, Lee-Ing
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/gmq987

碩士 === 國立交通大學 === 工業工程與管理系所 === 105 === The conventional Shewhart’s control charts require that the process data follow a normal distribution and a large data set is needed for setting up the control limits. However, constructing the Shewhart’s control charts for a start-up process is difficult because not enough data can be collected to estimate the process parameters accurately. To solve this problem, Quesenberry(1991) proposed the Q chart for the start-up process. Q chart also assumes that the process distribution follows some specific distributions such as Normal or Binomial distributions. That is, the Q chart is not appropriate if the data of a start-up process follow a non-normal distribution. The Weibull distribution is widely used to describe the reliability data. Padgett et al. (1990)’s developed a Shewhart-type control chart for the Weibull process. However, no control charts has been developed for a start-up Weibull process. Turkey’s control chart can be applied to any distribution with small data set. Therefore, the main objective of this study is to utilize Turkey’s control chart to monitor the percentile of a start-up Weibull process. The sensitivity analysis is conducted to verify the effectiveness of the proposed percentile Tukey’s control chart for a start-up Weibull process. Through simulations, we found out the suitable control limit coefficient k of Turkey’s control chart under parameters, sample sizes for monitoring the percentile of Weibull distribution. We also compared our works with Q charts and Padgett et al. (1990)’s Shewhart-type control chart. The results of the sensitivity analysis indicated that when the process is stable or has a positive shift, the Weibull percentile Turkey’s control chart outperforms the Shewhart-type control chart and the Q chart. When the process mean has a negative shift, Shewhart-type control chart performs better than Weibull percentile Turkey’s control chart and Q charts. Moreover, the detective ability of the Weibull percentile Turkey’s control chart and Shewhart-type control chart increase when the sample sizes increase.