A Mixed CUSUM-EWMA Control Chart for Monitoring Weibull Distributed Time Between Events

• Main Author: Temesgen Hailegiorgis Abebe
• Other Authors: Fu-Kwun Wang
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/9zwu47

碩士 === 國立臺灣科技大學 === 工業管理系 === 105 === The progress of the quality control techniques and new technological developments have led to high-quality processes in which small amount of defects occur. However, when dealing with high-quality processes, the existing control charting schemes may face some difficulties. Time-between-events (TBE) charts can overcome the difficulties with traditional attributes control chart, and they are particularly suitable when the events rarely occur. The Weibull Distribution is one of the most widely used statistical models for the analysis of reliability problems. Because of its flexibility, it may assume shapes similar to some other distributions, such as exponential and normal. In this research, we have designed mixed cumulative sum (CUSUM)-exponentially weighted average (EWMA) control chart (MCE) for monitoring Weibull distributed TBE with individual measurements and compare it with existing control charts, such as Weibull CUSUM (WCUSUM), Weibull EWMA (WEWMA) and mixed EWMA-CUSUM (MEC). The objective of this study is to design a mixed CUSUM-EWMA control chart for Weibull distributed TBE and to monitor the TBE mean scale change with a different scale parameters of Weibull distribution with fixed shape parameters. The performance of a control chart is usually evaluated by analyzing the properties of its run length (RL) distribution such as Average run length (ARL) and the standard deviation of the run lengths (SDRL). These two metrics help us to describe the entire profile of RL of the chart and they are computed using Monte Carlo simulation with 104 iterations. Relative mean index (RMI) is also utilized to measure the overall performance of the proposed control chart and other three existing control charts. According to the results, the proposed control chart is more efficient than the WCUSUM and the WEWMA charts next to MEC charts to detect downward scale changes swiftly, whereas the WEWMA and the MEC chart performs better than other charts in detecting upward scale changes swiftly. From real data, two illustrative examples are provided to show the application of existing (WCUSUM, WEWMA, MEC) and the proposed control charts for monitoring Weibull distributed TBE.