On the average run lengths of quality control schemes using a Markov chain approach

✍ Scribed by James C. Fu; Fred A. Spiring; Hansheng Xie

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 122 KB
• Volume: 56
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00183-3

✦ Synopsis

Control schemes such as cumulative sum (CUSUM), exponentially weighted moving average (EWMA) and Shewhart charts have found widespread application in improving the quality of manufactured goods and services. The run length and the average run length (ARL) have become traditional measures of a control scheme's performance. Determining the run length distribution and its average is frequently a di cult and tedious task. A simple uniÿed method based on a ÿnite Markov chain approach for ÿnding the run length distribution and ARL of a control scheme is developed. In addition, the method yields the variance or standard deviation of the run length as a byproduct. Numerical results illustrating the results are given.