Exploring Statistical Processes with Mathematica7

Non

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

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 difficult and tedious task. A simple unified method based on a finite Markov chain approach for finding 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.