Power functions of the Shewhart control chart

Abstract

The Shewhart control chart is used to check for a lack of control (a shift in the process). However it is insensitive to small shifts. To increase the sensitivity of the Shewhart control chart, some actions can be taken. These include reducing the width of the control limits, increasing the subgroup size to reduce the variance of the sample mean and making use of detection rules to increase the sensitivity of the chart. All of these actions will influence the power functions of the Shewhart control chart. A probability table showing the probabilities of detecting sustained shifts in the process mean, calculated using the formulae have been recommended. However, the calculations of the probabilities using the formulae are complicated and time consuming. In this paper, a Monte Carlo simulation using the Statistical Analysis System (SAS) is conducted to compute the necessary probabilities. These probabilities are closed to that obtained by using the formulae. The Monte Carlo simulation method is recommended as a better way to calculate the probabilities, as it provides savings, in terms of time and cost. Besides, the Monte Carlo simulation method also provides a higher flexibility in calculating the probabilities, for different combinations of the detection rules. The results obtained will assist practitioners in designing and implementing the Shewhart chart effectively. © IOP Publishing Ltd 2013.