Economically optimum design of Tukey's control chart with asymmetrical control limits for controlling process mean of skew population distribution

Abstract

Statistical process control is the application of statistical methods to the monitoring of process variations. The control chart is a key tool in statistical process control. Tukey’s chart is easy to set up and can use a single observation to monitor a process. Using asymmetrical control limits, Tukey’s chart can quickly detect positive and negative mean shifts when the monitoring variable has a skewed distribution. The control limit width and sampling interval must be determined before Tukey’s chart is used. In this study, Duncan’s cost function was modified to construct an optimal economic design model of Tukey’s chart with asymmetrical control limits. This design model is applied to integrated circuits packaging as an illustration. A sensitivity analysis indicated that the negative shift size coefficient, the cost of investigating a false alarm, and the loss cost per hour for the negative shift are sensitive to the cost.