Economic statistical design of adaptive control schemes for monitoring the mean and variance: An application to analyzers

Several individuals control chart schemes are contrasted for the problem of monitoring the mean and variance of a normal process variable, with special consideration given to monitoring process analyzers, such as electrochemical devices, chromatographs, potentiometers, refractometers, and spectrometers. The combination of the exponentially weighted moving average (EWMA) chart and the Shewhart X chart that uses a variable sampling interval (VSI) policy is shown to be very effective for this problem. We develop a comprehensive economic model for the design of control schemes based on this chart combination. The economic model expresses the long-run cost per time unit of operating the combined VSI EWMA and VSI X chart scheme as a function of its design parameters, the parameters that describe the behavior of the process, and the cost parameters associated with the operation of the scheme. This economic model can be used to quantify the cost reduction that can be achieved by using the combined VSI scheme instead of traditional control schemes that use fixed sampling rates. We show that the reduction in cost as well as gains in performance are substantial.