Economic-Statistical Design of a Logarithmic Transformed S2 EWMA Chart

Exponentially Weighted Moving Average (EWMA) control charts are an efficient means in detecting small process shifts, both in position and dispersion of the collected data. Implementing an EWMA chart to control a manufacturing process requires the computation and plotting of a random variable which is a function of the current sample statistic and of the past samples collected from the process. This allows the EWMA to prevail over the traditional Shewhart chart in terms of statistical sensitivity when small shifts in the process position and/or dispersion are expected. The aim of this chapter is to present the economic-statistical design of a S2 EWMA control chart for the on-line control of the process dispersion. The investigated chart operates through a control statistic based on a logarithmic transformation of the sample variance to make possible working on an approximately standard normally distributed random variable. Since the implementation of control charts to monitor process stability has become an usual practice within an industrial manufacturing environment, designing economically the control chart is an important managerial aspect of SPC which should be carefully taken into account by practitioners. However, as widely suggested in the literature, the statistical reliability of the chart with respect to the probability of signalling false alarms should not be neglected. For this reason, in this chapter the economic design of the S2 EWMA chart is discussed and achieved respecting a statistical constraint related to the in-control Average Run Length (ARL0), which allows the expected number of false alarms to be controlled and maintained at an acceptable level. An extensive data set of examples is presented to show how process costs and parameters affect the design of the S2 EWMA chart. The numerical analysis has been organized as a 27 unreplicated factorial plan. The first step of the analysis presents a comparison with a S2 Shewhart chart to quantify the cost savings achievable through the EWMA; then a sensitivity analysis on the EWMA chart design variables is performed to show how the input parameters derived from the process affect the decisions concerning the chart design.