Guidelines for automating Phase I of control charts by considering effects on Phase-II performance of individuals control chart

Abstract

With the advances in measurement technologies, today products and processes may have hundreds of variables that can be monitored. As the number of variables to be monitored in a process increases, a cumbersome task is the design of control charts, especially when one needs to estimate unknown process parameters. In Phase-I control chart implementations, a set of samples that are ideally from an in-control process is formed by iteratively eliminating/retaining potentially out-of-control samples and this is then used in parameter estimation. Nevertheless, sampling variability and samples from an out-of-control process that are not eliminated from a Phase-I data set may have effects on the online process monitoring (Phase II) performance of a control chart due to the control chart design with estimation errors. To provide Phase-I control chart design guidelines, here we investigate in detail the iterative use of the individuals control chart (I-control chart) in Phase I for identifying potentially out-of-control process observations when the initial Phase-I data set consists of contaminated observations, which is then followed by another Phase-II I-control chart designed with the parameter estimates obtained in Phase I. Using the sample size and the width of I-chart’s control limits as design factors in Phase I, process parameters are estimated, and these are used to design an I-chart with 3-sigma control limits for Phase II. In Phase II, expected value (AARL) and standard deviation (SDARL) of the average run lengths are evaluated. Six standard deviation estimators and three different contamination levels are considered. Guidelines for selecting the control limit width, sample size, and standard deviation estimator for the Phase I implementations are provided to yield desirable Phase II AARL performance with a small SDARL. Our contribution is neither in the theory of control charts nor in the individual techniques. Results of this study would be especially useful in automating control chart design processes where there are many control charts to be designed by well-trained operators in statistical process control. With transformations to Industry 4.0, which is a trend for automation and data exchange in manufacturing, utility of procedures for control chart design automation is expected to increase.