A UNIFIED APPROACH FOR SHEWHART-TYPE PHASE I CONTROL CHARTS FOR THE MEAN

The false alarm probability (FAP) is the metric typically used to design and evaluate the performance of Phase I control charts. It is shown that in situations where the exact or the asymptotic joint p. d. f. of the standardized charting statistics follows a singular standard multivariate normal distribution with a common negative correlation, the FAP of some Shewhart-type Phase I charts for the mean can be expressed as a multiple integral of the joint p.d.f. Hence the required charting constants can be calculated (and the control chart can be implemented) by evaluating this integral. A table with the charting constants is provided for some popular choices of the nominal FAP (denoted FAP(0)) and the number of Phase I samples, m. The proposed methodology is useful to unify some existing Phase I charts and is illustrated with two charts from the literature: the p chart for the fraction nonconforming and the X chart for the mean. A summary and some conclusions are provided.