A Program for Retrospective Change-Point Analysis of Individual Observations

Abstract

In the retrospective (preliminary) analysis of individual observations collected over time, the in-control parameters of the process are unknown, and there is the possibility of a shift in the mean or standard deviation at any point in the observations. In many cases a special cause of variation will produce a single, sustained shift in the mean, standard deviation, or both. Presented here is a FORTRAN program for detecting such shifts, developed from a likelihood ratio test under the assumption of normality. The advantages over use of the standard X- chart and moving range chart are much higher probabilities of detection of sustained shifts and much improved diagnostic information. When a shift is detected, the most likely location is given, as well as whether it is primarily due to a shift in the mean, standard deviation, or both. Multiple shifts can often be detected by recursive application of the algorithm under the user's direction. The program calculates an approximate upper control limit, using an expression that is determined from simulation by Sullivan and Woodall (1996). Alternatively, the user can provide the desired upper control limit.

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