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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.
Additional information
Notes on contributors
Cleveland D. Turner
Mr. Turner is a Business Analyst.
Joe H. Sullivan
Dr. Sullivan is Associate Professor of Quantitative Analysis in the College of Business and Industry. He is a Member of ASQ. His email address is [email protected].
Robert G. Batson
Dr. Batson is Professor of Industrial Engineering. He is a Fellow of ASQ.
William H. Woodall
Dr. Woodall is a Professor of Statistics. He is a Fellow of ASQ.
