An Extension of the MOSUM Technique for Quality Control

Abstract

The use of moving sums of squares of recursive residuals (MOSUM-SQs) in addition to MOSUMs (Bauer and Hackl, 1978) is demonstrated for testing the constancy of a limited series of T independent observations normally distributed with equal variance. The cases of known and unknown process level as well as process variance are treated separately and conservative probability limits are derived. An assessment of the power in the cases of sudden changes of the process level and/or variance is based on a simulation study. The combined use of MOSUMs and MOSUM-SQs for the interpretation of the nature of the nonconstancy is discussed and demonstrated in an example. Finally, the application of the moving sum techniques in the situation of a continuing series of observations is discussed.

KEY WORDS:

• Recursive residuals
• Moving sums
• Moving sums of squares
• Nonconstancy of process level
• Nonconstancy of process variance