Memorandum 1559
W. Albers & W.C.M. Kallenberg
Abstract:
The influence of the estimation of parameters in Shewhart control charts is
investigated. It is shown by simulation and asymptotics that (very) large
sample sizes are needed to accurately determine control charts if estimators
are plugged in. Correction terms are developed to get accurate control
limits for common sample sizes in the in-control situation. Simulation and
theory show that the new corrections work very well. The performance of the
corrected control charts in the out-of-control situation is studied as
well. It turns
out that the correction terms do not disturb the behavior of the control
charts in the out-of-control situation. On the contrary, for moderate sample
sizes the corrected control charts remain powerful and therefore, the
recommendation to take at least 300 observations can be reduced to 40
observations when corrected control charts are applied.
Keywords:
Statistical process control, Phase II
control limits, second order unbiasedness, out-of-control
Mathematics Subject Classification: 62F12, 62P30