ISBIS4 Abstract

Contact Author's Name: Chin-Diew Lai
Title of Abstract: Variance Issues in the Statistical Design of Control Charts
Author(s): C. D. Lai and K. Govindaraju
Affiliation: Massey University, Palmerston North, New Zealand
Variance Issues in the Statistical Design of Control Charts

C. D. Lai and K. Govindaraju
Institute of Information Sciences and Technology (IIST)
Massey University,
Private Bag 11 222
Palmerston North
NEW ZEALAND


The design of control charts is not free from controversies, see Woodall (2000). The design methodologies in the quality literature are either statistically based or economically based or a combination of them. The statistical design of control charts often uses the concept of Average Run Length (ARL). Some authors criticise the use of ARL, and instead prefer to use probabilities (of declaration of a state of in the state of statistical control or not). Both approaches to the statistical design of the control chart ignore the variability issues in the administration of the control chart. For example, the ARL at a given acceptable process level may be 200, but may involve a huge variance. This basically poses difficulties in the shop-floor due to widely varying frequencies of false alarms or delays in the detection of a process level change. In many cases the chart signals are ignored or acted upon selectively due to the excessive variability in the signals received f!
rom the control charts.

Another difficulty with the concept of ARL is that it is a “worst” long run average, which can be interpreted only if we assume an infinite production length. No process can be expected to be stable for an infinite length of time. Therefore, interpretation of ARL for short or medium production lengths is also difficult. In order to give a more appropriate meaning to the concept of ARL for short production length, a method of adjustment that considers the production length to be explicitly will be presented.

This talk will address how some of the current deficiencies in the statistical design of control charts can be overcome using some of the methodologies from the acceptance sampling literature. Simple examples will be presented showing how the new design method can lead to a significant reduction in the variance of the run length. Directions for future research in this direction will also be presented.