Statistical process control of correlated discrete manufacturing processes

Don Gerald Wardell, Purdue University

Abstract

Traditional statistical process control (SPC) charts assume data independence; however, many times in practice, data are actually correlated. A time-series model has been developed by Alwan and Roberts (1988) to account for correlation by modeling the process utilizing time-series methodology. We investigate the properties of the Alwan and Roberts procedure, especially of the Special-Cause Control (SCC) chart which is a plot of the residuals obtained after fitting the time-series model. We derive the run length distribution of the SCC chart for a shift in the process mean for any AR(p) model, and approximate run length distributions for the more general ARMA(p,q) model. We also use the run length distribution to obtain the average run length (ARL) and the standard deviation of the run length (SRL). We show that for the ARMA(1,1) model, when the process is negatively autocorrelated, the ARL and SRL are lower than when the process is positively autocorrelated. We also show how the run length distribution found, as well as any other run length distribution, can be used to assess the validity of out-of-control signals. The method is simple, and since false alarms are often costly, the procedure has the potential to save practitioners time and money. Finally, we compare the ARL of the SCC chart to the ARL of more traditional Shewhart and exponentially weighted moving average (EWMA) charts when SPC data can be described by ARMA(1,1) models. We also add control limits to the second chart proposed by Alwan and Roberts, the Common-Cause Control (CCC) chart, which is a plot of the fitted or forecasted values of the correlated quality characteristic, in an attempt to predict out of control situations earlier than can be done with the SCC chart alone. We show that no one control chart is dominant in all cases, although the EWMA chart is quite robust, and thus should be considered in cases where processes are correlated, but it is too costly or difficult to set up the SCC and CCC charts.

Degree

Ph.D.

Advisors

Plante, Purdue University.

Subject Area

Statistics|Management|Industrial engineering

COinS