Statistical process control of correlated discrete manufacturing processes

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

Estimation of media and liner wear in a grinding mill using the Kalman Filter

honors thesisCollege of Mines and Earth SciencesMaterials Science & EngineeringJohn A. HerbstFerron A. OlsonThe problems of corrosion and abrasion of media and liner in a wet grinding mill have been reviewed. The Kalman filter has been suggested as a method for estimating the ball and liner wear within a mill. The principles behind the Kalman filer have been explained, and then the has been implemented with simulated mill data to estimate the rock holdup, the water holdup, the ball holdup, the liner weight, the ball wear rate constant, and the liner wear rate constant within the mill as a function of time. Measurements of power and bearing pressure were used to make the estimates. The filter made fairly accurate estimates of the ball holdup, and even better estimates of the water holdup. The ball holdup and liner weight estimates, however, were off by about 10 tons each; the ball holdup was estimated high and the liner weight was low. This suggested that the filter was unable to distinguish between ball and liner weights. One modification was made in the power model equation to include diameter in hopes that it would help distinguish liner weight (which depends on mill diameter) from ball hold up. The improvement was minimal. Therefore, further suggestions were made for improvement of estimates which can be made in the future. Once good estimates are made, the relative importance of abrasion and corrosion can be made