Constable Ph.D., Gordon; Yen Ph.D., Vincent (1991, ASQC) Wright State University, Dayton, OH
This paper compares the results of a Shewhart control chart to an autocorrelated chart for a variety of situations using a Monte Carlo simulation. The Monte Carlo simulation generates the initial set of serially-correlated data that then determines the control chart parameters for each chart.
The classic Shewhart control chart assumes: (1) The observations under consideration come from a process in a state of statistical control; (2) The observations are statistically independent; and (3) The observations are normally distributed by applying the Central Limit Theorem when the sample size is two or more. However, the Central Limit Theorem is not applicable for individual charts, especially those for batch and process type operations. The CUMSUM control chart is more effective for studying batch and process type operations and for identifying positive or negative trends over time.
The authors reach two conclusions: (1) A process exhibiting negative serial correlation needs control limits based on the serial correlation in order to include sample results that indicate a change has occurred in the process; and (2) In the case of positive correlation, the results are mixed because the tighter control limits resulting from the uncorrelated approach will result in more samples beyond the control limits than the standard three out of 1,000 as well as increasing the probability of out-of-control conditions where "zone" rules are employed.
Chemical and process industries,Control charts,Shewhart control chart,Central Limit Theorem