Reliability Testing of Statistical Process Control Procedures for Manufacturing with Multiple Sources of Variation

Quality inconsistencies can be caused by processes with multiple sources of variation. Therefore, the development of control charts that perform properly for both producer's and consumer's risk can be very complex. This is particularly true for real-time SPC systems that collect a great deal of data through noncontact sensing. In this paper, we demonstrate the use of a Monte Carlo simulation procedure that can be used to test SPC charts for both consumer's and producer's risk, and an experimental design procedure to analyze the results. This procedure is shown to be especially useful where design factors interact to cause high variation in a quality characteristic of a product. The approach is illustrated for a practical problem taken from the lumber manufacturing industry and demonstrates that commonly used industrial practices to control product dimensions lead to erroneous conclusions. To that end, a new mathematical approach that yields the correct results is described. The Simulation / ANOVA procedure described in this paper may have applicability in the control of many other industrial processes.