Statistical Process Control for the Number of Defectives with Limited Memory

A limited memory influence diagram model is utilized for statistical process control in a system where qualitative data on the number of defectives in a sample is available in each period of a finite production horizon. Based on the number of defective units observed, a decision is made on whether to stop the process and repair an assignable cause of variation. The model has no requirement to maintain the history of sample results and corrective actions taken in previous sampling periods. Despite the limited memory of process history, the nature of the decision rule and solution algorithm result in quality-related costs that are comparable to those of existing methods for Bayesian quality control with information on number of defectives. When sampling interval and sample size can be selected as design parameters for a system with a fixed time between scheduled maintenance, the limited memory influence diagram model can be constructed to provide similar costs with reduced computational requirement as compared with a partially observed Markov decision process technique.