Economical control chart with supplementary rules to monitor the average number of defects

This study proposes a procedure for an on-line process control system to monitor the average number of defects using a Shewhart-like chart with two sets of limits (viz., control and warning limits). After the production of m units, the mth item is inspected. If the number of defects exceeds the upper control limit or if, in a sequence of the last h inspections, all inspected items exhibit a number of defects between the warning and control limits, then the process is stopped for adjustment; otherwise, production continues. The properties of an ergodic Markov chain are used to obtain an expression for the average cost per item produced. The inspection interval (m), warning and control limits (W and C, respectively), and the sequence size (h) are determined by minimizing the average cost per produced item. A numerical example illustrates the proposed procedur