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 m th 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 procedure.