Economic Design of Cumulative Conformance Count Charts with Variable Sampling Intervals

The cumulative conformance count (CCC) charts have been shown to be useful in high-quality processes. The CCC-charts regarded every individual item inspected as a sample and called the time between two successive samples the sampling interval. Typically, the length of sampling interval they employed is constant and fixed (FSI). Recently, the use of CCC-charts with the variable sampling interval (VSI) scheme has been proposed to enhance the efficiency of CCC-charts without increasing the rate of inspected items and false alarm occurrences. This paper presents an economic model for designing the VSI CCC-chart. In the economic design, a cost function is constructed, involving the cost of sampling and testing, the cost of false alarms, the cost to detect and remove the assignable cause, and the cost when the process is operating out-of-control. A heuristic method of finding optimal values of adaptive design parameters for minimizing the cost function is also presented. The VSI and FSI CCC-charts are compared with respect to the expected loss per unit time. In addition, the effects of process and cost parameters upon the operating cost and the design parameters for charting are discussed.