Economic Design of an Attribute np Control Chart Using a Variable Sample Size

The design of a control chart requires the specification of three decision variables, namely, the sample size, the sampling interval, and the action limit under which the process must be stopped for potential repair. A significant part of recent research relaxed the constraint of setting fixed parameters to open the way to a new class of charts called adaptive ones in which at least one of the design parameters may change according to the actual state of the process. The adaptive schemes have proven their effectiveness from statistical and economical point of views. In this article, the economic design of an attribute np control chart using a variable sample size is formulated. A sensitivity analysis is conducted to search for optimal design parameters minimizing the expected cost per hour and to reveal the impact of process and cost parameters on the behavior of the optimal solutions. It is found that the cost savings achieved from the use of the adaptive strategy instead of the static one depends on the set of input parameters.