An optimal design of joint X‐ and S control charts using quadratic loss function

Cost models for the design of control charts based on Duncan’s approach have been studied in recent years. Presents a double assignable‐cause cost model, which is in terms of Taguchi’s loss imparted to society from the time a product is shipped, using renewal theory approach. The expression for the expected cycle length and the expected cost per cycle are easier to obtain by the proposed approach, and the cost model, including the customer’s voice, reveals the importance of quality. Sensitivity analysis performed on a large number of numerical examples illustrates that the cost of repair or replacement and customers’ tolerance, which are related to loss function, are critical when designing economically based on X‐ and S control charts.