Economic Design of the Variable Parameters &Xmacr; Control Chart with a Corrected A&L Switching Rule

The variable parameters (VP) &Xmacr; control chart is more efficient than the fixed parameters &Xmacr; control chart. However, an obvious shortcoming of the VP &Xmacr; control chart is its excessive number of switches among different design parameters, which significantly increases the complexity of operations for administer and the costs of maintaining the control chart. Amin and Letsinger (1991) proposed a switching rule, denoted by A&L switching rule, to reduce the number of switches. In this paper, we investigated the economic design of the VP &Xmacr; control chart by using the corrected A&L switching rule scheme, which makes some corrections to the existing study of the A&L switching rule scheme. A three‐state Markov model is proposed to derive the performance measures of the suggested control chart. An expected cost model for the process is established with the cost function derived. The genetic algorithm is then employed to search for the solution for the economic design of the proposed control chart. The results obtained show that the developed model can significantly reduce the average number of the parameter's switches and save the expected cost in comparison with the conventional VP control scheme in detecting small and moderate mean shifts. A sensitivity analysis is also carried out to examine the effects of cost and model parameters on the solution of the economic design for the proposed control chart. The analysis demonstrates the expected cost per time unit is positively affected by the cost associated with a false signal, the average cost of repairs when a true signal is identified, the sampling cost and the cost associated with a switch, and is negatively affected by the cost associated with running the process in‐control per hour.