Economic Robustness Analysis of Adaptive Chart Schemes for Monitoring the Total Nonconformities Number in Inspection Units

In recent years, a variety of enhanced schemes for the c chart have been developed aimed at the effectiveness improving of the related statistical process control (SPC) procedures. However, the performance of such chart schemes can be very sensitive to values assumed for some operating and cost parameters, in particular to the considered process shift magnitude arising from out-of-control conditions. In such a circumstance, the effectiveness of such chart schemes can be subjected to substantial reductions when they are implemented in operative contexts given that, in practice, such value is unknown and it can be very difficult to accurately estimate. For this reason, in the present paper it is developed an economic optimization approach able to find out the optimal configurations of the main adaptive c chart schemes. Subsequently, economic performances of such configurations are compared in order to derive information on their relative economic robustness, considering the difference between the estimated process shift magnitude and the actual one as influential factor and costs arising from the related SPC operations as performance comparison index. In addition, also a sensitivity analysis based on a 25−1 V fractional factorial design scheme, to investigate on influence of several operating and cost parameters on charts economic robustness, is carried out and the related considerations are given. The obtained results show that the parameters having the most impact on economic robustness, when the out-of-control process shift is not accurately estimated, are the cost associated with the production of non-conforming parts and the failure rate of the manufacturing system