Economic Design Approach for an SPC Inspection Procedure Implementing The Adaptive C Chart

The present paper proposes a design approach for a statistical process control (SPC) procedure implementing a c control chart for non‐conformities, with the aim to minimize the hourly total quality‐related costs. The latter take into account the costs arising from the non‐conforming products while the process is in‐control and out‐of‐control, for false alarms, for assignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. The proposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as the available labor resource level. A mixed integer non‐linear constrained mathematical model is developed to solve the treated optimization problem, whereas the Generalized Reduced Gradient Algorithm implemented on the solver of Microsoft Excel is adopted to resolve it. In order to illustrate the application of the developed procedure, a numerical analysis based on a 2V5−1 fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. Finally, the obtained results show that only few parameters have a meaningful effect on the selection of the optimal SPC procedure.