Economic design approach for a 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 controlchart for non-conformities, with the aim to minimize the hourly total quality-related costs. The latter take into account thecosts arising from the non-conforming products while the process is in-control and out-of-control, for false alarms, forassignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. Theproposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as theavailable labor resource level. A mixed integer non-linear constrained mathematical model is developed to solve the treatedoptimization problem, whereas the Generalized Reduced Gradient Algorithm implemented on the solver of Microsoft Excel isadopted to resolve it. In order to illustrate the application of the developed procedure, a numerical analysis based on a 25 1Vfractional 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 meaningfuleffect on the selection of the optimal SPC procedure.