Determining optimal process means in a multi-stage production system with inspection errors in 100% inspection

The problem of determining optimal process parameters for multiple processes has not been widely addressed in the literature. Another important consideration that is frequently overlooked is the presense of inspection error during any inspection process due to factors related to human inspectors and measuring instuments. This paper investigates the optimal determination of process parameters in a multi-stage production system in the presence of inspection error. A mathematical model was developed for two processes producing a single product with two quality characteristics. The first quality characteristic was determined by the first process, and the second quality characteristic was determined by both processes. A 100% inspection was used as a means for product quality control and assumed to be error prone. A real case was used to test the developed model. Inspection error was found to have an impact on machine settings and hence the expected profit. The developed model provides quality managers with a mechanism to optimize their processes.