Generalising optimal mean setting for any number and combination of serial and parallel manufacturing operations

Consider a production system where products are continuously manufactured and their features inspected for conformance within specification limits. If produced above or below the limits, they either subject to rework product scrapped. Optimal mean setting may be applied adjust manufacturing means influence amount of scrap produced, maximising profit. Within system, then inspecting each feature in turn is termed serial production, whereas multiple before inspection parallel production. This paper develops generalised expression optimise values (optimal setting), n number any combination operations. Previous literature restricted considering two parallel. The combinations operations not fully considered. new validated by showing it consistent with specific cases from past literature. approach practical example gearbox shaft, expected profit eight possible sequences, as well deviation relative design intent. widely applicable component planning process capability index (Cpk) one. also forms basis trade-offs between profitability minimising deviations means, which further development.