Optimizing a Taguchi's Loss Function Based Economical Single Sampling Plan with Unknown Incoming Quality

This paper takes over the common dilemma facing a consumer receiving a lot from a supplier with unavailable information about the supplier's process level, or the information being available but untrustworthy or uncertain. This paper aims to model and optimize an economical single sampling plan that is independent of the supplier's process level, where the loss caused by accepting low quality lots is treated as a Taguchi's loss function; the model also considers inspection cost, and replacement cost. The Taguchi's loss function in this paper is a function of the expected percent defect in the accepted lots, which later through standardizing the Operating Characteristic (OC) curve becomes a function of the sample size $\boldsymbol{n}$, and the defectives rejection limit $c$ achieving independence from the supplier's process level. The standardization is attained through mathematical estimation and use of the beta function properties; the reliability associated with using the expectation is assessed later through the variance. The optimization technique used to find the value of $n$ and $c$ that minimizes the total cost associated with this sampling plan is direct search since both variables are discrete and bounded by the lot size.