Design of the optimum product specifications for S-type quality characteristics

Due to rapid advancement of automated inspection equipment, screening (100% inspection) schemes have recently drawn increased attention. To deal with the problem of determining the optimum specification limits in screening schemes, most studies assume the normal distribution for a quality characteristic. However, the practical distributions for the smaller-the-better (S-type) quality characteristics are usually positively skewed, and for this situation the gamma distribution is more appropriate. This paper introduces the new concept of a truncated quadratic loss function, derives the truncated statistics associated with the gamma-type quality characteristic, and presents a model for the most economical product specification.