Variables sampling plans with PPM fraction of defectives and process loss consideration

Acceptance sampling plans provide the vendor and the buyer decision rules for lot sentencing to meet their product quality needs. A problem the quality practitioners have to deal with is the determination of the critical acceptance values and inspection sample sizes that provide the desired levels of protection to both vendors and buyers. As today's modern quality improvement philosophy, reduction of variation from the target value is the guiding principle as well as reducing the fraction of defectives. The C_pm index adopts the concept of product loss, which distinguishes the product quality by setting increased penalty to products deviating from the target. In this paper, a variables sampling plan based on C_pm index is proposed to handle processes requiring very low parts per million (PPM) fraction of defectives with process loss consideration. We develop an effective method for obtaining the required sample sizes n and the critical acceptance value C₀ by solving simultaneously two nonlinear equations. Based on the designed sampling plan, the practitioners can determine the number of production items to be sampled for inspection and the corresponding critical acceptance value for lot sentencing.