7.1 Process Capability and the S _pk Index

Process yield has for a long time been a standard criterion used in the manufacturing industry as a common measure of process performance. Process yield is currently defined as the percentage of processed product units passing inspection, which indicates that the product characteristic falls within the manufacturing tolerance. Product units that are rejected (nonconforming) result in additional costs incurred to the factory for scrapping or repairing the product. However a factory does not induce additional costs for a product that departs from the nominal specifications but is still within the tolerance. For processes with two-sided manufacturing specifications, the process yield can be calculated as p = F(USL) ? F(LSL), where USL and LSL are the upper and the lower specification limits, respectively, and F( ) is the c.d.f. of the process characteristic. If the process characteristic is normally distributed, the process yield can then also be expressed as p = ?[(USL ? ?)/ ?] ? ?[(LSL ? ?)/ ?], where using the common notation ? is the process mean, ? is the process standard deviation, and ?( ) is the c.d.f. of the standard normal distribution N( 0,1).

As it was already mentioned in attempting to provide a common quantitative measure of process performance, Kane (1986) one of the pioneers of the process capability analysis utilized the capability index C _pk to determine process ability of...