On the expected parts per million nonconforming levels obtained from estimated process capability indices

Abstract

AbstractProcess capability indices (PCIs) and parts per million (PPM) nonconforming (NC) levels are widely used in quality improvement programs for quantifying the capability of a process to meet specification requirements. Calculation of PCIs requires knowledge of the process parameters, however, true parameter values are often unknown in practice and therefore estimates obtained from a sample of observations are utilized. On the other hand, as often done in practice, expected PPM NC levels may be evaluated by using a given value of a PCI. However, such estimates of the PPM NC levels might be significantly different from the actual levels due to the additional variability introduced through parameter estimation. In this paper, the effects of estimated PCIs on the PPM NC estimates are quantified. Through evaluating the distributions of PPM NC estimates, it is demonstrated that estimation error is critical and might have significant effects on the PPM NC estimates. Copyright © 2010 John Wiley & Sons, Ltd.