Distribution and moments in simplified form for a general class of capability indices

Abstract

class of capability indices, containing the indices C_p′, C_pk′, C_pm′ and C_pmk′, has earlier been defined by Vännman for the case of two-sided specification intervals. By varying the parameters of the class various indices with suitable properties can be obtained. Under the assumption of normality new and simplified expressions of the distribution and the moments of the class of the estimated indices are provided when the target value equals the mid-point of the specification interval. It is shown that the cumulative distribution function can be expressed using only the central x² -distribution and the normal distribution, which increases the utility of the class of indices

Keywords:

• Process capability indices
• estimation