A unified of capability indices, containing the indices Cp, Cpk, Cpm, and Cpmk, has earlier been defined by Spiring [6] for the case of two-sided specification intervals. In this paper, we investigate several properties of the estimators of the indices for different values of the weight function when the tolerances are symmetric. Again, we study the statistical properties of the natural estimator of Cpw (In Spiring [6] a family of capability indices, depending on a weight function, w, with symmetric tolerances) and an explicit form of the probability density function of pwCˆ under the assumption of normality and in statistical controlled.
