Obtaining confidence intervals for C_pk using percentiles of the distribution of Ĉ_p

Abstract

SUMMARŶ C pk is used as an estimate of process capability and can reflect performance degradation due to both shifts in the process mean and variability. Exact upper and lower confidence limits for the actual parameter value are elusive. Objections to existing estimators focus on two areas: the difficulty of executing the needed computations and the excessive widths of those confidence bounds. The CPE estimator (so called since it relies onĈ p ) which we derive in this paper is formed by simply multiplyingĈ pk by a value from the inverse chi-square distribution. A PASCAL computer program is supplied which generates those percentiles. Our CPE is compared via simulation to other estimators and is shown to be the preferred selection in most cases by providing the requisite probability coverage and narrow interval widths.

Generalized confidence intervals for assessing process capability of multiple production lines

“…When the confidence level is set to 100(1− ) 1/4 % = 98.73%, we may find the GLCBs for the smallest capability of four production lines, min 1≤i≤4 C pk i based on the lower bound of production line 2 by using Equation (5). In this case, we obtain min 1≤i≤4 C pk i = 1.026 instead of 1.1887.…”

“…Based on the given values of 1− and n, andĈ pk , calculated from the collected samples, we can obtain the GLCB for C pk by solving Equation (5). If the obtained GLCB for C pk is greater than the preset capability level c 0 , then we can conclude that the process meets the capability requirement (C pk >c 0 ).…”

Bootstrap approach for supplier selection based on production yield

“…Examples include Chou et al (1990), Zhang et al (1990), Franklin and Wasserman (1992a, b), Kushler and Hurley (1992), Nagata and Nagahata (1994), Tang et al (1997), Hoffman (2001, and many others. Under the assumption of normality of the estimated particularĈ pki defined in equation (7),Ĉ pi is distributed as ðn i À 1Þ 1=2 C pi ð À1 n i À1 Þ, and n 1=2…”

Properties of multivariate process capability in the presence of gauge measurement errors and dependency measure of process variables

“…Statistical methods for calculating a measure for the process capability have extensively been studied on a large scale since the early 1980s [2]. A common method for evaluating the process capability analysis introduces an index which can be used as a simple reporting measure, capturing the relative health of any process [3]. It has been proved that process capability indices provide very efficient measures of the capability of processes from many different perspectives [4].…”