On the Choice of a Capability Index for Asymmetric Tolerances

Abstract

For a process normally distributed and a target located at the mid-point of a twosided tolerance interval, Vännman suggests a family of indices depending on two parameters. In order to choose the parameters which allow to obtain an index that is sensitive to departures of the mean from the target, we need to take the properties of its estimator into account. For a target not located at the mid-point of the interval of tolerance, Chen and Pearn suggest a family of indices generalizing Vännman's. The moments of these indices are given, then their expected values and mean square errors are studied to choose an index that is sensitive to the deviations of the mean from the target.

New Process Capability Indices for One-Sided Tolerances

“…This corollary is deduced from theorem 5 and Grau [4]. and are obtained without difficulty since , 1 Note that only the moments of order 1 and 2 of " , 1 pk n C , 1…”

Tolerance design based on specified process capability value

“…Pearn, Kotz, and Johnson (1992) introduced another process capability index, C pmk , which considers the difference between process mean and specification center. Recently, some researchers, for example Grau (2010Grau ( , 2012, Maiti, Saha, and Nanda (2010), and Pearn and Wu (2013), proposed the generalization and application of the aforementioned capability indices. Kargar, Mashinchi, and Parchami (2013) adopted a Bayesian approach based on subsamples to check process capability.…”

Multiple Comparisons with the Best for Process Selection for Linear Profiles with One-sided Specifications

“…Yum and Kim provided relevant literature in process capability analysis. Recent research related to two‐suppliers selection problem for a process with one‐sided specifications can be found in the literature …”

“…Recent research related to two-suppliers selection problem for a process with one-sided specifications can be found in the literature. [7][8][9][10][11][12] In recent years, Hosseinifard and Abbasi 13 employed the proportion of nonconformance concept to estimate the process capability for linear profiles with one-sided specifications. Wang 14 proposed two new indices C puA and C plA to measure the process yield for simple linear profiles with one-sided specifications.…”