Title: Lower confidence bound for capability indices with asymmetric tolerances and gauge measurement errors

Authors: Daniel Grau

Addresses: Laboratory of Applied Mathematics, Universite de Pau et des Pays de l'Adour, CNRS UMR 5142, IUT de Bayonne, 17 Place Paul Bert, 64100 Bayonne, France

Abstract: The families of process capability indices Cp (u,v) and C″p (u,v) provide measurements of process performances for processes with symmetric or asymmetric tolerances. In literature, no attention has been paid to the cases in which sample data are affected by gauge measurement errors, except for the basic indices Cp, Cpk, Cpm and Cpmk. However, these errors are always present in real situations even when advanced measuring instruments are used. If these errors are not taken into account, conclusions drawn from process capability are therefore unreliable. In this paper, we study the probability distribution of the estimator of C″p (u,v) when the observations are affected by gauge measurement errors. We show here that using a lower confidence bound without taking these errors into account, severely underestimates the true capability. In order to improve the results, we suggest using an adjusted lower confidence bound, and we give a Maple program to obtain this bound. We finally present a real study on a carbon fibre manufacturing process to illustrate how to make use of our suggestion.

Keywords: quality technology; process capability indices; gauge measurement errors; asymmetric tolerances; lower confidence bound; carbon fibre manufacturing.

DOI: 10.1504/IJQET.2011.041228

International Journal of Quality Engineering and Technology, 2011 Vol.2 No.3, pp.212 - 228

Available online: 13 Jul 2011 *

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