International Journal of Metrology and Quality Engineering

Table of Contents - 2011 - Volume 2, Issue 01  

Research Article

Testing capability indices for manufacturing processes with asymmetric tolerance limits and measurement errors

D. Grau 

Laboratory of Applied Mathematics, CNRS UMR 5142, IUT de Bayonne, Université de Pau et des Pays de l’Adour, 17 Place Paul Bert, 64100 Bayonne, France

Abstract

Most research works related to process capability indices assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when advanced measuring instruments are employed. If we do not take into account these errors, conclusions drawn from process capability are therefore unreliable. In this paper we study the sampling distribution of capability indices Cp''(u,v) in the presence of measurements errors, and when small subsamples data are collected from past “in-control”. We show that using a critical value without taking into account these errors, severely underestimates the α-risk which causes a less accurate testing capacity. To improve the results we suggest the use of an adjusted critical value, and we give a Maple program to get it. An example in a nougat manufactory is presented to illustrate this approach.

(Received January 24 2011)

(Accepted March 3 2011)

(Online publication June 29 2011)

Key Words:

  • Process capability indices;
  • gauge measurement error;
  • asymmetric tolerances;
  • critical value;
  • power test

Correspondence:

Correspondence: daniel.grau@univ-pau.fr