ISBIS4 Abstract

Contact Author's Name: Eugenio K. EPPRECHT
Title of Abstract: The Non-central Chi-square Chart with Double Sampling to Control the Process Parameters
Author(s): Antonio F. B. COSTA, Eugenio K. EPPRECHT & Maysa S. DE MAGALHÃES
Affiliation: State University of Sao Paulo, Catholic University at Rio de Janeiro & National School of Statistical Sciences / Brazilian Institute of Geography and Statistics, Brazil

We consider a non-central chi-square chart with double sampling (DS Chi-Square chart) to control the process mean and variance. As in the case with Shewhart charts, samples of size n are taken from the process at regular time intervals. At the first stage, one item of the sample is inspected. If its X value is close to the target value of the process mean, then the sampling is interrupted. Otherwise, at the second stage, the remaining n-1 items are inspected and a statistic T, based on the sum of the differences between the target value and each one of the n values of X, is computed. The way the statistic T is defined, it follows a non-central chi-square distribution. A signal is triggered when the sample point, given by the T value, falls above the upper control limit of the proposed chart. The proposed chart (DS Chi-Square chart) performs better than the joint X-bar and R charts, except when there is a large change in the process mean. Furthermore, if the DS Chi-Square cha! rt is used for monitoring diameters, volumes, weights, etc., then appropriate devices, such as go-no-go gauges can be used to decide if the sampling should go to the second stage or not. When the process is stable, and the joint X-bar and R charts are in use, the monitoring becomes monotonous because an X-bar or R value rarely falls outside the control limits. The natural consequence is that the user pays less and less attention to the steps required to obtain the X-bar and R value. But in some cases, this lack of attention can result in serious mistakes. The DS Chi-Square chart has the advantage of interrupting most of the samplings and so, consequently, most of the time the user will be working with attributes. Our experience shows that the inspection of one item by attribute is much less monotonous than measuring four or five items at each sampling.