JSM 2005 - Toronto

Abstract #303245

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Activity Number: 29
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Quality and Productivity
Abstract - #303245
Title: Efficient Sampling Plans for Control Charts for Monitoring the Mean and Variance of an Autocorrelated Process
Author(s): Xin Zhong*+ and Marion R. Reynolds, Jr.
Companies: Virginia Polytechnic Institute and State University and Virginia Polytechnic Institute and State University
Address: 289 Highland Ave, Apt 207, Somerville, MA, 02144, United States
Keywords: autocorrelation ; concentrated sampling ; dispersed sampling ; exponentially weighted moving-average control charts ; shewhart control charts ; statistical process control
Abstract:

This paper investigates the effects of autocorrelation on the performances of various sampling plans for control charts used to detect special causes that may produce changes in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart charts and two exponentially weighted moving average (EWMA) charts are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans, it is assumed the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance is obtained by taking samples of n = 1 and using an EWMA chart combination. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times.

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