Designing Phase I X Charts with Small Sample Sizes
Document Type
Article
Publication Date
8-2004
Publication Title
Quality and Reliability Engineering International
DOI
10.1002/qre.662
ISSN
1099-1638
Abstract
Methods are examined for obtaining probability limits for Phase I Shewhart ―X charts when the process mean and standard deviation are estimated. The design methods assume m independent random samples of size n will be taken periodically from a normally distributed process. It is shown that the joint distribution of the standardized subgroup means follows either an approximate or exact multivariate t distribution, depending on the standard deviation estimator used. The multivariate t distribution is used to define the probability limits for the Phase I ―X chart. Extensive simulation compares the performance of the proposed limits with other design procedures. Tables of design constants are given for , and simple procedures for obtaining design constants are given for .
Recommended Citation
Champ, Charles W., L. Allison Jones.
2004.
"Designing Phase I X Charts with Small Sample Sizes."
Quality and Reliability Engineering International, 20 (5): 497-510.
doi: 10.1002/qre.662
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/496
