Short Run Capability Assessment Using the t Distribution

Article

Little, Thomas A.; Harrelson, C. Scott   (1993, ASQC)   Read-Rite Corporation; Milpitas, CA

Annual Quality Congress, Boston MA    Vol. 47    No. 0
QICID: 9955    May 1993    pp. 181-191
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Article Abstract

To predict defect rates using samples of 126 or fewer units, the t distribution is preferable to the traditional z distribution. The typical process capability study requires sampling at least 100 units from the production stream. However, when the sample size must be small, as in limited production runs, the t distribution is appropriate because it was specifically designed to analyze small samples. Four steps in a short run process analysis are: select the parameter to be analyzed; determine the sample size, keeping in mind that precision of estimation data show sizes of 6, 11, 16, 31, and 126 to be the best; determine the sample mean and standard deviation; compute the short run capability values of Cp(n) and Cpk(n). Validation of computations using the t distribution versus the z distribution was accomplished by tests on various distributions: uniform random, normal, �.75 sigma shifted normal, �1.5 sigma shifted normal, and typical industry process data. The t distribution method proved to be superior at predicting defect rates for small sample sizes. Lockheed has applied the new method to study the production of new tools. If the first article is acceptable, then a limited run is produced to test for defects. A process capability value of Cpk(n) => 1.5 allows the tool to be released for long term production.

Keywords

Capability study,Defects,Short runs,Statistical quality control (SQC),Statistics


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