A Development and Analysis of Multiple-Range Techniques for Controlling the Variability of a Process Characteristic with a Uniform Distribution.
Abstract
The Shewhart range chart is the most commonly used method of controlling process variability. The statistic plotted on this chart is the outer range of values of random samples from a repetitive process. As an extension of the use of ranges, the primary objective of this research is the development of quality control techniques in which two ranges are computed rather than just one. It is anticipated that two ranges provide more information and consequently are more discriminating at the expense of only a slight increase in necessary calculations. Several multiple-range plans and a single range plan are developed for random samples of size four from a uniform distribution. In each case, expressions for alpha and beta errors are derived. The operating characteristic (O.C.) curve, which is a plot of beta error against actual process variation, for a specified alpha level, is the principle criterion of comparison. The plan with the lowest overall O. C. curve is the most discriminating and consequently the most desirable. The conclusion drawn from this analysis is that multiple-range plans have no increase in discriminating ability over single range plans for samples of size four from a uniform distribution.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1974
- Accession Number
- ADA006478
Entities
People
- Richard Dan Abeyta
Organizations
- United States Army Materiel Command