Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T09:18:17.695Z Has data issue: false hasContentIssue false
  • English
  • Français

A renewal look at switching rules in the MIL-STD-105D sampling system

Published online by Cambridge University Press:  14 July 2016

Grace L. Yang
Grace L. Yang*
Affiliation:
University of Maryland
*
∗Postal address: Department of Mathematics, University of Maryland, College Park, MD 20742, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A sampling system, MIL-STD-105D, used in quality control consists of three sampling plans with different acceptance probabilities used in turn for lot inspection. The decision to switch plan is based on the history of the lot acceptance records and a set of stopping rules. We derive the performance measure, average outgoing quality (AOQ), of this sampling system from a renewal process in which AOQ is expressed in terms of the moments of the stopping times. The renewal approach is simpler than that of the Markov chain generally used in computing AOQ for an infinite sequence of lots; it also provides a formula for AOQ for a finite sequence of lots.

Keywords

RENEWAL PROCESSSTOPPING TIMEQUALITY CONTROLACCEPTANCE SAMPLINGAVERAGE OUTGOING QUALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 183 - 192
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Also affiliated to the National Institute of Standards and Technology, Gaithersburg, MD.

References

American Society For Quality Control (1981) Sampling Procedures and Tables for Inspection by Attributes. ANZI/ASQC Z1.4-1981, Milwaukee, Wisconsin.Google Scholar
Burnett, T. L. (1967) Markov chains and attribute sampling plans. IBM Tech. Report No. 67-825-2175, IBM Federal Systems Division, Oswego, New York.Google Scholar
Dodge, H. F. (1965) Evaluation of a Sampling Inspection System having Rules for Switching between Normal and Tightened Inspection Tech. Report No. 14, Statistics Center, Rutgers University.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Huntington, R. (1976) Mean recurrence times for k successes with M trials. J. Appl. Prob. 13, 604–607.CrossRefGoogle Scholar
Jennison, C. and Turnbull, B. W. (1983) Confidence intervals for a binomial parameter following a multistage text with applications to MIL-STD 105D and medical trials. Technometrics 25, 49–58.CrossRefGoogle Scholar
Koyama, T. (1979) Switching characteristics under MIL-STD-105D. Technometrics 21, 9–20.CrossRefGoogle Scholar
Li, S.-Y. R. (1980) A martingale approach to the study of occurrence of sequence patterns in repeated experiments. Ann. Prob. 8, 1171–1176.CrossRefGoogle Scholar
Mil-Std 105D (1963) Military Standard Sampling Procedures and Tables for Inspection by Attributes. U.S. Government Printing Offices, Washington, D.C. Google Scholar
Schilling, E. G. (1982) Acceptance Sampling in Quality Control. Marcel Dekker, New York.Google Scholar
Schilling, E. G. and Sheesley, J. H. (1978) The performance of MIL-STD-105D under the switching rules. J. Quality Technol. Part 1, 10, 76–83; Part 2, 10, 104-124.CrossRefGoogle Scholar
Stephens, K. S. and Larson, K. E. (1967) An evaluation of the MIL-STD-105D system of sampling plans. Indust. Quality Control 23, 310–319.Google Scholar
U.S. ARMY (1974) Single and Multi-Level Continuous Sampling Procedures and Tables for Inspection by Attributes. MIL-STD-1235A (1974).Google Scholar
Yang, G. L. (1983) A renewal process approach to continuous sampling plans. Technometrics 25, 59–67.CrossRefGoogle Scholar