Skip to main content

Statistical Quality Control and Reliability Tests

  • Chapter
Reliability Engineering
  • 456 Accesses

Abstract

Statistical quality control and reliability tests are performed to estimate or demonstrate quality and reliability characteristics (figures) on the basis of data collected from sampling tests. Estimation leads to a point or interval estimate of an unknown characteristic, demonstration is a test of a given hypothesis on the unknown characteristic in an acceptance test. Estimation and demonstration of an unknown probability is investigated in Section 7.1 for the case of a defective probability p and applied in Section 7.2.1 to reliability, maintainability, and availability figures. Estimation and demonstration of a constant failure rate λ (or MTBF = 1/λ) and of an MTTR are discussed in depth in Sections 7.2.2 and 7.3. Basic models for accelerated tests and for goodness-of-fit tests are considered in Sections 7.4 and 7.5, respectively. To simplify the notation, the term sample will be used instead of random sample. Theoretical foundations for this chapter are given in Appendix A8. Empirical and graphical methods are considered in Section 7.5 and Appendices A8.1 and A9.8.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

Statistical Quality Control

  1. ANSI Z1.1 and Z1.2–1958: Guide for Quality Control and Control Chart Method of Analyzing Data; Z1.3–1959: Control Chart Method of Controlling Quality During Production.

    Google Scholar 

  2. IEC 60410: Sampling Plans and Procedures for Inspection by Attributes, 1973; see also MIL-STD-105, DIN 40080, DGQ-SAQ-OeVQ 16–01, ISO 2859.

    Google Scholar 

  3. SAQ-DGQ-OeVQ, DGQ16–01: Attributprüfung 9th Ed. 1986; 16–26: Meth. zur Ermittlung geeigneter AQL-Werte. 4rd Ed. 1990; 16–31/-32/-33: SPC 1/2/3 Statistische Prozesslenkung, 1990.

    Google Scholar 

  4. Sarkadi K.,Vincze I., Mathematical Methods of Statistical Quality Control, 1974,Academ. Press, N.Y.

    MATH  Google Scholar 

  5. Uhlmann W., Statistische Qualitätskontrolle, 2nd Ed. 1982, Teubner, Stuttgart.

    Book  MATH  Google Scholar 

Statistical Reliability and Maintainability Tests

  1. Ascher H.E., Hansen C.K., “Spurious exponentiality observed when incorrectly fitting a distribution of nonstationary data”, IEEE Trans. Rel., 47(1998)4, pp.451–459.

    Article  Google Scholar 

  2. IEC 60605: Equipment Rel. Testing (Part 1 to 4, 6), 1978 – 97; 60706: Guide on Maintainability of Eq. (Parts 5–6), 1994; 61070: Compliance Test Proc. for Steady-State Availability, 1991; 61123: Rel. Testing — Compl. Test Plans for Success Ratio, 1991; 61124: Rel. TestingCompl. Test Plans for Const. Failure Rate, 1997; 61649: Goodness-of-fit Tests & Conf. Intervals for Weibull Distr. Data, 1997; 61650: Rel. Data Analysis Techniques, 1997; see also 60319: Presentation and Spec, of Rel. Data, 1978, rev. draft 1998.

    Google Scholar 

  3. Hu J.M., Dasgupta A., Arora A.K., “Rate of failure-mechanisms identification in accelerated testing”, Proc. Ann. Rel. & Maint. Symp., 1992, pp. 181–188.

    Google Scholar 

  4. Klinger D.J., “On the notion of activation energy in reliability: Arrhenius, Eyring, and thermodynamics”, Proc. Ann. Rel. & Maint. Symp., 1991, pp. 295–300.

    Google Scholar 

  5. MIL-STD-471: Maintainability Verif, Demonstr. Eval, Ed. A 1973 (see also -HDBK-472);-STD-781: Rel. Testing for Eng. Dev., Qualif, and Product., Ed. D 1986 (see also -HDBK -781).

    Google Scholar 

  6. Nelson W., Accelerated Testing, 1990, Wiley, New York.

    Book  Google Scholar 

  7. Peck D.S., Trapp O.D., Accelerated Testing HDBK, 1987, Techn. Ass., Portola Valley CA.

    Google Scholar 

  8. Snaked M., Singpurwalla N.D., “Nonparametric estimation and goodness-of-fit-testing of hypotheses for distributions in accelerated life testing”, IEEE Trans.Rel., 31(1982)1, pp. 69–74.

    Article  Google Scholar 

  9. Thomas E.F., “Reliability testing pitfalls”, Proc. Ann. Rel. & Maint. Symp., 1974, pp. 78–83.

    Google Scholar 

  10. Viertl R., Statistical Methods in Accelerated Life Testing, 1988, Vandenhoeck, Göttingen.see also [1.23, A8.1 to A8.30]

    MATH  Google Scholar 

  11. Taguchi G., System of Experimental Design-Engineering Methods to Optimize Quality and Minimize Costs, Vol. 1 & 2., 1987, Unipub, White Plains NY.

    Google Scholar 

  12. Bain L., Engelhardt M., Statistical Analysis of Rel. and Life-Testing Models, 1991, Dekker NY.

    Google Scholar 

  13. Barlow R.E., Bartholomew D.J., Bremner J.M., Brunk H.D., Statistical Inference Under Order Restrictions, 1972, Wiley, New York;

    MATH  Google Scholar 

  14. Barlow R.E., Campo R.A., Total Time on Test Processes and Applications to Failure Data Analysis, 1975, Tech. Rep. 75–0195, Aerospace Res. Lab., Ohio.

    MATH  Google Scholar 

  15. Belyayev J.K., “Unbiased estimation of the parameter of an exponential distribution”, Eng. Cybernetics, (1983)3, pp.78–81.

    MathSciNet  Google Scholar 

  16. Birnbaum Z.W., “Numerical tabulation of the distribution of Kolmogorov’s statistic for finite sample size”, Annals Stat. Ass., 47(1952), pp. 425–441.

    Article  MathSciNet  MATH  Google Scholar 

  17. Cantelli F.P., “Considerazioni sulla legge uniforme dei grandi numeri e sulla generalizzazione di un fondamentale teorema del Sig. Paul Lévy”, Giornale Attuari, 1933, pp. 327–338; “Sulla determinazione empirica delle leggi di probabilità”, Giorn. Attuari, 1933, pp. 421–424.

    Google Scholar 

  18. Chernoff H., Lehmann E.L., “The use of maximum Likelihood estimates in χ2 goodness-of-fit”, Ann. Math. Stat., 25(1954), pp. 579–586.

    Article  MathSciNet  MATH  Google Scholar 

  19. Clopper C.J., Pearson E.S., “The use of confidence or fiducial limits illustrated in the case of the binomial”, Biometrika, 26(1934), pp. 404–413.

    Article  MATH  Google Scholar 

  20. Cochran W.G., “The χ2 tests of goodness of fit”, Ann. Math. Stat., 23(1952), pp. 315–345.

    Article  MathSciNet  MATH  Google Scholar 

  21. Cramér H., Mathematical Methods of Statistics, 1958, Univ. Press, Princeton.

    Google Scholar 

  22. d’Agostino R.B., Stephens M. A., Goodness-of-fit-Techniques, 1986, Dekker, New York.

    MATH  Google Scholar 

  23. Darling D.A., “The Kolmogorov-Smirnov, Cramer-von Mises tests”, Ann. Math. Stat., 28(1957), pp. 823–838.

    Article  MathSciNet  MATH  Google Scholar 

  24. Epstein B, et al, “Life testing”, J. Amer. Stat. Ass., 48(1953), pp. 486–502; “Sequential life tests in the exponential case”, Ann. Math. Stat., 26(1955), pp. 82–93; “The exact analysis of sequential life tests with particular application to AGREE plans”, Rel. & Maint. Conf, 1963, pp. 284–310.

    Article  MATH  Google Scholar 

  25. Feller W., “On the Kolmogorov-Smirnov limit theorems for empirical distributions”, Ann. Math. Stat., 19(1948), pp. 177–189.

    Article  MathSciNet  MATH  Google Scholar 

  26. de Finetti B., “Sull’approssimazione empirica di una legge di probabilità”, Giorn. Attuari, 1933, pp. 415–420.

    Google Scholar 

  27. Fisher R.A.,“On the mathematical foundations of theoretical statistics”, Phil. Trans., A 222(1921), pp. 309–368; “The conditions under which χ2 measures the discrepancy between observation and hypothesis”, J. Roy Stat. Soc, 87(1924), pp. 442–450; “Theory of statistical estimation”, Proc. Cambridge Phil. Soc, 22(1925), pp. 700–725.

    Google Scholar 

  28. Gliwenko V.,“Sulla determinazione emp. delle leggi di probabilità”, Giorn. Attuari, 1933, pp.92–99.

    Google Scholar 

  29. Gumbel E.J., Statistics of Extremes, 1958, Columbia Univ. Press, New York.

    MATH  Google Scholar 

  30. Heinhold J., Gaede K.W., Ingenieur-Statistik, 4th Ed. 1979, Oldenbourg, Munich.

    Google Scholar 

  31. Kalbfleisch J.D., Prentice R.L., Statistical Analysis of Failure Time Data, 1988, Wiley, New York.

    Google Scholar 

  32. Kolmogoroff A.N., “Sulla determinazione empirica di una legge di distribuzione”, Giorn. Attuari, 1933, pp. 83–91.

    Google Scholar 

  33. Lawless J. F., Statistical Models and Methods for Lifetime Data, 1982, Wiley, New York.

    MATH  Google Scholar 

  34. Lehmann E.L., Testing Statistical Hypotheses, 1959, Wiley, New York.

    MATH  Google Scholar 

  35. Mann N.R., Schafer R.E., Singpurwalla N.D., Methods for Statistical Analysis of Reliability and Life Data, 1974, Wiley, New York.

    MATH  Google Scholar 

  36. Martz H.F. and Waller R.A., Bayesian Reliability Analysis, 1982, Wiley, New York.

    MATH  Google Scholar 

  37. Miller L.H., “Table of % points of Kolmogorov statistics”, J. Amer. Stat. Ass., 51(1956), pp.111–121.

    Article  MATH  Google Scholar 

  38. Pearson K., “On deviations from the probable in a correlated system of variables”, Phil. Magazine, 50(1900), pp. 157–175.

    Article  MATH  Google Scholar 

  39. Rohatgi V.K., An Introduction to Probability Theory and Mathematical Statistics, 1976, Wiley, New York.

    MATH  Google Scholar 

  40. Serfling R.J., Approximation Theorems of Mathematical Statistics, 1980, Wiley, New York.

    Book  MATH  Google Scholar 

  41. Smirnov N., “On the estimation of the discrepancy between empirical curves of distribution for two independent samples”, Bull. Math. Moscow Univ., 2(1939), fasc. 2

    Google Scholar 

  42. Wald A.,Sequential Analysis 1947, Wiley, New York;

    MATH  Google Scholar 

  43. Wald A.,Statistical Decision Functions, 1950, Wiley, New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Birolini, A. (1999). Statistical Quality Control and Reliability Tests. In: Reliability Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03792-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03792-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03794-2

  • Online ISBN: 978-3-662-03792-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics