Approximately optimum confidence bounds for system reliability based on component test data

Technometrics

Volumn 16, Issue 3, 1974, Pages 335-347

  Mann, Nancy R ^a   Grubbs, Frank E ^b  

^a Rockwell International   (United States)

^b U S ARMY RESEARCH LABORATORY   (United States)

Author keywords

Binomial Failure Data; Combining Component Failure Data; Exponential Failure Data; Life Testing; Reliability; System Reliability Confidence Bounds

Indexed keywords

RELIABILITY;

EID: 0016094652     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1974.10489202     Document Type: Article

References (29)

1. Bartholomew, D. J. (1963). The Sampling Distribution of an Estimate Arising in Life Testing, Technometrics4, 361-374.
2. Birnbaum, Z. W., Esary J. D. and Saunders S. C. (1961). Multicomponent. Systems and Structures and Their Reliability, Technometrics3, 55-77.
3. Bolshev, L. N. and Loginov E. A. (1966). Interval Estimates in the Presence of Nuisance Parameters, in Theory of Probability and Its Applications, 11, No. 1, 82-94, U.S.S.R.
4. Buehler, R. J. (1957). Confidence Intervals for the Product of Two Binomial Parameters, J. Amer. Stat. Assoc.52, 482-93.
5. Davis, Phiup J. (1964). Gamma Function and Related Functions in Handbook of Mathematical Functions, Eds. M. Abromowitz and I. A. Stegun, U. S. Government Printing Office, Washington, D. C.
6. Easterling, Robert G. (1972a). Approximate Confidence Limits for System Reliability, J. Amer. Stat. Assoc.67, 220-22.
7. Easterling, Robert G. (1972b). Approximate Confidence Limits for System Reliability: Exponentially Distributed Component Lifetimes. (To be submitted for publication).
8. El Mawaziny, A. H. (1965). “Chi-Square Distribution Theory with Applications to Reliability Problems,” Ph.D. Thesis, Iowa State Univ., Ames.
9. El Mawaziny, A. H. and Buehler R. J. (1967). Confidence Limits for the Reliability of a Series Systems,.J. Amer. Stat. Association62, 1452-9.
10. Gnunns, Frank (1971). Approximate Fiducial Bounds for the Reliability of a Series System for Which Each Component has an Exponential time-to-fail Distribution, Technomelrics, 15, 865-71.
11. Harris, Bernard (1971). Hypothesis Testing and Confidence Intervals for Products and Quotients of Poisson Parameters with Applications to Reliability, J. Amer. Slat. Assoc.66, 609-13.
12. Lieberman, Gerald J. and Ross Sheldon M. (1971). Confidence Intervals for Independent Exponential Series Systems, J. Amer. Slat. Assoc.66, 837-840.
13. Lipow, M. and Riley, J., “Tables of Upper Confidence Bounds on Failure Probability of One, Two, and Three Component Series Systems,” Vols. 1 and 2, Space Technology Laboratories Report AD-690-100, AD-636- 718, Redondo Beach, California, 1959.
14. Madansky, Albert (1965). Approximate Confidence Limits for the Reliability of Series and Parallel Systems, Technometrics, 7, 495-503.
15. Mann, Nancy R. (1970). Computer-aided Selection of Prior Distributions for Generating Monte Carlo Confidence Bounds on System Reliability, Nav. Research hoy. Quart.17, 41-54.
16. Mann, Nancy R. (1972a). Simplified Expressions for Obtaining Approximately Optimum Confidence Bounds on Series-System Reliability for Exponential Time to Failure, J. Amer. Statist. Assoc., 1974.
17. Mann, Nancy R. (1972b). Survey Paper Invited for Presentation, 1972 NATO Conference on Reliability Testing and Reliability Evaluation, The Hague, Netherlands, September 4-8, 1972.
18. Mann, Nancy R. (1973). Approximately Optimum Randomized and Nonrandomized Confidence Bounds on Series-and Parallel-System Reliability for Systems with Binomial Subsystem Data, I.E.E.E. Transactions on Reliability. To appear.
19. Mann, Nancy R. and Grubbs Frank E. (1972). Approximately Optimum Confidence Bounds on Series- System Reliability for Exponential Time to Fail Data, Biometrika, 69, 191-204.
20. Mann, Nancy R. and Fertxg Kenneth W. (1973). “Approximately Optimum (Randomized and Nonrandomized) Confidence Bounds on the Reliability of a Logically Complex Coherent System, Rocketdyne Research Report RR 72-02, Rocketdyne, Canoga Park, California. (To be submitted for publication).
21. Myhrk, Janet and Saunders Sam C. (1968a). Comparison of Two Methods of Obtaining Approximate Confidence Intervals for System Reliability Technometrics10, 37-49.
22. Myhrb, J. M. and Saunders S. C. (1968b). On Confidence Limits for the Reliability of Systems, Ann. Math. Stat.39, 1463-72.
23. Myhre, J. M. and Saunders S. C. (1971). Approximate Confidence Limits for Complex Systems with Exponent ial Component Lives, Ann Math. Slat., 8, 342-348.
24. Patnaik, P. B. (1949). The non-central x2 and F Distributions and Their Applications, Biometrika, 36, 202-232.
25. Saunders, Sam C. (1972). “On Confidence Bounds for System Reliability When the Components have Exponentially Distributed Lives,” Boeing Document D1180-14820-1, The Boeing Company, Seattle.
26. Stack, G. P. (1957). “Upper Confidence Limits for the Failure Probability of Complex Networks,” Sandia Corporation SC-433 (TR).
27. Wilks, S. S. (1935). The Large-sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses, Ann. Math. Stat. 9, 60-62.
28. Wilson, E. B. and Hilferty M. M. (1931). The Distribution of Chi-square, Proc. National Academy Sciences17, 684-688.
29. Winterbottom, A. (1972). “Series Systems Reliability in the Attribute Case,” Research Memorandum No. 8, Department of Mathematics, The City University, London.