Abstract
The regression model for survival analysis introduced by Cox (1972) has had major impact on the biometry field. It is surprising, therefore, that Cox’s model, which is equally applicable to the reliability of nonrepairable items, has almost never been applied to such problems. This model has recently been extended to the analysis of multiple events, such as recurring infections experienced by a single subject, by Prentice, Williams and Peterson (1981), (PWP 1981). Some modifications to the PWP model are useful for optimum application to reliability problems but basically their model applies to repairable systems by simply replacing words like “infections” with “repairable failures.”
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. E. Ascher (1979), “Application of a New Estimation Technique to Repairable System Reliability”, Proc. RELCOMEX ’79, Wroclaw, Poland, Vol. II, pp. 229–237.
H. E. Ascher (1980), “Distribution-Free Estimation of System Reliability,” Annual Reliability and Maintainability Symposium (ARMS), IEEE-80CH1513–1R, pp. 374–378.
H. E. Ascher and H. Feingold (1978a), “Is There Repair after Failure?,” in ARMS, IEEE-77CH1308–6R, pp. 190–197.
H. E. Ascher and H. Feingold (1978b), “Application of Laplace’s Test to Repairable System Reliability,” in Proc. Int. Conf. on Reliability and Maintainability, Société Pour La Diffusion Des Sciences Et Des Arts, France, pp. 219–225.
H. E. Ascher and H. Feingold (1979), “The Aircraft Air Conditioner Data Revisited,” in ARMS, IEEE-79CH1429–0R, pp. 153–159.
H. E. Ascher and H. Feingold (1981), “Repairable Systems Reliability: Modeling, Inference, Misconceptions and their Causes,” to be published by Marcel Dekker, New York.
R. E. Barlow and F. Proschan (1975), “Statistical Theory of Reliability and Life Testing Probability Models,” Holt, Rinehart and Winston, New York.
Z. W. Birnbaum and S. C. Saunders (1969), “A New Family of Life Distributions,” J. of Appl. Prob., 6, 319–327.
M. C. Bryson and M. E. Johnson (1981), “The Incidence of Monotone Likelihood in the Cox Model,” Technometries, Vol. 23, pp. 381–383.
D. R. Cox (1972), “Regression Models and Life Tables (with Discussion),” J. Roy. Stat. Soc., Ser. B., 34, 187–220.
D. R. Cox (1975), “Partial Likelihood,” Biometrika, 62, 269–276.
H. T. Davis, K. Campbell and R. M. Schrader (1980), “Improving the Analysis of LWR Component Failure Data,” Los Alamos Scientific Laboratory Report, LA-UR 80–92.
M. E. Johnson, H. D. Tolley, M. C Bryson and A. S. Goldman (1982), “Covariate Analysis of Survival Data-A Small Sample Study of Cox’s Model,” to appear in Biometrics.
J. D. Kalbfleisch and R. L. Prentice (1980), “The Statistical Analysis of Failure Time Data,” John Wiley, New York.
E. L. Kaplan and P. Meier (1958), “Nonparametric Estimation from Incomplete Observations,” J. Amer. Stat. Soc., 53, 457–481.
R. Kay (1977), “Proportional Hazard Regression Models and the Analysis of Censored Survival Data,” J-Roy. Stat. Soc., Ser. C, 26, 227–237.
S. W. Lagakos, C. J. Sommer and M. Zelen (1978), “Semi-Markov Models for Partially Censored Data,” Biometrika, 65, 311–317.
J. F. Lawless (1982), “Statistical Models and Methods for Lifetime Data,” John Wiley, New York.
P. M. Nagel and J. A. Skrivan (1982), “Software Reliability: Repetitive Run Experimentation and Modeling,” Boeing Computer Services Co. Report, BCS-40366, NASA Report No. CR-165856.
E. Parzen (1962), “Stochastic Processes,” Holden-Day, San Francisco.
R. L. Prentice, B. J. Williams and A. V. Peterson (1980), Draft Manuscript of Prentice et al. (1981).
R. L. Prentice, B. J. Williams and A. V. Peterson (1981), “On the Regression Analysis of Multivariate Failure Time Data,” Biometrika, 68, 373–379.
D. Schoenfeld (1982), “Partial Residuals for the Proportional Hazards Regression Model,” Biometrika, 69, 239–241.
A. A. Tsiatis (1981), “A Large Sample Study of Cox’s Regression Model,” Ann. of Stat., 9, 93–108.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ascher, H. (1983). Regression Analysis of Repairable Systems Reliability. In: Skwirzynski, J.K. (eds) Electronic Systems Effectiveness and Life Cycle Costing. NATO ASI Series, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82014-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-82014-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82016-8
Online ISBN: 978-3-642-82014-4
eBook Packages: Springer Book Archive