Abstract
Similar models are often used in various disciplines. For example, models for time to an event or for times between successive events are needed in biometry and sociology applications, as well as in reliability. The specific circumstances of a particular discipline may suggest a particular family of distribution functions, e.g., the Weibull distribution, when modeling time to an event. Alternatively, a specific point process, e.g. the power law process (a nonhomogeneous Poisson process of specific functional form, see Ascher and Feingold (1984)) may be appropriate in a particular reliability application dealing with times between successive failures of a repairable system. In a biometry application, in which times between successive nonfatal illnesses of a patient are studied, another point process might be suggested. In practice, however, instead of considering that models are suggested by circumstances, there is far too much reliance on a priori specification of models. For example, in hardware reliability applications it is usually assumed that the exponential distribution is the appropriate model to use, regardless of the application. If this model is generalized at all, the “generalization” usually is restricted to using a Weibull distribution. In fact, one or the other of these distributions is usually invoked even when no distribution whatsoever is the appropriate model! That is, when dealing with a repairable system—and most systems are designed to be repaired rather than replaced after failure—the correct model is a sequence of distribution functions, i.e., a point process. Distribution functions and point processes are not equivalent models, even in the most special cases. A homogeneous Poisson process (HPP) can be defined as a nonterminating sequence of independent and identically exponentially distributed times between events. Ascher and Feingold (1979, 1984) show that there are important distinctions between the exponential distribution and HPP models.
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References
O. Aalen (1978), “Nonparametric Inference for a Family of Counting Processes,” Annals of Statistics, 6, 701–726.
P.D. Allison (1984), Event History Analysis: Regression for Longitudinal Event Data, Sage Publications, Beverly Hills.
M. Anderson, A.K. Jardine, and R.T. Higgins (1982), “The Use of Concomitant Variables in Reliability Estimation,” Proceedings of the Thirteenth Annual Pittsburgh Modeling and Simulation Conference, Instrument Society of America, pp. 73–81.
J.E. Angus (1984), “The Application of Software Reliability Models to a Major C3I System,” Proceedings Annual Reliability and Maintainability Symposium, IEEE Cat. No. 84CH1992-7, pp. 268–274.
H.E. Ascher (1983), “Regression Analysis of Repairable Systems Reliability,” in Electronic Systems Effectiveness and Life Cycle Costing, J.K. Skwirzynski, ed., Springer-Verlag, Berlin, pp. 119–133.
H.E. Ascher and H. Feingold (1979), “The Aircraft Air Conditioner Data Revisited,” Proceedings Annual Reliability and Maintainability Symposium, IEEE Cat. No. 79CH1429-OR, pp. 153–159.
H.E. Ascher and H. Feingold (1984), Repairable Systems Reliability: Modeling, Inference, Misconceptions and Their Causes, Marcel Dekker, New York and Basel.
A. Bendell (1984), “Proportional Hazards Modelling in Reliability Assessment,” to appear in Reliability Engineering.
B. W. Brown, Jr., M. Hollander, and R.M. Korwar (1974), “Nonparameteric Test of Independence for Censored Data, with Application to Heart Transplant Studies,” in Reliability and Biometry, F. Proschan and R.F. Serfling, eds., Society for Industrial and Applied Mathematics, Philadelphia, pp. 327–354.
D.R. Cox (1972a), “Regression Models and Life Tables (with Discussion),” Journal of the Royal Statistical Society, Series B, 34, 187–220.
D.R. Cox (1972b), “The Statistical Analysis of Dependencies in Point Processes” in Stochastic Point Processes, P.A. Lewis, ed., Wiley-Interscience, New York, pp. 55–66.
D.R. Cox (1975), “Partial Likelihood,” Biometrika, 62, 269–276.
C. J. Dale (1983), “Application of the Proportional Hazards Model in the Reliability Field,” Proceedings of the Fourth National Reliability Conference—Reliability ′83, United Kingdom.
L. Fisher and P. Kanarek (1974), “Presenting Censored Survival Data when Censoring and Survival Times may not be Independent,” in Reliability and Biometry, F. Proschan and R.J. Serfling, eds., Society for Industrial and Applied Mathematics, Philadelphia, pp. 303–326.
A.K. Jardine and P.M. Anderson (1984), “Use of Concomitant Variables for Reliability Estimation,” Proceedings of the 8th Symposium on Advances in Reliability Technology, Bradford University, United Kingdom.
A.K. Jardine and J.A. Buzacott (1985), “Equipment Reliability and Maintenance,” European Journal of Operational Research, 19, 285–296.
G.J. Kujawski and E.A. Rypka (1978), “Effects of ’On-Off’ Cycling on Equipment Reliability,” Proceedings Annual Reliability and Maintainability Symposium, IEEE Cat. No. 77CH1308-6R, pp. 225–230.
J.F. Lawless (1982), Statistical Models and Methods for Lifetime Data, Wiley-Interscience, New York.
J.F. Lawless (1983), “Statistical Methods in Reliability (with Discussion),” Technometrics, 25, 305–335.
B. Littlewood (1981), “Stochastic Reliability Growth: A Model for Fault Removal in Computer- Programs and Hardware-Designs,” IEEE Reliability Transactions, R-30, 313–320.
W.Q. Meeker, Jr. (1983), Discussion of Lawless (1983), pp. 316–320.
R.L. Prentice, B.J. Williams, and A.V. Peterson (1981), “On the Regression Analysis of Multivariate Failure Time Data,” Biometrika, 68, 373–379.
F. Proschan and R.J. Serfling, eds. (1974), Reliability and Biometry: Statistical Analysis of Life length, Society for Industrial and Applied Mathematics, Philadelphia.
R.A. Rosanoff (1969), “A Survey of Modern Nonsense as Applied to Matrix Computation,” Technical Papers for Meeting, AIAA/ASME 10th Structures, Structural Dynamics and Materials Conference, New Orleans.
M.L. Shooman (1984), “Software Reliability: A Historical Perspective,” IEEE Reliability Transactions, R-33, 48–55.
J. Spragins (1984), “Limitations of Current Telecommunication Network Reliability Models,” Proceedings IEEE Global Telecommunications Conference, IEEE Product No. CH 2064- 4/84/0000, pp. 836–840.
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© 1986 Springer-Verlag Berlin Heidelberg
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Ascher, H. (1986). The Use of Regression Techniques for Matching Reliability Models to the Real World. In: Skwirzynski, J.K. (eds) Software System Design Methods. NATO ASI Series, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82846-1_13
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DOI: https://doi.org/10.1007/978-3-642-82846-1_13
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