A point-process model incorporating renewals and time trends, with application to repairable systems

Technometrics

Volumn 38, Issue 2, 1996, Pages 131-138

  Lawless, J F ^a   Thiagarajah, K ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Estimation; Poisson process; Recurrent events; Renewal process; Simulation; Trend tests

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; ESTIMATION; FAILURE ANALYSIS; FUNCTIONS; MATHEMATICAL MODELS; REPAIR;

POINT PROCESS MODEL; POISSON PROCESS; RECURRENT EVENTS; RENEWAL PROCESS; TREND TESTS;

RELIABILITY THEORY;

EID: 0030150789     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1996.10484458     Document Type: Article

References (21)

1. Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1993), Statistical Methods Based on Counting Processes, New York: Springer-Verlag.
2. Ascher, H., and Feingold, H. (1984), Repairable Systems Reliability: Modelling, Inference, Misconceptions and Their Causes, New York: Marcel Dekker.
3. Bain, L. J., and Engelhardt, M. (1980), “Inferences on the Parameters and Current System Reliability for a Time Truncated Weibull Process,” Technometrics, 22, 421-426.
4. Bain, L. J., Engelhardt, M., and Wright, F. T. (1985), “Tests for an Increasing Trend in the Intensity of a Poisson Process: A Power Study,” Journal of the American Statistical Association, 80, 419-422.
5. Berman, M., and Turner, T. R. (1992), “Approximating Point Process Likelihoods With GLIM,” Applied Statistics, 41, 31-38.
6. Cox, D. R. (1972), “The Statistical Analysis of Dependencies in Point Processes,” in Stochastic Point Processes, ed. P. A. W. Lewis, New York: John Wiley, pp. 55-66.
7. Cox, D. R., and Isham, V. (1980), Point Processes, London: Chapman and Hall.
8. Cox, D. R., and Lewis, P. A. W. (1966), The Statistical Analysis of Series of Events, London: Methuen.
9. Crow, L. H. (1974), “Reliability Analysis for Complex, Repairable Systems,” in Reliability and Biometry, eds. F. Proschan and R. J. Serfling, Philadelphia: SIAM, pp. 379-410.
10. Crow, L. H. (1982), “Confidence Interval Procedures for the Weibull Process With Applications to Reliability Growth,” Technometrics, 24, 67-72.
11. Crowder, M. J., Kimber, A. C., Smith, R. L., and Sweeting, T. J. (1991), Statistical Analysis of Reliability Data, London: Chapman and Hall.
12. Lawless, J. F. (1982), Statistical Models and Methods for Lifetime Data, New York: John Wiley.
13. Lawless, J. F. (1987), “Regression Methods for Poisson Process Data,” Journal of the American Statistical Association, 82, 807-815.
14. Lee, L. (1980), “Testing Adequacy of the Weibull and Log Linear Rate Models for a Poisson Process,” Technometrics, 22, 195-199.
15. Lee, L., and Lee, K. (1978), “Some Results on Inference for the Weibull Process,” Technometrics, 20, 41-45.
16. Lewis, P. A. W., and Robinson, D. W. (1974), “Testing for a Monotone Trend in a Modulated Renewal Process,” in Reliability and Biometry, eds. F. Proschan and R. J. Serfling, Philadelphia: SIAM, pp. 163-182.
17. Oakes, D., and Cui, L. (1994), “On Semi-parametric Inference for Modulated Renewal Processes,” Biometrika, 81, 83-90.
18. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1986), Numerical Recipes, Cambridge, U.K.: Cambridge University Press.
19. Proschan, F. (1963), “Theoretical Explanation of Observed Decreasing Failure Rate,” Technometrics, 5, 375-383.
20. Ross, S. M. (1983), Stochastic Processes, New York: John Wiley.
21. StatSci Inc. (1994), S-Plus For Windows, Version 3.2, Seattle: Author.