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A Numerical Algorithm for Recursively-Defined Convolution Integrals Involving Distribution Functions

Author

Listed:
  • Robert Cleroux

    (University of Montreal)

  • Denis J. McConalogue

    (University College, Dublin)

Abstract

Reliability studies give rise to families of distribution functions F (n) defined recursively by the repeated convolution of a distribution function F with itself according to the scheme 0 t P (s) (t - x)Q (r) (x) dx where P (s) and Q (r) are the sth and rth members of families generated from distribution functions P and Q, not necessarily distinct. It is seldom possible or convenient to express the F (n) in analytical form. An algorithm based on cubic spline interpolation is given here for recursively generating continuous numerical approximations to the F (n) in a form which allows them to be convoluted together to provide useful approximation to the second of the above integrals.

Suggested Citation

  • Robert Cleroux & Denis J. McConalogue, 1976. "A Numerical Algorithm for Recursively-Defined Convolution Integrals Involving Distribution Functions," Management Science, INFORMS, vol. 22(10), pages 1138-1146, June.
    • Handle: RePEc:inm:ormnsc:v:22:y:1976:i:10:p:1138-1146
    DOI: 10.1287/mnsc.22.10.1138
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    Cited by:

    1. D. Ait Kadi & C. Beaucaire & R. Cléroux, 1990. "A periodic maintenance model with used equipment and random minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(6), pages 855-865, December.
    2. Chelbi, Anis & Ait-Kadi, Daoud, 2001. "Spare provisioning strategy for preventively replaced systems subjected to random failure," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 183-189, December.
    3. Chelbi, Anis & Ait-Kadi, Daoud, 2000. "Generalized inspection strategy for randomly failing systems subjected to random shocks," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 379-384, March.
    4. Daoud Ait Kadi & Robert Cléroux, 1988. "Optimal block replacement policies with multiple choice at failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 99-110, February.
    5. Badinelli, Ralph D., 1996. "Approximating probability density functions and their convolutions using orthogonal polynomials," European Journal of Operational Research, Elsevier, vol. 95(1), pages 211-230, November.
    6. Dubi, A., 1998. "Analytic approach & Monte Carlo methods for realistic systems analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 243-269.

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