Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T13:27:50.984Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Simple Numerical Method for Computing Stieltjes Integrals in Reliability Theory

Published online by Cambridge University Press:  27 July 2009

T. K. Boehme ,
W. Preuss  and
V. van der Wall
T. K. Boehme
Affiliation:
Department of Mathematics University of California, Santa Barbara, California
W. Preuss
Affiliation:
Department of Mathematics Wismar Technical University, Wismar, GDR
V. van der Wall
Affiliation:
Department of Mathematics Wismar Technical University, Wismar, GDR
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple method of calculating Stieltjes integrals is proposed. The method is essentially the two-point (trapezoidal) rule from numerical analysis. Two theorems yielding error bounds are given. When error requirements are modest (two or three significant decimal places) the method is fast and inexpensive. Examples are given solving the Renewal equation from reliability theory. A program for an HP-41C hand calculator is given, which solves the renewal equation.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 113 - 128
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Apostol, T.M. (1960). Mathematical analysis. Reading, Massachusetts: Addison-Wesley.Google Scholar
Mason, M.J. (1987). Numerical analysis. New York: Macmillan.Google Scholar
Preuss, W. (1986). Formulas for the availability of units with age replacement policy. Elektronische Informationsverarbeitung und Kybernetick (Berlin) EIK22(2/3): 125–129.Google Scholar
Riesz, F. & Sz.-Nagy, B. (1955). Functional analysis. New York: Fredrick Ungar Publishers.Google Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. San Francisco: Holden-Day.Google Scholar
Van der Wall, V. & Preuss, W. (1989). A simple numerical procedure for solving Volterra-Stieltjes integral equations. Proceedings of the conference on complex analysis, Sofia, 424–430.Google Scholar
Xie, M. (1989). On the solution of the renewal-type integral equations. Communications in Statistics and Simulation 18(1): 281–293.CrossRefGoogle Scholar