Statistics for Maintenance Modelling: Renewal Processes

# The Monte-Carlo Numerical Calculation¤

A much more direct method that is very easy to program is to generate random variates from the distribution f(t), and to then simply count the number of renewals by time t. Repeating this many times gives the expectation M(t). This Monte-Carlo method will be slow, but with a modern computer, it doesn't matter.

This method (using a cunning algorithm to make it run very fast) was developed by Baker (1993) as a method of computing nonparametric estimates of the renewal function from observed data on times to failure. The Monte-Carlo method would be to arrange the sample of n failure times in all n! possible ways, and so to compute M(t). A recursive algorithm makes this calculation very fast indeed. This approach removes the need for fitting a parametric form to f(t) and then computing M(t) from that.

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