Appendix A: Generating Random Numbers from a Distribution
Simulation involves generating random numbers that belong to a specific distribution. We will illustrate this methodology using the Weibull distribution.
Generating Random Times from a Weibull Distribution
The cdf of the 2-parameter Weibull distribution is given by:
The Weibull reliability function is given by:
To generate a random time from a Weibull distribution, with a given and , a uniform random number from 0 to 1, , is first obtained. The random time from a weibull distribution is then obtained from:
The Weibull conditional reliability function is given by:
The random time would be the solution for for .
BlockSim's Random Number Generator (RNG)
Internally, ReliaSoft's BlockSim uses an algorithm based on L'Ecuyer's [RefX] random number generator with a post Bays-Durham shuffle. The RNG's period is approximately 10^18. The RNG passes all currently known statistical tests, within the limits the machine's precision, and for a number of calls (simulation runs) less than the period. If no seed is provided the algorithm uses the machines clock to initialize the RNG.
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- L'Ecuyer, P., 2001, Proceedings of the 2001 Winter Simulation Conference, pp.95-105
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