The R Book

A Monte Carlo Experiment

With data on time to death, the most important decision to be made concerns the error distribution. The key point to understand is that the variance in age at death is almost certain to increase with the mean, and hence standard models (assuming constant variance and normal errors) will be inappropriate. You can see this at once with a simple Monte Carlo experiment. Suppose that the per-week probability of failure of a component is 0.1 from one factory but 0.2 from another. We can simulate the fate of an individual component in a given week by generating a uniformly distributed random number between 0 and 1. If the value of the random number is less than or equal to 0.1 (or 0.2 for the second factory), then the component fails during that week and its lifetime can be calculated. If the random number is larger than 0.1, then the component survives to the next week. The lifetime of the component is simply the number of the week in which it finally failed. Thus, a component that failed in the first week has an age at failure of 1 (this convention means that there are no zeros in the dataframe).

The simulation is very simple. We create a vector of random numbers, rnos, that is long enough to be certain to contain a value that is less than our failure probabilities of 0.1 and 0.2. Remember that the mean life expectancy is the reciprocal of the failure rate, so our mean lifetimes will be 1/0.1 = 10 and 1/0.2 = 5 weeks, respectively. A length of 100 should be ...