09/01/1990 09:00 AM
Computer Science
It is often assumed that the failure and repair rates of components are exponentially distributed. This hypothesis is testable for failure rates, though the process of gathering the necessary data and reducing it to a usable form can be difficult. While no amount of testing can prove that a sample is drawn from an exponential distribution, the hypothesis that a population distribution is exponential can in many cases be rejected with confidence. For this study, data were collected from as many hosts as was feasible using only data that could be obtained via the Internet with no special privileges or added monitoring facilities. The Internet was used to poll over 100,000 hosts to determine the length of time that each had been up, and again polled after several months to determine average host availability. A surprisingly rich collection of information was gathered in this fashion, allowing estimates of availability, mean-time-to- failure (MTTF) and mean-time-to-repair (MTTR) to be derived. The measurements reported here correspond with common experience and certainly fall in the range of reasonable values. By applying an appropriate test statistic, some of the samples were found to have a realistic chance of being drawn from an exponential distribution, while others can be confidently classed as non-exponential. With very large sample sizes, sufficient evidence could be accumulated to reject the exponential hypothesis. However, for moderately-sized samples, it was often not possible to exhibit the deviation from exponentiality, lending credence to the common practice of assuming the MTTF is exponentially distributed.