Investigation of a fit of beta and normal distributions to a product of beta distribution.

Abstract

Excessive costs prohibit the Department of Defense and industry from testing entire systems to obtain estimates of system reliability. Thus, individual component tests must be combined in such a way as to yield an accurate estimate of the system reliability. Assuming each component reliability to have a prior distribution which is beta distributed, Bayesian techniques result in the posterior distributions also being beta distributed. The system reliability for a series system would then by the product of the posterior distributions. Computer simulation techniques were used to determine the system reliability distribution for a series system of beta distributed components. Method of Moments techniques were then used to fit beta and normal distributions to the system distribution. The twentieth percentile points of the fitted and the actual distributions were then compared as a measure of accuracy of the fit. The fit of the beta distribution proved to be accurate for all parameter ranges and number of components in each system. The fit of the normal distribution was accurate only when used with limited parameter values.