The Prediction and Measurement of System Availability: A Bayesian Treatment

For any physical system there is always some degree of uncertainty regarding the values of the parameters governing the performance of that system. Uncertainties in the values of the failure rate ¿ and the repair rate ß reflect themselves in an uncertainty in the value of the point availability, A = ß/(ß + ¿). Treating these uncertain parameters as random variables, exact expressions for the mean, variance, and distribution of the point availability are derived by combining the distributions of the failure and repair rates. Hence we can construct estimates and confidence statements for the availability which are consistent with the equivalent statements on the failure-rate and repair-rate parameters. Exact mean and variance results are also provided for mission, transient, and other time-dependent availability expressions. The acquisition of failure and repair data introduces additional information as well as additional uncertainties. A Bayes transformation is developed which utilizes the two data sets to readily convert prior estimates and confidence statements on the availability into posterior versions. This particular paper is restricted to a basic model involving an alternating sequence of independent exponentially distributed operational and repair intervals with the respective rate parameters described by distinct gamma distributions. For this model the point availability proves to have an Euler distribution.