On the Availability of 1-out-of-2 Standby Systems

The accuracy of the approximation (a1 +a2)/(1 + a1a2) for the availability of a 1-out-of-2:G standby system with unit availabilities a1, a2 is examined. The units have exponential failure and repair time distributions. The approximation is exact for equal repair rates. An expression is developed in terms of a1 and a2 only for the case of equal failure rates, but the approximation is remarkably accurate in this case. A computer run of 5000 evaluations, using random values of failure rates from a uniform distribution from 0 to 0.1 and repair rates from 0 to 1 showed a total range of error from 3.5% over-estimation to 5.2% under-estimation of the true value and a rms error of 0.73%. The approximation is therefore quite good enough for rough work in the early stages of system planning. It is useful because it allows studies to be made entirely in terms of availability, leaving detailed trade-offs between reliability and maintainability until later.