Approximation of mean time between failure when a system has periodic maintenance

This paper describes a simple technique for estimating the mean time between failure (MTBF) of a system that has periodic maintenance at regular intervals. This type of maintenance is typically found in high reliability, mission-oriented applications where it is convenient to perform maintenance after the completion of the mission. This approximation technique can greatly simplify the MTBF analysis for large systems. The motivation for this analysis was to understand the nature of the error in the approximation and to develop a means for quantifying that error. This paper provides the derivation of the equations that bound the error that can result when using this approximation method. It shows that, for most applications, the MTBF calculations can be greatly simplified with only a very small sacrifice in accuracy.