Estimation of Error From Treating Travel Time as Additional Repair Time

We consider the unavailability of a two-unit parallel system with one traveling repair person, and common statistically independent exponential unit life lengths. The unavailability can be approximated by treating travel time as an additional repair time for each unit failure before returning to the duplex state, where the two units are functioning. This is an approximation because travel time extends the repair time only for the first unit failure before returning to the duplex state. We derive error bounds for this overestimation for arbitrary travel and repair time distributions. The error bounds show that the percent overestimation has a theoretical maximum of 27% (and can be as low as zero when the travel time distribution is degenerate at zero). Thus, this paper has important contributions for practice because it provides insight to the errors that occurred due to using an approximation.