Graphical/Statistical Approach to Repair Limit Replacement Problem

The total time on test (TTT) concept has proved to be a very useful tool in many reliability applications. The graphical solution procedure based on this concept gives geometrical interpretations to the solutions of reliability problems as well as the optimal policies from empirical data directly. In fact, some kinds of reliability models such as age replacement and burn-in problems have been analyzed by applying the TTT concept. In this paper, we discuss the optimal repair limit replacement policy, which determines the timing to stop repairing a unit after it fails. We propose two kinds of solution procedures for the repair limit replacement problem with a time constraint, where one is a straightforward/algebraic procedure and another is a geometrical one based on the TTT concept. Also, we develop a computer software utilizing the computer graphics to calculate the optimal repair limit policy numerically, and refer to its educational effect.