Optimal repair/replacement policy for a general repair model (Q2726725)

The repair degree \(\theta= 0\) corresponds to replacement, \(\theta=1\) to minimal repair and \(0<\theta< 1\) to a general repair. The general repair model under consideration has the form of recurrence \(V_n= V_{n-1}+ \theta X_n\), where \(V_n\) is the virtual age at the failure time after the \(n\)th repair and \(X_n\) is the length of the operating time between \((n-1)\)th and \(n\)th repair. Here, \(\theta\) is a random function of virtual age and random repair cost. The authors obtain the cost-optimal policy using the method of dynamic programming. An illustrative numerical example is included.