Maintenance Replication Rate Prediction and Measurement

This paper addresses itself to the special industrial replacement problem of determination of maintenance replication rate and spares provisioning. Because of its great representational flexibility, the quadparametric generalized gamma function1 is assumed as the distribution of life length. Starting with the traditional convolution integral form of the renewal equation, the Laplace transform of the replacement rate is derived. Then, an infinite series representation of this transform is ev lved. Next, an inverse transform is developed which obtains the distributional form for the general term of the series. This turns out to be another generalized gamma function. Hence, the replacement rate has this form of probability density. Finally, the expression for the replacement rate is integrated to obtain the formula for calculating the expected number of replacements in a general period of time t = t1 to t = t2.