An Approximate Solution to the G-Renewal Equation With an Underlying Weibull Distribution

An important characteristic of the g-renewal process, of great practical interest, is the g-renewal equation, which represents the expected cumulative number of recurrent events as a function of time. Just like in an ordinary renewal process, the problem is that the g-renewal equation does not have a closed form solution, unless the underlying event times are exponentially distributed. The Monte Carlo solution, although exhaustive, is computationally demanding. This paper offers a simple-to-implement (in an Excel spreadsheet) approximate solution, when the underlying failure-time distribution is Weibull. The accuracy of the proposed solution is in the neighborhood of 2%, when compared to the respective Monte Carlo solution. Based on the proposed solution, we also consider an estimation procedure of the g-renewal process parameters.