Complete parametric estimation of the Weibull model with an optimized inspection interval

The time for the occurrence of failure in a machine has been predicted using a Weibull model. The model uses the information of past failures and fits it into a probability distribution that yields a prediction of future failures. The operational data used for analysis is a series of failure times procured from an industrial machine used in a manufacturing system. This paper discusses three methods of parametric estimation of the Weibull distribution, namely the maximum likelihood estimation, the method of moments, and the least squares method, and compares their errors in estimation. In addition, for the maximum likelihood estimation method, we identify the parametric estimation error for various observation lengths to show the tradeoff between inspection load and error, and a time-to-failure prediction based on the parameters estimated.