Estimating the time of a change in Poisson rate parameter with a genetic algorithm

Although control charts can indicate the out-of-control process, the indication is usually with a noticeable delay. Identifying the real time of the change in a process would provide a starting point for further investigation of an assignable cause. In this paper, we apply the genetic algorithm to estimate the change point of a Poisson process. For this purpose an objective likelihood function was considered such that its global maximum can find the optimized parameters approximately for the step change model in Poisson process. Through extensive simulations, the performance of proposed change point estimation method is analyzed and compared with the MLE, designed for step change for a wide range of change in Poisson rate parameter. The results show that the proposed estimator outperforms the MLE with regard to speed. Furthermore, it has a smaller variance for the values of increases in Poisson rate parameter.