Intelligent parameter estimation for the power-law non-homogeneous Poisson process using a hybrid ANN–ABC framework

Abstract

Reliability estimation and failure modeling in repairable system design requires accurate models and parameter estimations to determine when failures will occur and when they can be repaired. The objective of this study is to evaluate the use of a Hybrid Artificial Neural Network-Artificial Bee Colony (ANN-ABC) approach to estimate the parameters of the Power Law Non-Homogeneous Poisson Process (PLPNHP) referred to as the Crow AMSAA Model. Additionally, we compare our results with maximum likelihood estimates (MLE) and particle swarm optimization (PSO). We conduct a comparison based on their ability to accurately estimate parameters, predict future events independently and their computation times. We perform a Monte Carlo Study using 1000 iterations and three different expected event counts; 50, 100 and 500. All iterations used a power law shape parameter of 1.4 and scale parameter of 500. A data set consisting of 48 valve seat replacement events and 41 observation ending records from 41 diesel engines was analyzed. Engine specific observation period was included in the likelihood function. Our results show that MLE and PSO have similar levels of estimation accuracy, however, the ANN-ABC had larger estimation errors than both MLE and PSO at a faster level of computational time. At a total number of events equal to 100, the Root Mean Square Error (RMSE) value for the power-law shape parameter was .14117 for MLE, .14103 for PSO and .16711 for ANN-ABC. Our empirical case illustrates the potential of the PLPNHP to describe recurring repair events. However, it is necessary to interpret our comparisons carefully due to differences in methods. In general, the analytical method of MLE was superior to both methods of estimation and efficiency in all comparisons.