Authors: Kouroush Jenab, Amir Kazeminia, Diane Suk-Ching Liu
Addresses: Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada. ' Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada. ' Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada
Abstract: Fitting probability distributions, like Weibull distribution to data related to electronic components, is an essential activity in warranty forecasting model and lifetime analysing. This paper presents an evolutionary statistical approach (ESA), which yields both accurate and robust parameter estimates of lifetime distribution function for two parameters Weibull. Almost all estimation methods produce accurate results for the large sample size; however, more care must be taken in the selection of the estimation methods for extremely small sample size. It is known, for example, maximum likelihood estimation (MLE) estimates of the shape parameter for the Weibull distribution are biased for small sample sizes and the effect can be increased depending on the amount of censoring. In the Weibull distribution, the scale and shape parameters are calculated as an evaluation function by minimising the product of sum of squared errors (SSE) on both XY axes. Using SSE, the least squares estimation (LSE) and real-coded genetic algorithm methods, a simulation is carried out to compare the quality of these approaches. The results show that the ESA is superior to LSE and real-coded genetic algorithm methods, specifically, for a small sample size of data related to electronic components.
Keywords: evolutionary statistical approach; Weibull distribution; warranty forecasting models; bath tub curve; computational approaches; probability distributions; lifetime analysis; parameter estimates; sample size; maximum likelihood estimation; censoring; scale parameters; shape parameters; sum of squared errors; least squares estimation; real-coded genetic algorithms; electronic components; industrial engineering; systems engineering.
International Journal of Industrial and Systems Engineering, 2010 Vol.6 No.1, pp.62 - 78
Published online: 06 Jul 2010 *Full-text access for editors Access for subscribers Purchase this article Comment on this article