Application of Complex Lifetime Models for Analysis of Product Reliability Data

Abstract

Proper data collection and analysis are very important for effective investigation of product reliability. Data is critical for building and selecting suitable statistical models and model provides new insights for improvements to maintenance and management operations in manufacturing industries. Regarding variations in product quality and reliability, component nonconformance and assembly error are two important problems which occur frequently in manufacturing industries. In such situations, the complex lifetime models are required for analyzing product reliability data. This thesis proposes a general model for modeling the effects of quality variation. This model includes the mixture model and competing risk model as the special cases. The thesis applies these models for analysis of three sets of product reliability data - Aircraft windshield failure data, Battery failure data and Hydraulic pump failure data. A set of competitive 2-fold and 3-fold mixture models are considered for modeling the data sets. The maximum likelihood estimation method via the Expectation Maximization (EM) algorithm is applied mainly for estimating the parameters of the models and reliability related quantities. For the Aircraft windshield failure data, results indicate that the method of estimation with the EM algorithm procedure is better than the Weibull Probability Paper (WPP) plot procedure. For Battery failure data, based on the measures of lifetime quantities, it can be concluded that data without maintenance information provides approximately similar results with the data having maintenance information. According to the graphical representation and estimated values of different model selection criterions, we found that the 3-fold Weibull-Normal-Exponential mixture model can be selected as the best model for the Hydraulic pump failure data. The selected distribution for pumps with assembly errors failure mode is Normal and the distribution for pumps without assembly error failure mode is Weibull. According to the optimization of the proposed objective function, the 3-fold Weibull mixture model gives a bit larger optimal maintenance period, however the Weibull-Normal-Exponential model shows a reduction in the maintenance cost for the pump. Simulation studies are conducted for investigation the performances of the proposed models and methods. The simulation results indicate that the proposed models and methods of estimation are applicable for analyzing 2-fold and 3-fold mixture models for censored product reliability data with incomplete information. The results presented in this thesis would be useful for managerial implications in assessing and predicting the reliability and maintenance cost of the products. Keywords: Product reliability, Data analysis, EM algorithm, Mixture model, Competing risk model, Simulation.