Statistical Analysis of Manufactured Materials

Abstract

This work is about the application of Poisson models for count data on surface defects of manufactured and machined sheet steel. Based on a hypothetical polishing process, different models of Poisson processes were set up and analysed. In addition, research was conducted on linear models with factors of similar tool cutting processes.The relevant theory on Poisson processes and basic statistical tests, such as distribution tests, was developed and then applied on the data set. The nonparametric run tests of independence of the data and the Chi-squared distribution test rejected the hypothesis of a homogeneous Poisson process. The Bayesian Poisson-Gamma model didn’t show significant differences between informative and non-informative priors. The test results of a simulated homogeneous Poisson process confirmed the conclusions drawn from the tests carried out at the beginning. For the inhomogeneous Poisson process, a change point model was designed to fit the data well. The maximum posterior estimates of the Bayesian model, calculated by using a MCMC Gibbs sampler, showed similar results. Furthermore, a marked Poisson process model which categorised the defects into two types of size, was analysed. The marking parameter was estimated and a nonparametric runs test confirmed the randomness of the marking. Then, simulated data of the marked process were compared to the original data set. Moreover, the problem of estimating the repair time of all defects was modelled by a compound Poisson process. The estimate had a high variance. In addition, a study was found on the application of a 23 factorial design for the analysis of a grinding process. The basic approach could also be applied to the process in question.