Statistical Analysis Of Product's Quality Based On Level Data

Modern manufacturing industry get a large amount of data when they are manufacturing products.To control or improve the quality of the products,it's very necessary to analysis and predict the quality with data by using statistical methods.This dissertation focuses on the products which are assembled with multiple components and the variables of components are marked by level data.The contents of this dissertation mainly has two parts.1.When the distribution of the variables of components is known,one could estimate the parameter of the distribution with level data and thereby simulate the yield of the population using Monte Carlo method.The EM algorithm can hardly get explicit expression of the expectation when the distribution is complicated.The MCEM algorithm has overcome this difficult by giving the approximation of the expectation and can get the maximum likelihood estimation by iteration with level data.This paper has simulated the case with normal distribution.2.If the distribution is unknown,one could classify the qualified products and ones failed the test with the variables related to the quality by using some classification methods.When the data are marked by level,the traditional methods may be inapplicable which usually deal with the continuous quantitative data.This dissertation gives one discriminant method by defining a new distance of the level data based on the frequency of the sample.It turns out that this discriminant method is better than Fisher discriminant method on accuracy.Furthermore,more complicated cases are discussed in this dissertation,that one component has multiple level variables which is a high-dimension problem.Tensor linear discriminant analysis could reduce the dimension with projection matrix.It's popular in pattern recognition which deals with quantitative data like images etc.It may not suit for level data which is one kind of qualitative data.Some adjustment methods are discussed in the end of this paper.