Access Type
Open Access Dissertation
Date of Award
January 2011
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Industrial and Manufacturing Engineering
First Advisor
Kai Yang
Abstract
This research aims to introduce a number of contributions for enhancing
the statistical performance of some of Phase II linear and polynomial profile monitoring techniques.
For linear profiles the idea of variable sampling size (VSS) and variable
sampling interval (VSI) have been extended from multivariate control charts to the profile monitoring framework to enhance the power of the traditional T^2 chart in detecting shifts in linear quality models. Finding the optimal settings of the proposed schemes has been formulated as an optimization problem solved by using a Genetic Approach (GA). Here the average time to signal (ATS) and the average run length (ARL) are regarded as the objective functions, and ATS and ARL approximations, based on Markov Chain Principals, are extended and modified to capture the special structure of the profile monitoring. Furthermore,the performances of the proposed control schemes are compared with their fixed sampling counterparts for different shift levels in the parameters. The extensive comparison studies reveal the potentials of the proposed schemes in enhancing the performance of T^2 control chart when a process yields a simple linear profile.
For polynomial profiles, where the linear regression model is not sufficient, the relationship between the parameters of the original and orthogonal polynomial quality profiles is considered and utilized to enhance the power of the orthogonal polynomial method (EWMA4). The problem of finding the optimal set of explanatory variable minimizing the average run length is described by a mathematical model and solved using the Genetic Approach. In the case that the shift in the second or the third parameter is the only shift of interest, the simulation results show a significant reduction in the mean of the run length distribution of the EWMA4 technique.
Recommended Citation
Abdella, Galal M., "An optimization of on-line monitoring of simple linear and polynomial quality functions" (2011). Wayne State University Dissertations. 365.
https://digitalcommons.wayne.edu/oa_dissertations/365