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Monitoring Generalized Linear Profiles Using Change-Point Approach

Shadman, Alireza | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46400 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Mahlooji, Hashem; Akhavan Niaki, Taghi
  7. Abstract:
  8. There are many cases in industrial and non-industrial sections where the quality characteristics are in the form of profiles. A profile is the functional relationship between a response variable and one or more predictor variables used to describe the quality of a process. Profile monitoring is the implementation of statistical process control techniques for this purpose. According to the type of relationship between response variable and predictor variables, profiles are classified into many categories such as: simple linear profiles, multiple linear profiles, nonlinear profiles and generalized linear profiles. Most of the research efforts in the area of profile monitoring have been conducted under the assumption that the response variable is continuous with the normal behavior. In practical applications, however, it is not uncommon to encounter quality characteristics that are either count data or categorical in nature. Generalized Linear Models (GLMs) include many commonly encountered types of dependent variables and error structures as special cases. In addition to regression models for continuous dependent variables, models for rates and proportions, binary, ordinal and multinomial variables, and counts can be handled as GLMs. In recent years, some works have been done in the special cases of GLM profiles (for example in the binary profiles) both in phase I and phase II. Our major motivation for undertaking the current work is to try to provide a unified framework for developing phase I and phase II control charts for monitoring Generalized Linear Profiles (GLPs). Such a unified framework will not only include some of the existing charts as special cases but provide a systematic approach for developing new control charts. The fundamental underpinning of our proposed framework is based on a change point model coupled with a generalized linear model (GLM) used to describe the relationship between the response variable and one or more predictor variables. We propose both the phase I and phase II control charts based on the change point approach and then evaluate the performance of our control charts relative to the existing charts under binomial and Poisson profiles. The proposed control charts both in phase I and phase II have a good performance relative to competing method based on the simulated results. Some diagnostic procedures are also discussed. A real data set obtained from a test lab concerning the dispersion of carbon black filler in a rubber mix is used to demonstrate how the proposed charts can be used in practical applications. Some future research directions are also discussed
  9. Keywords:
  10. Profile Monitoring ; Statistical Process Control ; Change Point ; Control Chart ; Generalized Linear Profiles (GLPs)

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