Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis

The work in this thesis is concerned with the development of techniques for the assessment of statistical process control in data that include censored observations. Various regression models with censored data are presented and we concentrate on four competing risks models namely, two parametric Co...

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Main Author:	Mohamed Elfaki, Faiz Ahmed
Format:	Thesis
Language:	English English
Published:	2004
Subjects:	Process control - Statistical methods. Reliability (Engineering) - Statistical methods.
Online Access:	http://psasir.upm.edu.my/id/eprint/5553/1/FSAS_2004_27.pdf
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spelling	my-upm-ir.55532013-05-27T07:23:40Z Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis 2004 Mohamed Elfaki, Faiz Ahmed The work in this thesis is concerned with the development of techniques for the assessment of statistical process control in data that include censored observations. Various regression models with censored data are presented and we concentrate on four competing risks models namely, two parametric Cox’s model that is, Cox’s with Weibull distribution, Cox’s with exponential distribution and two semiparametric Cox’s model with subdistribution function that is, the weighted score function (W) and censoring complete (CC). The Expectation Maximization (EM) algorithm is utilized to obtain the estimate of the parameters in the models. A generated data where the failure times are taken as exponentially distributed are used to further compare these two parametric models. From the simulation study for this particular case, we can conclude that Weibull distribution describes well the nature of the model concerned as compared to the exponential distribution in terms of the mean value of parameter estimates, bias, and the root means square error. Plots of survival distribution function against failure time are used to examine the predicted survival patterns for the two types of failures. In this thesis we develop a modified Fine and Gray methods to increase the sensitivity of the models and these methods are tested and compared. A simulation data using subdistribution function for the two types of failure are carried out to compare the performance of the modified model. The results of the study indicate the models show better result compared to Fine and Gray models. However, the weighted score function (W) shows better result compared to the censored complete data (CC). Residual-based approaches are used to assess the validity of the two models (MW, CC) assumptions. Plots of this residual against failure time are used to investigate whether important explanatory variables have been omitted from the model. The study also carries out an investigation of the causes of failure for statistical process control. The x chart, R chart and Cp, and Cpk are examined for the possibility of being used to detect the state of control of the covariates in the two competing risks models (Cox’s with Weibull distribution (PHW2) and modification of weighted score function (MW)). The result of this study indicates that both models are successful in investigating the causes of failure for statistical process control. However, the results from the real data sets which involves the measurement of stress against three covariates (aluminum, wood and plastic) showed that the tubes wrapped on plastic mandrel have excellent crashworthiness performance with respect to the x chart, R chart, Cp, and Cpk. Process control - Statistical methods. Reliability (Engineering) - Statistical methods. 2004 Thesis http://psasir.upm.edu.my/id/eprint/5553/ http://psasir.upm.edu.my/id/eprint/5553/1/FSAS_2004_27.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Process control - Statistical methods. Reliability (Engineering) - Statistical methods. Faculty of Science and Environmental Studies English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Process control - Statistical methods. Reliability (Engineering) - Statistical methods.
spellingShingle	Process control - Statistical methods. Reliability (Engineering) - Statistical methods. Mohamed Elfaki, Faiz Ahmed Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
description	The work in this thesis is concerned with the development of techniques for the assessment of statistical process control in data that include censored observations. Various regression models with censored data are presented and we concentrate on four competing risks models namely, two parametric Cox’s model that is, Cox’s with Weibull distribution, Cox’s with exponential distribution and two semiparametric Cox’s model with subdistribution function that is, the weighted score function (W) and censoring complete (CC). The Expectation Maximization (EM) algorithm is utilized to obtain the estimate of the parameters in the models. A generated data where the failure times are taken as exponentially distributed are used to further compare these two parametric models. From the simulation study for this particular case, we can conclude that Weibull distribution describes well the nature of the model concerned as compared to the exponential distribution in terms of the mean value of parameter estimates, bias, and the root means square error. Plots of survival distribution function against failure time are used to examine the predicted survival patterns for the two types of failures. In this thesis we develop a modified Fine and Gray methods to increase the sensitivity of the models and these methods are tested and compared. A simulation data using subdistribution function for the two types of failure are carried out to compare the performance of the modified model. The results of the study indicate the models show better result compared to Fine and Gray models. However, the weighted score function (W) shows better result compared to the censored complete data (CC). Residual-based approaches are used to assess the validity of the two models (MW, CC) assumptions. Plots of this residual against failure time are used to investigate whether important explanatory variables have been omitted from the model. The study also carries out an investigation of the causes of failure for statistical process control. The x chart, R chart and Cp, and Cpk are examined for the possibility of being used to detect the state of control of the covariates in the two competing risks models (Cox’s with Weibull distribution (PHW2) and modification of weighted score function (MW)). The result of this study indicates that both models are successful in investigating the causes of failure for statistical process control. However, the results from the real data sets which involves the measurement of stress against three covariates (aluminum, wood and plastic) showed that the tubes wrapped on plastic mandrel have excellent crashworthiness performance with respect to the x chart, R chart, Cp, and Cpk.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohamed Elfaki, Faiz Ahmed
author_facet	Mohamed Elfaki, Faiz Ahmed
author_sort	Mohamed Elfaki, Faiz Ahmed
title	Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
title_short	Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
title_full	Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
title_fullStr	Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
title_full_unstemmed	Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis
title_sort	parametric and semiparametric competing risks models for statistical process control with reliability analysis
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science and Environmental Studies
publishDate	2004
url	http://psasir.upm.edu.my/id/eprint/5553/1/FSAS_2004_27.pdf
_version_	1747810450382258176

Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis

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