Parametric and Semiparametric Competing Risks Models for Statistical Process Control with Reliability Analysis - Mohamed Elfaki, Faiz Ahmed (2004)
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.