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 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

A Bayesian approach to competing risks model with masked causes of failure and incomplete failure times

We present a Bayesian approach for analysis of competing risks survival data with masked causes of failure. This approach is often used to assess the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection in production engineering. In this study, Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. Markov chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. -e effectiveness of the proposed approach is illustrated with simulated and production engineering applications

Analysis and ratio of linear function of parameters in fixed effect three level nested design

The aims of this study are first to build the linear model of the fixed effect three level nested design. The model is not full column rank and has a constraint on its parameters; second is to transform the non full column rank model with a constraint into full column rank and unconstraint model by using method of model reduction; and third is to derive statistics for testing various hypotheses by using Generalized Likelihood Ratio (GLR) test and to derive the ratio of linear function of parameters by using Fieller’s Theorem . Based on the full column rank and unconstraint model the analysis to be conducted is : to estimate the parameters, to derive statistics for testing various hypotheses and to derive confidence intervals of the ratio of the linear function of parameters. The estimation of parameters and the statistics for testing some hypotheses are unbiased. Based on the simulation results, it can be shown that the tests are unbiased and in line with the criteria given by Pearson and Please. The simulation results for the (1-α) confidence interval of the ratio of the linear function of parameters tau (τi), beta (βj(i)) and gamma (γk(ij)) are presented for different values of ρ’s and in all cases the values of ρ’s are contained in the 95% confidence intervals

Cox's model for prison partly interval censored data

The term survival analysis has been used in examines and models the time until the events occur. The most common tool for studying the dependency of survival time on predictor variables is Cox model proportional hazards regression model. In this paper we present a simple modification of Cox’s proportional hazards model using the partial likelihood principle technique based on Newton Rapson method. Simulation is conducted based on prison partly interval censored data set with particular sample sizes to evaluate the performance of the proposed model, and it shows that the model is feasible and works well

Time series modeling and forecasting of the consumer price index Bandar Lampung

The aims of this study are to find the best Time Series model for forecasting the Consumer Price Index (CPI). To find the best model, first we evaluate the stationary of the data by using time series plot, Autocorrelation Function (ACF), and Unit root Test. Then the Time Series model was found by using ACF and Partial Autocorrelations Function (PACF). The best model was found by using the criteria: Mean Squares Error (MSE), Akaike Information Criteria (AIC) and Bayesian Information Criterion (BIC. Based on this criteria the best modelfound in this paper is ARIMA (1,1,0) compare to ARIMA (0,1,1), and ARIMA(1,1,1)

BT-201: Investigation of the spider web for antibacterial activity

Spiders build their webs with a material called silk. Spider silk contain protein fiber that have many advantages and functions. One of them is to capture their prey such as flies, insects, and others. The needs on the research of antibacterial activity are important for human health because of importance of finding a new cure for some diseases that occur because of microorganisms. Some of the microorganisms, especially bacteria are becoming resistant to many antibacterial agents. The purpose of this new investigation was to determine if spider webs exhibit antibacterial properties. In order to determine antibacterial properties, the spider webs were extracted using different solvents such as methanol, ethanol, acetone, and water in different conditions (extraction time, and concentration used for optimization). These extracts were screened for antibacterial activity using disc diffusion assay. Two bacteria were used in the antibacterial assay namely Bacillus subtilis, and Escherichia coli. The determination of spider webs exhibiting antibacterial properties was based, at least in this study, solely upon the definite appearance of inhibition zone around the well of plates. In screening, acetone solvent was shown the best for antibacterial activity compare to other solvents with 10 mm of diameter of inhibition zone for Bacillus subtilis and 9 mm of diameter of inhibition zone for Escherichia coli. In optimization, the maximum inhibition zone on the Bacillus subtilis was 15 mm at a time of 48 hours and concentration of 0.035 g/ml. Meanwhile, the maximum diameter of inhibition zone on the Escherichia coli was 12 mm at a time of 48 hours and concentration of 0.035 g/ml. Therefore, this study showed that spider webs could be potential source of new antibacterial agents

Markov chains analysis and mechanism of migration in Indonesia in the period 1980-2010

The aims of this study are to find the Markov Chain model for the migration in Indonesia, to find the properties of the transition probability matrices, to find the stationary probability, and to find the behavior of the mechanism of the migration in 1980,1990, 2000, 2010 and the combined data from 1980 to 2010. In the Markov Chain model the states are Sumatra, Jawa, Kalimantan, Sulawesi, and Maluku and Papua and are abbreviated as S, J, K, SL and OI respectively. From the transition probability matrices, the states are communicated to each other and irreducible. From the results of analysis, there are similar stationary probability within the states Jawa, Sulawesi and Maluku and Papua, but slightly change in the Sumatra and Kalimantan. From the stationary probability results it shows that in the long run that the stationary probability of migration enter Sumatra decrease from 0.3895 in 1980 to 0.2720 in 2010. On the other hand, the stationary probability of migration enter Kalimantan increase from 0.0726 in 1980 to 0.1537 in 2010. From the analysis of mechanism of migration in 1980,1990, 2000 and 2010. Jawa becomes the main destination of migration from other islands. The people from Sumatra, if they migrate high probability they will migrate to Jawa. On the other hand, the people from Jawa, if they migrate high probability they will migrate to Sumatra. The people from Kalimantan, if they migrate high probability they will migrate to Jawa or Sulawesi in 1980 and in 2010, but high probability only to Jawa in 1990 and in 2000. The people from Sulawesi, if they migrate high probability they will migrate to Jawa, Kalimantan or Maluku and Papua in 1980 and in 1990, but in 2000 and in 2010, high probability they will migrate to Kalimantan and Maluku and Papua. The people from Maluku and Papua, if they migrate high probability they will migrate to Sulawesi or Jawa

Experimental design for scientists and engineers

This book is intended as an intermediate text for students in experimental design. The following can benefit from it if they have attended an introductory course in experimental design: •Undergraduate majors and postgraduate students in engineering, biotechnology, psychology, education and agriculture •Medical students •Graduate students who need an overview of the major topics in experimental design •Researchers and practitioners in different fields of study who need a comprehensive reference when conducting their experiment