This research proposes the variance estimation method of Pareto data and to compare three variance estimation methods. Those methods are simple method the adjusted variance method with term (n - 1)/n and the adjusted variance method with term (n - 2)/n. The research was considered by the absolute of bias (|Bias|) the mean absolute errors (MAE) and the mean square errors (MSE) of variance estimator. This research used Monte Carlo Simulation method. Results of this research show that the |Bias| of simple method is the lowest for almost all conditions. We can arrange the methods as follows: the adjusted variance method with term (n - 1)/n and the adjusted variance method with term (n - 2)/n respectively. For all situations the MAE and MSE the of adjusted variance method with term (n - 2)/n is the lowest. We can arrange the methods as follows: the adjusted variance method with term (n - 1)/n and simple method respectively.

The objectives of this research are to propose the mode estimation method of Inverse Gaussian data and to compare three mode estimation methods. Those methods are simple method adjusted mode method with term (n+1)/n and adjusted mode method with term (n+2)/n. The performance of each method can be measured by the absolute bias (|Bias|) and the mean square errors (MSE). This study was performed by using different sample sizes (n) of 5 10 20 30 and 50 whereas the parameter  is fixed to be 1 and parameters  are fixed to be 1 3 5 10 15 and 20. This research used the Monte Carlo Simulation technique. The experiment was repeated 50000 times for each condition. The results showed that the adjusted mode method with term (n+2)/n gave the lowest value of |Bias| and MSE in most of the criterions of sample sizes and parameter values.

The objectives of this research are to propose a proper model for detecting defective machines in auto parts factories to apply the proposed model to the defective product data and to investigate the factors influencing on the machine producing defective products. A Bayesian hidden Markov model (HMM) is adopted. The results show that if the number of defective products increases the machine will be in the hidden bad state. The probability of changing from a hidden bad state to a hidden good state is higher than the probability of changing from a hidden good state to a hidden good state. The highest probability that the machine will be in a good state is at the work process 4 followed by 1 3 and 2 respectively. The highest probability that the machine will be in hidden good state is at the Worker no. 10 followed 9 3 12 7 2 1 6 11 4 8 and 5 respectively and The highest probability that the machine will be in the hidden good state is at the product type 1 followed by 2 and 3 respectively.

The objectives of this research are to propose a proper model for defective products in an autoparts manufacturing industry to apply the proposed model to the defective products data to investigate the factors related to the machines producing defective products and to compare the proposed model with the generalized estimating equations model (GEE). The proposed model is a generalized linear mixed model (GLMM) in which the dependent variables have a Poisson distribution. The parameter are estimated using a Bayesian method. The data were collected from 12 machines 15 days for each machine from an autoparts manufacturing factory. The data collection dates vary depending on the working steps and the product types. The results show that the proposed model fits the data. The factors related to the machines producing defective products are working steps workers and product types. According to the estimates of the factors effects the working step producing the largest number of defective products is the working step 2 followed by the working steps 3 1 and 4 respectively. The worker producing the largest of defective products is the worker 4 followed by the workers 10 5 8 6 2 3 1 7 and 9 respectively. The product type 3 has the largest number of defective products followed by the product types 2 and 1 respectively. If the population-averaged effects are focused the GEE is applied. However the subject-specific is focused the GLMM is applied.