| Confidence intervals are an important part of the statistical world. Confidence intervals are used to better understand the uncertainty in a point estimate and can be used to perform hypothesis testing. Drawing on recent theoretical developments, generalized confidence intervals are adapted for new problems in capability analysis and variance component analysis.; In this research, generalized confidence intervals are created to compare capability indices to determine if there has been a process change. Two popular capability indices, Cpk and Cpm, are considered. The generalized confidence interval technique is compared with four other methods.; In addition, a technique for estimating the variability contributed by a fixed factor is created. Traditionally, only random factors have associated variance estimates. The generalized confidence interval is compared to a Modified Large Sample approach with an adjustment for the fixed factor.; A generalized confidence interval is also developed to statistically test if an improvement in the process has changed the total variability. The specific scenario considered is a balanced, mixed model. These intervals are compared with a Modified Large Sample approach for a two-factor model and an interval based on the Satterthwaite approach for a three-factor model.; In the validation step, the performance of the different intervals for the three application environments are compared with respect to the stated confidence level, average interval lengths, and the power associated with a particular hypothesis test. For all scenarios, a designed experiment is conducted. For the generalized confidence interval method, 10,000 simulated values are used to calculate the intervals. For each confidence interval method considered, 2000 simulation runs are generated for each treatment in the experiment.; Although this technique is viable for the testing of capability indices, it is not the preferred method of those studied. However, it suggests that the generalized confidence intervals may be used in other applications related to capability indices. The generalized confidence interval technique is found to be the preferred method for the other two scenarios: estimating fixed factor variability and estimating a change in total variability. |
