Applying Bootstrap Method to the Types Ⅰ-Ⅱ Errors in the Measurement System

摘要

This paper attempts to evaluate different methods of calculating the type-Ⅰ and type-Ⅱ errors in the measurement system. Furthermore, we apply the Bootstrap method to construct the confidence intervals for the type-Ⅰ and type-Ⅱ errors. Also, the proposed method is compared with the generalized inference method. Several factors such as the sample size, the measurement error, the process mean, and the process variation are simulated to validate the performance. The simulation results show that both methods almost have the same performance. In addition, we develop a computer program that can evaluate the error of measurement system without changing information or data. Two case studies of the nano measurement data are used to demonstrate the application. The simulation results indicate that the sample size has an influence for all cases. The type-Ⅰ and type-Ⅱ errors are decreased when the measurement error is increased. The type-Ⅰ and type-Ⅱ errors are affected by the measurement error, the process mean, and the process deviation. The case studies show that the development of nano technology requires the immediate attention of the measurement capability.