| In this dissertation we have developed methods to statistically evaluate and analyze form and profile errors based on discrete measurement data from a coordinate measuring machine (CMM). The definitions of form and profile errors in the current standards assume ideal inspection systems. However, there is no such ideal inspection systems actuality. Therefore, we establish practical mathematical definitions of form and profile errors which can be applied for continuous or discrete measurements. They consider the characteristics of manufactured surfaces by assuming that the deviations from the manufactured surface follow a normal distribution. These definitions can serve as practical guideline for real inspection systems.;In current CMM practice, there are no commonly accepted sample sizes for estimating form and profile errors which have a statistical basis. Practically, sample size planning is important for the geometric tolerance inspection systems using a CMM. We determine and validate appropriate sample sizes for form and profile error estimation. Also, we develop form and profile errors estimation methods with certain confidence levels based on the obtained sample sizes in various form and profile errors: straightness, flatness, circularity, cylindricity, and bicubic surface. The determination of sample sizes uses a new approach based on the maximum expectation of the prediction interval width at a certain confidence level. The maximum prediction interval is a new development which covers the variations of manufactured surfaces. This approach for estimating form and profile errors, based on the proposed sample sizes, is superior to the current practice because it leads to better measurement approximations. The proposed sample sizes and estimating methods are verified by a simulation study and case studies of real part measurements.;We further develop a method for analyzing manufacturing processes and tolerance capabilities. This method is based on the study of process capability ratio. To compensate for uncertainty in estimated process capability ratios, we find the upper and lower limits with a certain confidence level depending on the purpose of the usage of the ratio. These limits can be used not only for the form and profile errors estimation problems but also for more general process and tolerance analysis problems. |
