Application of multivariate statistical methodologies to body-in-white assembly process.

The primary objective of this research is to develop and apply methodologies to monitor, detect, and diagnose quality problems in the body-in-white assembly process. The important issues are to detect and resolve problems as quickly as possible using all the relevant data available. To accomplish these objectives, three multivariate statistical tools are adopted in this work. These are: (1) principal component models, (2) multivariate cusum charts, and (3) canonical correlation analysis. A brief description of the process is given in Chapter 1 of the dissertation. Deficiencies in the current practice are stated to motivate the research involved. In Chapter 2, the principal component model is introduced. The use of principal component models in quality control is described. The deviation of an observation from the target value is partitioned into two mutually orthogonal vectors. The first vector, $\{\bf f}$, consists of the principal component scores. This vector represents the deviation due to systematic variation in the process. The second vector, ${\bf r}$ is called a residual vector and it represents the noise in the process. Procedures to obtain the statistical lengths of these vectors are developed. Multivariate cusum charts are used to enhance the detection rate of a problem in the process. Two multivariate cusum charts are introduced in Chapter 3. Monte Carlo simulation is used to determine the upper limits for these cusum charts. Simulation is also used to obtain the average run lengths (ARL) to assess the performance of the cusum charts. The cusum charts were shown to have a shorter ARL than the Shewhart charts at deviations equal to or less than two standardized units. Canonical correlation analysis is introduced in Chapter 4. This analysis is used to determine the inter-dependency between two sets of measurements. In the current example, variation of the full body is related back to variation of the underbody for root cause analysis. Canonical correlation analysis for two sets of principal component scores is developed. The methodology is used in an out-of-control case study to determine which process station is the root cause of the problem.PhDApplied SciencesIndustrial engineeringMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130999/2/9825256.pd