Multivariate quality control: statistical performance and economic feasibility

Wichita State University (Ph.D.)-- College of Engineering, Dept. of Industrial and Manufacturing EngineeringShewhart control charts have been used to monitor uncorrelated quality characteristics. Advancement in manufacturing technology and increased complexity of products and systems raise the need to monitor correlated characteristics. The literature provides numerous examples of research pertaining to the misuse of traditional charts when the charted characteristics are correlated. This research is aimed at quantifying the statistical and economic consequences of utilizing the Hotelling’s T2 multivariate control chart as an alternative to the traditional Shewhart chart. Consequently, there were two main objectives of this research. The first objective was to identify the levels of correlation between the charted variables where the statistical performance of the x chart deteriorates compared to that of an equivalent T2 chart. Statistical analyses of simulated data generated under varying levels of process and chart variables indicated a correlation threshold value of ± 0.48, outside of which the T2 chart is better. The second objective was to assess the economic feasibility of utilizing a T2 chart as an alternative to the two x(bar) charts. Knappenberger and Grandage’s (1969), and Montgomery and Klatt’s (1972) economic design models for and T2 charts were utilized, respectively, in constructing an incremental cost model to examine the cost and worth of switching from the x(bar) charts to a T2 chart under specified levels of process and chart parameters. Results indicated that the switch to multivariate T2 chart would result in economic savings under all levels of the process and chart variables considered. It is hoped that this research will encourage practitioners to implement appropriate multivariate statistical techniques in monitoring their processes