Necessary and sufficient condition for the stability of process variability

Nowadays complexity in industries are increasing, hence the need of tools to serve these complexities are inevitable. It is difficult to find a big scale industry that only monitoring one critical to quality (CTQ) parameter. In statistical process control (SPC) point of view the use of univariate statistical process control (USPC) is no longer appropriate. Therefore, multivariate statistical process control (MSPC) is the more appropriate tools to use. Unfortunately, the MSPC tools available today are not reliable in terms of the appro- priateness, the desired probability false alarm, and the in-controlled process. All the tools available for monitoring process control is based on two major measures, gen- eralize variance (GV) and vector variance (VV) which later will be shown to be not reliable as they only provide the necessary chart, not necessary and sufficient chart. This thesis will overcome those problems by proposing a new reliable necessary and sufficient chart based on two distance measures, Mahalanobis distance-based and Euclidean distance-based. In this thesis we will construct the multivariate process variability (MPV) monitoring based on distance measure with its cut-off values. It will cover both the theoretical and simulation aspects. Control chart will also be provided for the new proposed methods for both constant sub-group size and general sub-group size. Industrial ex- amples will also be provided for the sake of comparison with the currently available tools. Lastly, the root causes analysis will be carried out. It is an analysis to identify the cause of out of control (OOC) signal. Industrial examples will also be provided for root causes analysis. The newly proposed MPV monitoring tools are considered very good as they can solve the reliability problems by providing the necessary and sufficient chart and able to detect the OOC signal from the simulation studies and industrial examples provided.