Optimal Multivariate Control Chart Designs for Continuous Process Monitoring

In this research, the aim is to investigate ways of designing efficient and effective methods for monitoring continuous processes especially for the manufacturing environment. One of the possible means is through the use of standard process control methodologies such as the multivariate exponentially weighted moving average (MEWMA) control chart. Such control charts have been proven to improve the process efficiencies in continuous manufacturing processes. However, the standard MEWMA chart employs a fixed sample size at equal sampling interval. The drawback of such setting is that the chart developed is slow in detecting shifts in the process' trend when operating in the continuous manufacturing environment. Consequently, this research proposed to investigate the feasibility of adding adaptive sample size or adaptive sampling interval as new features in the MEWMA control chart with the aim to improve the performance of the said chart. An optimal statistical design of the adaptive MEWMA control chart is done by minimizing the out-of-control performance measure which will be modelled as a nonlinear minimization problem, subjected to some specific constraints, in which the performance measure will be derived by using a Markov chain approach. A new procedure for the optimal design will be provided for both zero and steady-state modes. Based on this new procedure, a heuristic search will be performed to generate the optimal chart parameter combination of the control chart (i.e. smoothing constant, small sample size, large sample size, long sampling interval, short sampling interval, warning limit and control limit) for different desired values of decision variables such as number of quality characteristics, in-control performance measure, in-control average sample size, in-control average sampling interval and process mean shift. This nonlinear constrained optimization algorithm aims at optimizing the statistical performance. This proposed algorithm can assist the end user in both optimally designed and implementing the control chart. The aforementioned approach will be adopted in the designs of the (i) standard MEWMA control chart; (ii) MEWMA chart with variable sample size (VSS); and (iii) MEWMA chart with variable sampling interval (VSI). After that, the statistical performances of these control charts will be compared in order to check the effectiveness of these control charts in improving process productivity and preventing defects rising to a higher level. Furthermore, percentiles or probabilities of run length distribution will be computed to provide a better understanding of the performance for the said chart and this helps to increase the end user's confidence in using the proposed chart.