The Performance of the MEWMA Control Chart when Parameters are Estimated

• Published in: Communications in statistics. Simulation and computation Vol. 39; no. 9; pp. 1803 - 1817
• Main Authors: Mahmoud, M. A., Maravelakis, P. E.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 29.10.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applications; Average run length; Control charts; Estimation effect; EWMA; Exact sciences and technology; Experimental design; Linear inference, regression; Mathematics; Multivariate control charts; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Reliability, life testing, quality control; Sciences and techniques of general use; Statistical process control; Statistics; Studies; Parameter estimation; Average run length; Multivariate analysis; Variance; Estimation effect; Industry; Engineering; Optimal strategy; Sampling; Statistical process control; 62P30; Control chart; Smoothing methods; Covariance analysis; Moving average; EWMA; Statistical estimation; Covariance matrix; Variance analysis; Mean estimation; Statistical method; Statistical regression; Multivariate control charts; Smoothing; Experimental design; Numerical simulation; Optimal design(statistics); 62H99; Physical Sciences
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2010.518269

In the present article, we study the effect of estimating the vector of means and variance-covariance matrix in the performance of the multivariate exponentially weighted moving average (MEWMA) control chart. We show through simulation that the performance of the MEWMA control chart is affected when the parameters are estimated compared to the known parameters case. We show also that larger number of Phase I samples are required to achieve the expected statistical performance of the MEWMA chart when smaller smoothing constants are used in designing it. Under some sampling scenarios, more than 2,500 samples are needed to estimate the unknown parameters to satisfy the intended statistical performance. The control limit that achieves the desired in control ARL when estimating the parameters is computed in several cases and formulas used to find approximately its values are given. Finally, an optimal design strategy for the MEWMA chart with estimated parameters is presented.