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ABSTRACT
The usual practice in control charts is to assume that the chart parameters are known or can be accurately estimated from in-control historical samples and the data are free from outliers. Both of these assumptions are not realistic in practice: a control chart may involve the estimation of process parameters from a very limited number of samples and the data may contain some outliers. In order to overcome these issues, in this article, we develop an Exponentially Weighted Moving Average (EWMA) median chart with estimated parameters to monitor the mean value of a normal process. We study the run length properties of the proposed chart using a Markov Chain approach and the performance of the proposed chart is compared to the EWMA median chart with known parameters. Several tables for the design of the proposed chart are given in order to expedite the use of the chart by practitioners. An illustrative example is also given along with some recommendations about the minimum number of initial subgroups m for different sample sizes n that must be collected for the estimation of the parameters so that the proposed chart has identical performance as the chart with known parameters. From the results we deduce that (i) there is a large difference between the known and estimated parameters cases unless the initial number of subgroups m is large; and (ii) the difference between the known and estimated parameters cases can be reduced by using dedicated chart parameters.
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Notes on contributors
Philippe Castagliola
Philippe Castagliola graduated (Ph.D. 1991) from the UTC (Université de Technologie de Compiègne, France). He is currently professor at the Université de Nantes, Institut Universitaire de Technologie de Nantes, France, and he is also a member of the IRCCyN (Institut de Recherche en Communications et Cybernétique de Nantes), UMR CNRS 6597. His research activity includes development of new SPC techniques.
Petros E. Maravelakis
Petros E. Maravelakis is an Assistant Professor in the Department of Business Administration at the University of Piraeus, Greece. He is an Associate Editor of the Journal of Quality Technology and Quantitative Management. His main research fields are statistical process control (control charts and process capability indices) and reliability.
Fernanda Otilia Figueiredo
Fernanda Otilia Figueiredo received her master's and Ph.D., both in Probability and Statistics, from the Faculty of Sciences, Lisbon University (FCUL). She is currently an Assistant Professor at Faculdade de Economia da Universidade do Porto (FEP.UP) and her research activity is developed as a member of Centro de Estatística e Aplicações da Universidade de Lisboa (CEAUL). Her areas of research are statistical quality control (main area), extreme value theory, data analysis, sampling techniques, location/scale estimators, and applications of statistics in economics.