A weibull process failure mechanism for the economic design of MEWMA control charts

The design parameters of the multivariate exponentially weighted moving average (MEWMA) control chart may be chosen according to economic and/or statistical considerations. The economic model proposed for the design of the MEWMA chart assumes a Markovian process failure mechanism following an exponential distribution. We assess the sensitivity of the resulting economic design for the MEWMA to deviations from this assumption. In particular, the generalization, from an exponential to a Weibull distribution of process failure, is used to study the selection of MEWMA chart parameters given process cost and time information. We conclude that the quality of the resulting design (in terms of expected cost) is not substantially affected by mis-specification of the distribution of process failure.