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For monitoring processes, exponentially weighted moving average (EWMA) control charts have been found to be very powerful and reliable tools. Meanwhile, some processes require great attention at the startup to ascertain that the processes are free from any disturbances. In this article, we propose a generalized time-varying fast initial response for EWMA control charts. This chart is a special case of the previously proposed time-varying EWMA control chart. The proposed scheme is highly sensitive in detecting small shifts in a given process, particularly at the process startup. The proposed chart is compared with its counterparts using the zero state average run length. We also show an application of the proposed EWMA chart to a real-life situation. K E Y W O R D Sexponentially weighted moving average control charts, fast initial response, generalized timevarying fast initial response, process with startup problems, average run length, statistical process monitoring 1 GFIR-EWMA Control Charts.

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This paper deals with the study of minimum and maximum principle sufficiency properties for nonsmooth variational inequalities (in short, NVI) by using gap functions. Several characterizations of these two sufficiency properties are provided. We also discuss the error bound for nonsmooth variational inequalities. Two open questions are given at the end.

In this paper, we consider a system of vector variational inequalities and a system of nonsmooth variational inequalities defined by means of Clarke directional derivative. We also consider the Nash equilibrium problem with vector pay-offs and its scalarized form. We present some relations among these systems and problems. The existence results for a solution of system of nonsmooth variational inequalities are given. As a consequence, we derive an existence result for a solution of Nash equilibrium problem with vector pay-offs.