Page 191 - Special Topic Session (STS) - Volume 3

STS540 Zhi Song et al.
Optimal design of some distribution-free EWMA
schemes for simultaneous monitoring of location
and scale with dynamic fast initial
response feature
1,3
Zhi Song , Amitava Mukherjee , Jiujun Zhang 3
2
1 Shenyang Agricultural University, Shenyang, China
2 XLRI-Xavier School of Management, XLRI Jamshedpur, India
3 Liaoning University, Shenyang, China

Abstract
This paper proposes a new model to optimally design an exponentially
weighted moving average (EWMA) scheme with dynamic fast initial response
(FIR) feature. An EWMA scheme with the FIR usually detects an initial out-of-
control situation much quicker as compared to a standard EWMA scheme.
Almost all studies related to the effects of FIR features on monitoring schemes
focused on their out-of-control performance. However, when the process
actually operates in control set-up, the FIR feature may increase the number
of false alarms at the early stage of monitoring. In practice, it is important to
restrict the probability of an early false alarm along with improving the out-
of-control performance of a monitoring scheme. Noting this, we propose a
method to optimally design an EWMA scheme with the FIR feature that
guarantees both objectives simultaneously. The proposed method is an
improvement over the classical and popular statistical design approach. A
data-dependent estimation approach based on Kernel density estimation for
the optimal parameter is evaluated and discussed. We apply the proposed
optimization model to some distribution-free FIR-based EWMA schemes for
joint monitoring of location and scale. Simulation results exhibit that our
proposed procedure generally performs well under various continuous
distributions.

Keywords
Statistical process control; Exponentially weighted moving average; Fast initial
response; Nonparametric; False alarms

1. Introduction
Statistical process monitoring (SPM) schemes play a transformative role for
the improvement of product and service quality. Exponentially weighted
moving average (EWMA) monitoring schemes are widely used for the
detection of small shifts in process parameters. Sometimes it is important to
implement a monitoring scheme that is more sensitive than traditional EWMA
schemes and allows even quicker detection of a shift, see for example, Lucas
and Saccucci [1]. One can easily achieve this by incorporating the fast initial

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