Term of Award

Summer 2023

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Charles Champ

Committee Member 1

Divine Wanduku

Committee Member 2

Andrew Sills

Abstract

The exponentially weighted moving average (EWMA) chart X for monitoring a pro-
cess mean was introduced by Roberts (1959)[1]. Various authors have studied this
chart. Shamma and Shamma (1992)[19] introduced an EWMA of an EWMA chart,
referred to as the double EWMA chart. Since then the EWMA of the EWMA of
the EWMA (triple EWMA) chart and the EWMA of the EWMA of the EWMA
of the EWMA (quadruple EWMA) charts have been introduced into the literature.
Their claims are that the double EWMA X chart outperformed the EWMA chart
for the monitoring the process mean. Further it was claimed that the triple EWMA
X chart outperformed the double EWMA X chart and the quadruple EWMA chart
outperformed the triple EWMA X chart. We demonstrate that an EWMA X chart
can be designed that outperforms the double EWMA X chart. We show this using
simulation. The EWMA X has been used to predict the change point. We provide
a method using the likelihood function to predict the change point. A comparison is
made with the Shewhart X chart.

OCLC Number

1411251293

Research Data and Supplementary Material

No

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