DETERMINING OUT-OF-CONTROL VARIABLE(S) IN A MULTIVARIATE QUALITY CONTROL CHART FOR INDIVIDUAL OBSERVATIONS
DETERMINING OUT-OF-CONTROL VARIABLE(S) IN A MULTIVARIATE QUALITY CONTROL CHART FOR INDIVIDUAL OBSERVATIONS
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Date
2014-08
Authors
AGOG, NATHAN SAMUEL
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Abstract
The decomposition of the Hotelling’s T2 statistic into orthogonal components is
considered to be one of the most effective methods for detecting variable(s) responsible for an
out-of-control signal. In this work, an extension of the T2 decomposition from three variables
(p=3) to four (p=4) variables, where the number of decompositions increased from 3! = 6 to 4! =
24 and the decomposition terms also increased from 18 to 96 terms having 32 distinct terms were
provided. These distinct terms are the ones that were examined for possible contribution to the T2
signal. A dataset obtained from an Indomie company in Northern Nigeria was used to assess the
validity of constructed model by demonstrating the invariance property of the Hotelling’s T2
statistic. The model was also used to identify the variable(s) that significantly contribute to an
out-of-control signal. By comparing the critical values with the corresponding T2 values, we
were able to detect variation between the four (4) variables in their mean and also their variancecovariance
structure.
Description
A THESIS SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES,
AHMADU BELLO UNIVERSITY, ZARIA NIGERIA
IN PARTIAL FULFILMENT FOR THE AWARD OF MASTER OF SCIENCE (M.Sc)
DEGREE IN STATISTICS,
DEPARTMENT OF MATHEMATICS
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA.
AUGUST, 2014
Keywords
OUT-OF-CONTROL, VARIABLE, MULTIVARIATE QUALITY, CONTROL CHART, INDIVIDUAL OBSERVATIONS