Detecting
a change in a scale parameter – a combination of SPC and
change point procedures
Edna Schechtman*,
G. Bandner and S. Meginy
*Department
of
Industrial Engineering and Management.
Abstruct -
The primary objective is to compare between statistical and
SPC methods for monitoring process variance via an extensive
simulation. The statistical methods are Cumulative Sum (CUSUM)
and Likelihood Ratio Test (LRT), and the SPC methods are
Moving Range (MR) and Exponentially Weighted Mean Squared
deviation (EWMS). In addition, we examined a combination of
both statistical and SPC methods, denoted by ‘‘Schechtman on
S2’’. Random series were generated from three distributions:
normal, Poisson and lognormal. The parameters of interest
were: series length, size of the change, and location. The
criteria for comparison were: rates of false alarms, powers
and Mean Absolute Deviation (MAD). The main outcomes and
results of our simulations show that when the distribution
is normal, all procedures are slightly conservative.
However, when the distribution is not normal, the rates of
false alarm go up to around 0.8 for all but Schechtman on
S2. Assuming normal distribution, EWMS and CUSUM are
powerful for detecting changes, and LRT is capable of
estimating the time of change. Therefore, it is worthwhile
to complement SPC methods by adding LRT, which provides a
good estimate of the point of change. If there are n
observations per time point, Schechtman on S2 performs well
for all distributions under study.
International Journal of
Production Research, Vol. 45, No. 23, 1 December 2007,pp.
5535–5545
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