Suatu Pendekatan Langsung Dan Universal Mentaksir Prestasi Proses
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Date
1998-05
Authors
Syed Ahmad, Khatijah
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Abstract
The use of process capability indices to assess process performance has stirred interest
as well as controversy in the late 80's and early 90's. There are those who doubt their
effectiveness since these indices are not deterministic but rather random in nature and
hence their interpretation depends on the shape of the underlying distribution. Others
are skeptical as to how a single number can effectively summarise the behaviour of a
process distribution and fully capture the performance of the process. Others who were
enthusiastic about improving previous indices have transformed what began as a simple
index into various forms that only serve to increase confusion among practitioners since
their interpretation have become more blurred with each modification to the original
index.
We propose an approach whereby the two main criteria used to assess process
performance ate addressed separately and suggest the use of Cy for measuring process
yield or the proportion of output that meets some specification interval [LSL, USL], and
the use of C1 for measuring process targeting or nearness of process mean J.L to a target
value T. These two measures have an intuitive appeal since their values can be directly
translated in terms of percentage of process yield and the relative distance of J.l from T,
respectively, when the underlying distribution is known. Besides that, the natural
estimators of Cy and C1 have large-sample inferential properties that are applicable
universally.By demonstrating a close association between the ratio K = o I a, where o denotes the
mean absolute deviation of X, and the tail-end probabilities of density curves for a wide
spectrum of symmetric continuous distributions that are smooth and unimodal, we offer
the interpretation of Cy for different density curves. Another quantity that also gives an
indication of the nature of density curves at the tails is p, a quantity that involves the
sample range. For asymmetric distributions we select Q = (J..L- median) I a over two
other viable measures of skewness after carrying out a preliminary study on the
distributional characteristics of all three, and demonstrate the close association between
the tail-end probabilities, Q and K.
Using extreme quantiles of K:, Q and p obtained through simulation, we showed how
it is possible to narrow down the list of plausible density curves to get appropriate
interpretations of Cy and C1• For future work, we foresee how this approach can be
simplified by using a simple computer software which will select appropriate density
curves given a data set.
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