When the nonconformities are independent, a multivariate control chart for
nonconformities called a demerit control chart using a distribution approximation
technique called an Edgeworth Expansion, is proposed. For a demerit control chart,
an exact control limit can be obtained in special cases, but not in general. A proposed
demerit control chart uses an Edgeworth Expansion to approximate the distribution of
the demerit statistic and to compute the demerit control limits. A simulation study
shows that the proposed method yields reasonably accurate results in determining the
distribution of the demerit statistic and hence the control limits, even for small sample
sizes. The simulation also shows that the performances of the demerit control chart
constructed using the proposed method is very close to the advertised for all sample sizes.
Since the demerit control chart statistic is a weighted sum of the
nonconformities, naturally the performance of the demerit control chart will depend on
the weights assigned to the nonconformities. The method of how to select weights
that give the best performance for the demerit control chart has not yet been addressed
in the literature. A methodology is proposed to select the weights for a one-sided
demerit control chart with and upper control limit using an asymptotic technique. The
asymptotic technique does not restrict the nature of the types and classification scheme
for the nonconformities and provides an optimal and explicit solution for the weights.
In the case presented so far, we assumed that the nonconformities are
independent. When the nonconformities are correlated, a multivariate Poisson
lognormal probability distribution is used to model the nonconformities. This
distribution is able to model both positive and negative correlations among the
nonconformities. A different type of multivariate control chart for correlated
nonconformities is proposed. The proposed control chart can be applied to
nonconformities that have any multivariate distributions whether they be discrete or
continuous or something that has characteristics of both, e.g., non-Poisson correlated
random variables. The proposed method evaluates the deviation of the observed
sample means from pre-defined targets in terms of the density function value of the
sample means. The distribution of the control chart test statistic is derived using an
approximation technique called a multivariate Edgeworth expansion. For small
sample sizes, results show that the proposed control chart is robust to inaccuracies in
assumptions about the distribution of the correlated nonconformities. / Graduation date: 2004
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/29937 |
| Date | 05 September 2003 |
| Creators | Chattinnawat, Wichai |
| Contributors | Wurl, Robin C. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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