Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/43544
- Title
- Generalized control charts for non-normal data using g-and-k distributions
- Author/Creator
-
Haynes, Michele;
Mengersen, Kerrie;
Rippon, Paul
- Institution
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- Description
- Statistical control charts are often used in industry to monitor processes in the interests of quality improvement. Such charts assume independence and normality of the control statistic, but these assumptions are often violated in practice. To better capture the true shape of the underlying distribution of the control statistic, we utilize the g-and-k distributions to estimate probability limits, the true ARL, and the error in confidence that arises from incorrectly assuming normality. A sensitivity assessment reveals that the extent of error in confidence associated with control chart decision-making procedures increases more rapidly as the distribution becomes more skewed or as the tails of the distribution become longer than those of the normal distribution. These methods are illustrated using both a frequentist and computational Bayesian approach to estimate the g-and-k parameters in two different practical applications. The Bayesian approach is appealing because it can account for prior knowledge in the estimation procedure and yields posterior distributions of parameters of interest such as control limits.
- Relation
- Communications in Statistics: Simulation and Computation Vol. 37, Issue 9, p. 1881-1903
- Publisher Link
- http://dx.doi.org/10.1080/03610910802255170
- Date
- 2008
- Publisher
- Taylor & Francis
- Keyword(s)
-
average run length (ARL);
Bayesian estimation;
control chart;
g-and-k distributions;
non-normality;
robustness
- Resource Type
- journal article
- Identifier
- http://hdl.handle.net/1959.13/43544
- Identifier
- ISSN:0361-0918
- Reviewed
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