301. The run sum t control chart for monitoring process mean changes in manufacturing.
- Author
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Sitt, C., Khoo, Michael, Shamsuzzaman, M., and Chen, Chung-Ho
- Subjects
MANUFACTURING processes ,CONTROL theory (Engineering) ,ROBUST control ,STANDARD deviations ,SAMPLING errors ,MARKOV processes - Abstract
The $$ \overline{X} $$ type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the $$ \overline{X} $$ type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL and lower minimum cost. The run sum t chart surpasses the $$ \overline{X} $$ type charts by having lower ARL when the charts are optimally designed for large shifts but the run sum $$ \overline{X} $$ and EWMA $$ \overline{X} $$ prevail for small shifts. In terms of minimum cost, the $$ \overline{X} $$ type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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