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Economic statistical design of variable sampling interval X̅ control chart based on surrogate variable using genetic algorithms

Lee T.-H., Hong S.-H., Kwon H.-M., Lee M.

Management and Production Engineering Review

2016

Vol. 7, No. 4

54--64

In many cases, a X̅ control chart based on a performance variable is used in industrial fields. Typically, the control chart monitors the measurements of a performance variable itself. However, if the performance variable is too costly or impossible to measure, and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we present a model for the economic statistical design of a VSI (Variable Sampling Interval) X̅ control chart using a surrogate variable that is linearly correlated with the performance variable. We derive the total average profit model from an economic viewpoint and apply the model to a Very High Temperature Reactor (VHTR) nuclear fuel measurement system and derive the optimal result using genetic algorithms. Compared with the control chart based on a performance variable, the proposed model gives a larger expected net income per unit of time in the long-run if the correlation between the performance variable and the surrogate variable is relatively high. The proposed model was confined to the sample mean control chart under the assumption that a single assignable cause occurs according to the Poisson process. However, the model may also be extended to other types of control charts using a single or multiple assignable cause assumptions such as VSS (Variable Sample Size) X̅ control chart, EWMA, CUSUM charts and so on.

The use of graph grammars for model-based reasoning in diagnostic expert systems

Flasiński M., Lee M.

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Prace Informatyczne

1999

z. 9

147-165

The new approach to a construction of model and qualitative reasoning-based expert systems is presented in the paper. The main idea of the approach is the use of formalisms of the theory of graph languages and automata for defining reasoning schemes that process pre-defined graph-like models of complex systems diagnosed. The main adventage of the approach is the efficiency of such reasoning schemes due to the use of the ETPL(k) graph languages with a polynomial membership problem (Flasiński, Theoretical Computer Science 201 (1998), 189-231).