Some remarks on the physical models concerning two different approaches to inference in statistical process control |
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Authors: | Angelo Zanella |
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Institution: | (1) Instituto di Statistica, Università Cattolica del S. Coure, Largo Gemelli, 1-20123 Milano, Italy |
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Abstract: | Summary For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available
knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities
of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewhart's control
charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully
justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence
of time increasing hazard rates, Shewhart's control charts should be completed by a preventive intervention rule (preventive
maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized
by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients.
By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation
error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter
estimation and the definition of the optimum control rule. |
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Keywords: | rupture control charts preventive maintenance dynamic instability equation error adaptive control |
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