An approach to identification and optimization in quality control

Abstract

Comparing the procedure described here with the standard procedures used in quality control, we found that we are better off. The above procedure in fact is an adaptive one, while those are not. There is however a cost to be paid for adaptivity, namely the computing we need for each cycle.

The way we approached the identification of the possibly time-varying parameter p is not the only possible one, as also a regression analysis could serve the scope. If however the variation of p shows a rather irregular pattern, a regression analysis could not be sufficiently adequate and to obtain better adaptivity, a procedure as the one described would be preferable.

Looking for possible generalizations of the above method, we remark that for each lot, the quality control problem as described here may also be visualized as a particular decision process over a Markov chain, where transition probabilities are only partially known and may also vary with time. We therefore think the method may be extended to such more general problems.

As the restriction, that the expected ratio of defectives in the final production should not exceed the value p_d, involves the unknown parameter p, one could also think of approaching similarly stochastic programming problems with restrictions involving unknown and possibly time-varying parameters.