La costruzione razionale delle carte di controllo: Studio di un caso particolare

Abstract

In the first part of this paper the problem is outlined of finding control chart, taking account both of the “a priori” probability that in the long run the productive process is going out of statistical control and of the damage subsequent to a wrong decision. The problem is solved for the simple case of one-sided control of the mean of a normal population. It is shown that a mean value of damage exists wich doesn't depend upon the «a priori» probabilities; under the condition that such a mean value is a minimum, the parameters of the control chart (sample-size and region of acceptance) are defined.

The second part of the paper deals with the computational aspects of the problem. The authors describe concisely the procedure adopted for the numerical solution developing it as a particular application of the geometrical implications of the Lagrange multiplier rule.