Alcune relazioni generali tra funzioni descrittive degli effetti di un piano di campionamento per attributi nel controllo della qualità

In this paper the author proposes to determine some general relationships linking the functions that express the effectiveness of a sampling plan in lot acceptance sampling. The result is obtained through the introduction of a function which provides the expected number of units, to be drawn from a lot of given quality, with reference to accepted lots only. This function, together with the OC function, appears in the expression of the ASN, ATI and AOQ functions, which provide the economic design of a sampling plan. In addition, the author defines two functions by introducing some costs per unit of the inspection, substitution and utilization of defective items. The first one expresses the producer's expected gain from the application of a sampling plan to replace one hundred per cent inspection of lots, the second one expresses the consumer's expected gain from the application of a sampling plan to replace the acceptance of lots without inspection. For whichever type of sampling plan, single, double, multiple or sequential, it is sufficient to determine the form of the first function mentioned in the opening paragraph and the OC function, to express the remaining functions. Some examples are provided to clarify the proposed procedure. Of particular importance is the application in the case of sequential sampling plans where, through the use of some results related to random walks with two absorbing barriers, it is possible to obtain approximate expressions of all the above functions