Optimal economic solution for a normal sampling intervals method in quality control

The main purpose of this paper is to present an optimal economic solution for a different adaptive sampling method that is highly intuitive in its nature: the normal sampling intervals (NSI) method.

Considering costs associated with sampling, false alarms and imperfect operation per unit of time, the paper presents a new optimal simple solution that minimizes the expected total cost per cycle. This NSI method involves the density function of the standard normal variable, assuming that the distribution of averages is normal or approximately normal (on the basis of the central limit theorem). It depends on a single scale parameter while other methods depend on various parameters.

When this expected total cost associated with the new NSI method is compared with the fixed (FSI) and variable sampling intervals (VSI) methods, in identical situations, it may be seen that, in general, it is lower (and may be much lower) and, also, that it is lower for a wider range of changes in terms of quality. This feature is particularly important because, in practice, the degree of change that occurs is not known, so this greater robustness in terms of performance is relevant.

In the practice, the minimization of total expected costs is an important point of view in the life of companies, concerning quality and statistical process control (SPC). The paper holds that this NSI method has a great degree of potential, in particular considering that in industrial processes there is growing recourse to automated systems for the collection and analysis of samples, and thus there are no special additional costs associated with labour, management or administration.

The great advantages of this NSI method are its highly intuitive nature and the fact that it enables generally much better results to be achieved as compared with the use of FSI and VSI methods. An optimal economic solution for this NSI method is presented in this paper.