Using triangular fuzzy numbers in the tests of control charts for unnatural patterns

The control chart in essence is a set of statistical limits applied to a sequence of points representing a process under study. The data comprising each individual point are random, but the points themselves are plotted in some deliberately chosen non-random arrangement selected to represent the most important variable. The control chart tests the arbitrary or non-random arrangements of points to determine whether they behave as if they were random. If the plotted points indicate nothing but randomness, this tends to show that the variable which formed the base of the arrangement is not a significant variable. On the other hand, if the points indicate that non-randomness has entered the data, this tends to show that the variable on which the arrangement was based is actually a significant variable. The control chart tells when to look for trouble but it cannot, by itself, tell where to look or what cause will be found. The most important inadequacy of control charts is the case where all the points characterizing the process fall inside the limits even though the process is out of control. In such a case, one has an unnatural pattern. Some tests for unnatural patterns are given in most quality control books. These tests are applied by using a control charts of 60 divided into six equal zones. The authors propose an alternative method in this paper. Instead of using six equal zones of 1/spl sigma/ each, the authors use the corresponding degrees of membership of these zones.