An important characteristic of the fuzzy control charts
produced is that the central line, the control limits as well
as the data used are of fuzzy nature. In this section, a new
approach is developed which provides the ability of
determining the tightness of inspection, based on
estimations of control parameters from statistical data.
Let 0,1 be a control parameter used to decide if an
exceeding sample should indeed be rejected or not. We
will give an explicit measure of whether a sample value
has exceeded a control limit. Value of can be set
according to how strict the results are desired to be.
Let be a non asymptotic fuzzy estimator for the
mean value of a subgroup m of size n. The sample's
distribution is considered random e.g. binomial and the
-cuts of can be constructed as shown in previous
section. Thus we obtain all closed intervals
= , , 0,1 L R (20)
that needs to be compared against fuzzy upper control
limits (Eq. (12), Eq. (15)) and fuzzy lower control limits
(Eq. (10), Eq. (13)). For this purpose, we produce a
fuzzy measure inspired from fuzzy hypothesis testing [1]
taken a step further in order to be applied in fuzzy
control charts. The accept/reject decision is made
according to the following rule:
• H0 : the sample is in-control if / A A R T , therefore
accepted
• H1 : the sample is out-of-control if A A R T / > ,
therefore rejected
AT is calculated as the complete area of fuzzy number
:
R
T
L
A = u du