ABSTRACT
Let us consider Figure 5.1, in which the true value of the quality characteristic,
x
, falls in the acceptance region. Given that the true value is
x
, the distribution of the observed value,
Y
, is normally distributed with a mean at
x
and a variance equal to the variance of the measurement error,
V
, which is A part of this conditional distribution of
Y
given
x
falls in the rejection region, depending upon how close
x
is to the specification limits. This is represented by the shaded area in Figure 5.1, which is the conditional probability of rejecting a component, given that the true value of the characteristic is
x
. The probability of rejecting a good unit is the probability that
Y
falls in the rejection region when
X
is in the acceptance region. Let this probability be denoted by
P
. It is derived as follows:
(5.5)
σv 2.