## Measurement Error

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.