91Ó°ÊÓ

In case of ahighspecification limit,

if the process is focused, it will be calculated as follows

Z value x sample standard deviation + revised process average = 2.4

Here, Z =?

Sample standard deviation = 0.2096

The revised process mean = 1.9

Therefore, Z x 0.2096 + 1.9 = 2.4 ……. (1)

0.2096Z = 2.4 - 1.9

0.2096Z = 0.5 …………..… (2)

Z = 0.5 / 0.2096

Z = 2.385.

The probability of Z being 2.385 is 0.9914 from the standard distribution table.

As a result, the fraction of output greater than 2.4 mm is 1 - 0.9914 = 0.0086.

In the case of the lower specification limit, the possibility that the thickness will be maximal up to 1.4 mm if the process is centered is as follows:

Z value x sample standard deviation + revised process average = 1.4.

Here, Z =?

Sample standard deviation = 0.209.

The revised process mean = 1.9.

= Z x 0.2096 + 1.9 = 1.4 ……. (1)

0.2096Z = 1.4 - 1.9

0.2096Z = - 0.5……………… (2)

Z = 0.5 / 0.2096

Z = - 2.385

As a result, the fraction of output greater than 1.4 mm is 0.0086.

The fraction of output is expected to be out of tolerance.

As a result, the fraction of output expected to be more than 1.4 mm = 0.0086.

And the fraction of output expected to be higher than 2.4 mm = 0.0086.

Therefore,

The fraction of output expected to be more than 1.4 mm + the fraction of output expected to be higher than 2.4 mm

= 0.0086 + 0.0086

= 0.0172

= 1.72%.

The fraction of output expected to be out of tolerance is 1.72%.