In a textile company, it is important that the acidity of the solution used to dye fabric

Question:

In a textile company, it is important that the acidity of the solution used to dye fabric be within certain acceptable values. Data values are gathered for a control chart by randomly taking four observations from the solution and determining the average pH value and range. After 25 such samples, the following summary information is obtained.

The specifications for the pH value are 7.5 ±0.5.
TABLE 7-1

(a) Find the and /?-chart control limits.
(b) Find the 1ó and 2ó X-chart limits.
(c) What fraction of the output is nonconforming (assuming a normal of pH values)?
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