243.87 and 132.37 thts the answer
The lines that intersect is B
Complete Question
A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?
Answer:
The value required is
Step-by-step explanation:
From the question we are told that
The upper specification is ![USL = 1.68 \ mm](https://tex.z-dn.net/?f=USL%20%20%3D%20%201.68%20%5C%20mm)
The lower specification is
The sample mean is
The standard deviation is ![\sigma = 0.03 \ mm](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%200.03%20%5C%20mm)
Generally the capability index in mathematically represented as
![Cpk = min[ \frac{USL - \mu }{ 3 * \sigma } , \frac{\mu - LSL }{ 3 * \sigma } ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%20%5Cfrac%7BUSL%20-%20%20%5Cmu%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%20%2C%20%20%5Cfrac%7B%5Cmu%20-%20LSL%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%5D)
Now what min means is that the value of CPk is the minimum between the value is the bracket
substituting value given in the question
![Cpk = min[ \frac{1.68 - 1.6 }{ 3 * 0.03 } , \frac{1.60 - 1.52 }{ 3 * 0.03} ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%20%5Cfrac%7B1.68%20-%20%201.6%20%7D%7B%203%20%2A%20%200.03%20%7D%20%20%2C%20%20%5Cfrac%7B1.60%20-%20%201.52%20%7D%7B%203%20%2A%20%200.03%7D%20%5D)
=> ![Cpk = min[ 0.88 , 0.88 ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%200.88%20%2C%200.88%20%20%5D)
So
![Cpk = 0.88](https://tex.z-dn.net/?f=Cpk%20%20%3D%200.88)
Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2
Now let assuming that
![\frac{\mu - LSL }{ 3 * \sigma } = 2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmu%20-%20LSL%20%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%3D%20%202)
So
![\frac{ 1.60 - 1.52 }{ 3 * \sigma } = 2](https://tex.z-dn.net/?f=%5Cfrac%7B%201.60%20-%20%201.52%20%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%3D%20%202)
=> ![0.08 = 6 \sigma](https://tex.z-dn.net/?f=0.08%20%3D%206%20%5Csigma)
=> ![\sigma = 0.0133](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%200.0133)
So
![\frac{ 1.68 - 1.60 }{ 3 * 0.0133 }](https://tex.z-dn.net/?f=%5Cfrac%7B%201.68%20%20-%201.60%20%7D%7B%203%20%2A%20%200.0133%20%7D)
=> ![2](https://tex.z-dn.net/?f=2)
Hence
![Cpk = min[ 2, 2 ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%202%2C%202%20%5D)
So
![Cpk = 2](https://tex.z-dn.net/?f=Cpk%20%20%3D%202)
So
is the value of standard deviation required
Answer:
a book is something you read a notebook is something you write in.
Step-by-step explanation: