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Sagot :
Answer:
From the statements in the question, I and III is CORRECT
Step-by-step explanation:
First we take down the given data from the question for substitution;
Process mean = 16.9 ounces
Lower specification limit = 16.75 ounces
Upper specification limit = 17.05 ounces
Standard deviation = 0.04
Now, we get our Cpk;
Cpk = MINIMUM( (Upper specification limit - mean ) / 3 × Standard deviation), (mean - Lower specification limit) / 3 × Standard deviation) )
so we substitute
Cpk = MINIMUM( ((17.05 ounces - 16.9 ounces) / 3 × 0.04 ounces ), (( 16.9 ounces - 16.75 ounces) / 3 × 0.04 ) )
Cpk = MINIMUM( 0.15 / 0.12 ), ( 0.15 / 0.12 )
Cpk = MINIMUM( 1.25, 1.25 )
Cpk = 1.25
Next the Cp;
Cp = ( Upper specification limit - Lower specification limit ) / ( 6 × standard deviation )
we substitute
Cp = ( 17.05 ounces - 16.75 ounces ) / ( 6 × 0.04 ounces )
Cp = 0.3 / 0.24
Cp = 1.25
Hence;
Cpk calculation is not less than Cp calculation.
Since Cp is greater than 1, the process is cable.
Since the actual process mean is also 16.90 ounces, then the process is centered.
Therefore, From the statements in the question, I and III is CORRECT
The correct statement is "the Cp calculation indicates that the process is capable" and "the process is centered, so the Cp calculation should be used" and this can be determined by using the formula of Cpk and Cp.
GIven :
- Your firm bottles water in plastic bottles labeled for 16.9 ounces.
- The specifications are 16.75 ounces to 17.05 ounces.
- Your filling process has an average fill of 16.90 ounces with a standard deviation of 0.04 ounces.
The formula of Cpk is given below:
[tex]\rm Cpk = minimum\left( \dfrac{Upper \;specification \;limit - mean}{ 3 \times Standard \;deviation)}, \dfrac{ mean - Lower\; specification\; limit} { 3 \times Standard \;deviation}\right )[/tex]
Now, substitute the known terms in the above formula.
[tex]\rm Cpk = minimum \left(\dfrac{17.05-16.9}{3\times 0.04},\dfrac{16.9-16.75}{3\times 0.04}\right)[/tex]
[tex]\rm Cpk = minimum \left(\dfrac{0.15}{0.12},\dfrac{0.15}{0.12}\right)[/tex]
Cpk = 1.25
Now, the formula of Cp is given below:
[tex]\rm Cp = \dfrac{Upper\; specification\; limit - Lower\; specification \;limit} { 6 \times standard \;deviation }[/tex]
Now, substitute the known terms in the above formula.
[tex]\rm Cp = \dfrac{17.05-16.75}{6\times 0.04}[/tex]
Cp = 1.25
So, the correct statement is "the Cp calculation indicates that the process is capable" and "the process is centered, so the Cp calculation should be used".
Therefore, the correct option is D) I and III.
For more information, refer to the link given below:
https://brainly.com/question/15351734
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