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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. Which of the following statements are TRUE? I The Cp calculation indicates that the process is capable. II The Cpk calculation is less than the Cp calculation. III The process is centered, so the Cp calculation should be used. I only II only III only I and III II and III

Sagot :

Nuhulawal20idn

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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