High School

H₂O produces containers of drinking water for water coolers. The stated weight for a container of water is 100 pounds. Customers will accept an occasional container weighing as little as 96 ​pounds, as long as the average weight is at least 100 pounds. At the same​ time, H₂O​ doesn't want to give away​ water so it has set an upper tolerance limit of 104 pounds. The current filling process has an actual process mean of 101 pounds and a standard deviation of 0.65 pounds.
What is the process capability ratio (Cp)? (Round to 2 decimal places.)

Answer :

The formula used is Cp = (USL - LSL) / (6σ). Substituting the values, Cp is found to be 2.05.

Find the process capability ratio (Cp), which is calculated using the formula:

  • $$Cp = [tex]\frac{{USL - LSL}}{{6σ}}$$[/tex]

Where:

  • USL = Upper Specification Limit
  • LSL = Lower Specification Limit
  • σ = Standard Deviation

In this case:

USL = 104 poundsLSL = 96 poundsσ = 0.65 pounds

Substituting these values into the formula:

  • $$Cp = [tex]\frac{{104 - 96}}{{6 \times 0.65}}$$ = $$Cp = \frac{8}{3.9}$$[/tex]
  • $$Cp = 2.05$$

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