The specification limits for a product are 8 cm and 10 cm. A process that produces the product has a mean of 9.5 cm and a standard deviation

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The specification limits for a product are 8 cm and 10 cm. A process that produces the product has a mean of 9.5 cm and a standard deviation of 0.2 cm. What is the process capability, Cpk

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  1. Answer:

    The value of Cpk is 0.83.

    Explanation:

    Given that,

    Upper specification limits = 10 cm

    lower specification limits = 8 cm

    Mean = 9.5

    Standard deviation = 0.2 cm

    We need to calculate the process capability

    Using formula of Cpk

    [tex]Cpk=min(\dfrac{USL-mean}{3\times SD}, \dfrac{mean-LSL}{3\times SD})[/tex]

    Put the value into the formula

    [tex]Cpk=min(\dfrac{10-9.5}{3\times0.2}, \dfrac{9.5-8}{3\times0.2})[/tex]

    [tex]Cpk=min(0.83,2.5)[/tex]

    [tex]Cpk=0.83[/tex]

    Hence, The value of Cpk is 0.83.

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