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27 September, 20:04

Assume in a cookie packaging machine, the process average (the average weight of the packages) is 10.0 ounces and the process standard deviation is. 12 of an ounce. The customer is asking for a target value of 10.1 ounces with tolerances of plus or minus. 5 ounce. Is the machine capable of meeting customer expectation? (Support your answer.)

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  1. 27 September, 20:08
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    the machine is capable of meeting customer expectation see the explanation below

    Explanation:

    For this question, to determine if the machine is capable of meeting customer expectation, we are going to calculate the process capability (Cpk) of cookie packaging machine.

    Cpk = min (Cpl or CPU)

    Where Cpl = (USL - Mean) / 3 * standard deviation

    Cpu = (mean - LSL) / 3 * standard deviation

    Where

    The process average (Mean) = 10.0 ounces

    Tolerance = 0.5 ounces

    Process Standard deviation (sd) = 0.12

    Customer's Target value = 10.1 ounces (plus or minus 0.5 ounce)

    Therefore

    Upper standard limit (USL) = 10.1 + 0.5 = 10.6 ounces

    Lower standard limit (LSL) = 10.1 - 0.5 = 9.6 ounces

    So

    Cpl = (USL - Mean) / 3 * standard deviation

    = (10.6 - 10.0) / 3 * 0.12

    = 0.6/0.36

    = 1.67

    Cpu = (mean - LSL) / 3 * standard deviation

    = (10.0 - 9.6) / 3 * 0.12

    = 0.4/0.36

    = 1.11

    Since cpk = min (cpl, cpu)

    Cpk is taken as 1.11

    the machine is capable of meeting customer expectation
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