xyz snack pack., is attempting to determine an existing weight machine is capabl

Question

xyz snack pack., is attempting to determine an existing weight machine is capable of packing a snack bag. weight is a key specification set to be 5 plus/minus 0.5 OZ. After a trail run on this machine, C-Spec has determined that the machine has a sample of 5.1 OZ with a standard deviation of 0.1 OZ.

(a) Calculate the Cpk for this machine.

(b) Can XYZ snack packs Inc, use this machine to package this snack? Why or Why not?

(c) What are the option to reduced the DPMO (defects per million opportunities) in the context?

(d) If the specification limits were changed to 5 plus/minus 0.1 OZ and other things remain the same, what will be the DPMO?

Explanation / Answer

Lower Specification Limit, LSL = 5-0.5 = 4.5

Upper Specification Limit, USL = 5+0.5 = 5.5

Mean, m = 5.1

Std dev, s = 0.1

(a) Cpk = MIN{(USL-m)/3s, (m-LSL)/3s}

= MIN{(5.5-5.1)/(3*0.1), (5.1-4.5)/(3*0.1)}

= MIN{1.33, 2}

= 1.33

(b) For 6-sigma, Cpk should be at least 2. In this situation, Cpk is less than 2, therefore, XYZ snack packs Inc should not use this machine, if it needs 6-sigma quality.

(c) An option to reduce DPMO is to reduce the variability (standard deviation) of the process.

(d) Cp = (USL-LSL)/6s = (5.1-4.9)/(6*0.1) = 1/3

DPMO = (1-NORMSDIST(Cp))*10^6 = (1-NORMSDIST(1/3))*10^6 = 369441

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