The Good Chocolate Company makes a variety of chocolate candies, including a 12-

Question

The Good Chocolate Company makes a variety of chocolate candies, including a 12-ounce chocolate bar (340 grams) and a box of six 1-ounce chocolate bars (170 grams). a.Specifications for the 12-ounce bar are 328 grams to 352 grams. What is the largest standard deviation (in grams) that the machine that fills the bar molds can have and still be considered capable if the average fill is 340 grams? (Round your intermediate calculations to 2 decimal places and final answer to 3 decimal places.) Standard deviation grams b.The machine that fills the bar molds for the 1-ounce bars has a standard deviation of .84 gram. The filling machine is set to deliver an average of 1.03 ounces per bar. Specifications for the six-bar box are 155 to 185 grams. Is the process capable? Hint: The variance for the box is equal to six times the bar variance. Yes No c.What is the lowest setting in ounces for the filling machine that will provide capability in terms of the six-bar box? (Round your intermediate calculations to 2 decimal places and final answer to 3 decimal places.) Lowest setting ounces?

Explanation / Answer

Process Mean = 340 gms
LSL = 328 gms; USL = 352 gms

(USL+LSL)/2 = 680/2 = 340. So, the process is centered i.e. the capacity can be easured with Cp

Cp = (USL - LSL) / 6 x Std. Dev.

For process to be capable, the Cp should be 1.33

or, (USL - LSL) / 6 x Std. Dev. 1.33
or, 24 / (6 x Std dev.) 1..33
or, (6 x Std dev.) 24 / 1.33
or, Std. dev. 3.008

(a) The largest standard deviation should be 3.008 gms.

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For the box on the whole,

USL = 185 gms; LSL = 155 gms
(USL+LSL)/2 = 170.

Process Mean = 1.03 x 6 ounces = 1.03 x 170 gms = 175.1 gms. Thus, the process is shifted and we must take Cpk instead of Cp to get the measure of process capability.

S = process std. dev. = 0.84 x 6 = 2.058 gms.

Cpk = min{(USL - Mean)/3S, (Mean - LSL)/3S}
or, Cpk = min((185-175.1)/(3*2.058), (175.1-155)/(3*2.058)) = 1.60

(b) Since Cpk is 1..33, the process is capable.

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The lowest setting implies that the mean for the six-bar box is less than average (closer to the LSL). Set that part of the Cpk equation = 1.33:

(Mean - 155) / (3 x 2.058) = 1.33
or, Mean = 163.21 gms of box

(c) Ounce per bar = (163.21 / 170) = 0.96.

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