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 325 grams to 355 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 .80 gram. The filling machine is set to deliver an average of 1.03 ounces per bar. Specifications for the six-bar box are 153 to 187 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

Answer 1

(a)

Process mean, = 340 grams

LSL = 325 grams

USL = 355 grams

Specification mean = Average of USL and LSL = (325+355)/2 = 340

Process mean is equal to the specification mean.

Therefore, the process is centered. Hence, Cpk = Cp

For the process to be capable, value of Cpk should be at least 1

Cpk = Cp = (USL-LSL)/6

Substituting values of USL, LSL and equating it to 1, we get value of

(USL-LSL)/6 = 1

= (USL-LSL)/(6*1)

= (355-325)/6

= 5 grams

Standard deviation = 5.000 grams

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(b)

Standard deviation of 1 bar = 0.80 gram

Standard deviation of 6 bars, = 0.80*sqrt(6) = 1.96 gram

Process mean, = 1.03*6*28.33 = 175.1 grams   (1 ounce = 28.33 grams)

LSL = 153 grams

USL = 187 grams

Cpu = (USL-)/3 = (187-175.1)/(3*1.96) = 2.024

Cpl = (-LSL)/3 = (175.1-153)/(3*1.96) = 3.759

Cpk = Minimum of Cpu and Cpl

= Minimum of 2.024 and 3.759

= 2.024

Cpk is greater than 1, therefore, the process is Capable

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(c)

For lowest setting, Cpk must be at least 1

LSL = -3 = 175.1 - 3*1.96 = 169.22 grams = 5.972 ounces

Lowest setting = 5.972 ounces