Problem 10-27 The Good Chocolate Company makes a variety of chocolate candies, i
ID: 362981 • Letter: P
Question
Problem 10-27
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 336 grams to 344 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 .76 gram. The filling machine is set to deliver an average of 1.02 ounces per bar. Specifications for the six-bar box are 163 to 177 grams. Is the process capable? Hint: The variance for the box is equal to six times the bar variance.
No
Yes
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
To be capable, the Cp or Cpk value must be minimum 1
a) As the process is centered, Cp will be used
Cp = (UCL-LCL)/(6*SD)
1 = (344-336)/(6*SD)
6*SD = 8
SD = 1.333
Standard deviation of 1.333 gms
b) As process is centered, Cp will be used
Variance of bar = Standard deviation^2 = 0.76^2
Variance of box = 6*(0.76)^2
Standard deviation of box = sqrt(6*(0.76)^2) = 0.76*sqrt(6) = 1.86
Cp = (UCL-LCL)/(6*SD) = (177-163)/(6*1.86) = 1.25
As value is greater than 1, process is capable
c) 1 = (UCL-LCL)/(6*SD)
6*0.76 = (UCL-LCL)
UCL - LCL = 4.56
1 ounce = 28.34 grams
LCL = Mean - 4.56/2 = 1.02*28.34 - 2.28 = 26.627 grams or 26.627/28.34 = 0.940 ounces
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.