Assignment Problems (66 points in total):

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Assignment Problems (66 points in total):

1.      Several samples of size 5 each were taken from a fertilizer-bag-filling machines. The results were: Overall mean  lbs; Average range  lbs.

 

(a) Determine the upper and lower control limits of the  chart. Please give the formulas for calculating UCL and LCL and at least one step of calculation for full credit.(8 points)

 

(b) Determine the upper and lower control limits of the R chart. Please give the formulas for calculating UCL and LCL and at least one step of calculation for full credit.(8 points)

 

 

2.      The results of inspection of DNA samples taken over the past 10 days are given below. Sample size is 100.

Day

1

2

3

4

5

6

7

8

9

10

# of defectives

4

6

5

10

5

6

7

8

6

0

 

 

 

 

(a) Determine the fraction defective  of the p chart. Please give the formula and at least one step of calculation for full credit.(6 points)

 

(b) Determine the of the p chart. Please give the formula and at least one step of calculation for full credit.(6 points)

 

(c) Determine the 3-sigma upper control limit and the 3-sigma lower control limit of the p chart. For each control limit, provide at least one step of calculation for full credit.(8 points)

 

 

3.      Suppose the difference between the upper specification and the lower specification limits is 0.8 inches. The standard deviation is 0.1 inches. What is the process capability ratio ? Please provide the formula, at least one step of calculation, and the correct answer for full credit. (6 points)

 

 

4.      The specifications for a plastic liner for concrete highway projects calls for a thickness of 3.0 mm  0.2 mm. The standard deviation of the process is estimated to be 0.02 mm. The process is known to operate at a mean thickness of 3.0 mm.

 

(a) What is the  of the process? Please provide the formula, at least one step of calculation, and the correct answer for full credit. (10 points)

 

(b) Is the process capable based on the  value and why? (4 points)

 

 

5.      A company is considering producing a gear assembly that it now purchases from a supplier. The supplier charges $4 per unit, with an additional one-time payment of $8,000 units. The company estimates that it will cost $15,000 to set up the process and then $1.5 per unit for labor and materials.

 

(a)  What is the cross-over point? Please provide the formula, at least one step of calculation, and the correct answer for full credit. (6 points)

 

(b)  If the expected production volume is 5,000 units, which option gives a lower total cost? Please provide at least one step of calculation and the correct answer for full credit. (4 points)

 

 

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