# 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.

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

| 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)**

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(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)**

- 9 years ago

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