Question 1: Several samples of size 5 each were taken from a fertilizer-bag-filling machines. The results were: Overall mean x~ = 57.76lbs; Average range R~ =1.78 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.
(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.
Question 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
|
7
|
6
|
6
|
9
|
5
|
6
|
0
|
8
|
9
|
1
|
(a) Determine the fraction defective of the p chart. Please give the formula and at least one step of calculation for full credit.
(b) Determine the σp of the p chart. Please give the formula and at least one step of calculation for full credit.
(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.
Question 3: Suppose the difference between the upper specification and the lower specification limits is 0.5 inches. The standard deviation is 0.1 inches. What is the process capability ratio Cp? Please provide the formula, at least one step of calculation, and the correct answer for full credit.
Question 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 0.03 mm. The process is known to operate at a mean thickness of 3.0 mm.
(a) What is the Cpk of the process? Please provide the formula, at least one step of calculation, and the correct answer for full credit.
(b) Is the process capable based on the Cpk value and why?