(SPC and Process Capability)
1. Explain the difference between attribute charts and variable control charts.
2. Why and how are mean (X-bar) and range (R-) charts used together?
3. What is the difference between tolerances (design specifications) and control limits (natural variations)?
4. The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch. The machines have the following parameters: Machine 1 (
= 0.0995, σ = 0.004); Machine 2 ( = 0.1002, σ = 0.009); Machine 3 ( = 0.095, σ = 0.005). Determine which machines (if any) are capable of producing the products within the design specifications.
5. The Rollins Sporting Goods Co. manufactures baseballs for professional minor and major leagues at its plants in Costa Rica. According to the rules of major league baseball, a baseball must weigh between 142 and 149 grams. The company has taken 20 samples of five baseballs each and weighed the baseballs as follow:
|
Sample
|
Item 1
|
Item 2
|
Item 3
|
Item 4
|
Item 5
|
|
1
|
143.1
|
142.5
|
148.1
|
149.4
|
146.3
|
|
2
|
145.8
|
144.0
|
149.8
|
141.2
|
143.5
|
|
3
|
140.3
|
144.5
|
146.2
|
140.4
|
149.7
|
|
4
|
143.4
|
145.2
|
147.8
|
144.1
|
148.6
|
|
5
|
142.5
|
141.7
|
139.6
|
145.4
|
146.3
|
|
6
|
147.4
|
145.2
|
145.0
|
150.3
|
151.2
|
|
7
|
144.7
|
145.0
|
145.2
|
140.6
|
139.7
|
|
8
|
141.4
|
138.5
|
140.3
|
142.6
|
144.4
|
|
9
|
151.3
|
149.7
|
145.4
|
148.2
|
149.0
|
|
10
|
137.3
|
144.6
|
145.8
|
141.9
|
144.5
|
|
11
|
142.3
|
144.7
|
141.6
|
145.8
|
148.3
|
|
12
|
143.6
|
145.4
|
145.0
|
144.3
|
149.1
|
|
13
|
148.4
|
147.3
|
149.1
|
140.6
|
140.9
|
|
14
|
151.3
|
150.6
|
147.2
|
148.3
|
146.5
|
|
15
|
145.2
|
146.3
|
141.2
|
142.5
|
142.7
|
|
16
|
146.3
|
147.4
|
148.2
|
145.4
|
145.1
|
|
17
|
143.9
|
144.6
|
145.2
|
146.1
|
146.3
|
|
18
|
145.6
|
145.3
|
142.1
|
146.7
|
144.3
|
|
19
|
142.8
|
141.7
|
140.9
|
145.6
|
146.3
|
|
20
|
145.4
|
142.3
|
147.5
|
145.0
|
149.4
|
(a) Construct an x-bar chart in conjunction with an R-chart to monitor the baseball making process, comment on the capability of the process.
(b) Explain to what extent the process for manufacturing baseballs must be improved in order to achieve 6 sigma quality. (Hint: Use A2 R‾=3σ ).