Question

4. Stephen Lazy Co. produces electronic products. One critical part is AX200B5 which is designed to work under high temperature. Its conductivity is a critical concern. Higher conductivity performance is expected in higher temperature. The company currently is purchasing the part from Vendor A. Recently the company received a sample of AX200B5 from Vendor B who claimed that the sample performs as well as those of Vendor A. To investigate whether the two sources of AX200B5 perform the same and how the parts perform in different temperature settings (the higher the conductivity, the larger the conductivity tester reading, with 1 as the smallest and 100 as the highest), the Engineering Department has conducted a series of 2² experiment trials and obtained the data as follows:  

Sample	Conductivity reading	Vendor	Temperature (oC)
1	79	A	250
2	76	A	250
3	83	A	250
4	84	A	250
5	78	A	250
6	59	A	200
7	61	A	200
8	62	A	200
9	58	A	200
10	60	A	200
11	83	B	250
12	84	B	250
13	86	B	250
14	88	B	250
15	84	B	250
16	44	B	200
17	46	B	200
18	47	B	200
19	43	B	200
20	45	B	200

The following table reveals the result of design of experiment (DOE) for the data above:

Term                          Coefficient   SE Coefficient           T-Value P-Value  

Constant                         67.500          0.506                   133.34          0.000

Vendor                 -2.500           0.506                   -4.94             0.000

Temp                  15.000          0.506                   29.63            0.000

Vendor x Temp               5.000            0.506                   9.88              0.000

Questions:

1. What is the main effect of Vendor and Temperature, and what do they mean?
2. What is the Interaction effect and what does it mean?                          
3. What is the temperature that the component of A & B will perform the same?
4. Which vendor should Stephen select if AX200B5 is used at temperature >240^oC?

Answer 1

a. What is the main effect ov Vendor and Temperature and what do they mean?

Here both temperature and vendor are having an impact on the conductivity

The temperature and vendor when having an independent impact on conductivity without the influence of each other are called as main effect

Term	Coeff	SE Coeff	T-Value	P-value
Constant	67.5	0.506	133.34	0
Vendor	-2.5	0.506	-4.94	0
Temp	15	0.506	29.63	0
VendorXtemp	5	0.506	0.88	0

From the table above, the coefficient of temp and vendor given as -2.5 and 15 are the main effects. Further, the p-value of 0 signifies that these effects are significant and cannot be ignored

A vendor main effect of -2.5 means that for the change in vendor, there is a change of conductivity by -2.5

More specifically, when vendor A is changed to vendor B, the conductivity reduces by -2.5

Further temperature main effect of 15 implies that when temperature jumps from 200 deg C to 250 deg C,there is an increase in conductivity by 15 units

b. What is the Interaction effect and what does it mean ?

Interaction effect means combined impact of temperature and vendor change on the conductivity

The coefficient for VendorXtemp is 5. i.e when vendor changes from A to B and temperature increases from 200 to 250, the conductivity increases only by 5. This is different compared to main effects since those were independent impact on conductivity. As we saw earlier, only a temperature change was resulting in increase of conductivity by 15 however a vendor change simultaneously has bought it down to 5 since in the main effect we saw that vendor change from A to B is causing a reduction in conductivity by -2.5

3. What is the temperature that the component of A & B will perform the same?  

At lower temperature of 200, the average conductivity for A is 60 compared to 45 for B

At higher temperature of 250, the average conductivity for A is 80 compared to 85 for B

So as temperature has increased, the gap between average conductivity has reduced for vendors A and B and infact B has become better than A

So at a temperature of 250, the component of A and B will approximately perform the same

4. Which vendor should Stephen select if AX200B5 is used at temperature >240oC?

Considering the logic similar to question 3 above, as temperature has gone from 200 to 250, vendor B is giving a better conductivity than B. Hence for temperature > 240 oC, Stephen should select vendor B