Design of Experiment - 24 Samples per Run

[beejkelly]

I have 11 different runs - set by my design of experiments factorial design with center pt. For each run - production took 4 samples at 6 different intervals during the run.

I am used to in Minitab where for the run you have

StdOrder RunOrder CenterPt Blocks Hold psi Barrel Temp Mold Temp Overall Length ID(these are in order of column below but too wide to fit over each column)

6 1 1 1 19000 500 165 4.52701 0.73537
7 2 1 1 15000 530 165 4.52672 0.73520
11 3 0 1 17000 515 180 4.52729 0.73543
3 4 1 1 15000 530 165 4.52642 0.73516
10 5 0 1 17000 515 180 4.52690 0.73536
9 6 0 1 17000 515 180 4.52691 0.73538
2 7 1 1 19000 500 165 4.52703 0.73545
5 8 1 1 15000 500 195 4.52462 0.73494
8 9 1 1 19000 530 195 4.52969 0.73558
1 10 1 1 15000 500 195 4.52453 0.73491
4 11 1 1 19000 530 195 4.52950 0.73557

the second to last and last columns are the Mean of the 24 data points Per run.
Is there a better way to analyze of Design of Experiments in minitab to include all individual points ??

thanks,
Barb

[Statistical Steven]

In Reply to Parent Post by beejkelly

I have 11 different runs - set by my design of experiments factorial design with center pt. For each run - production took 4 samples at 6 different intervals during the run.

I am used to in Minitab where for the run you have

StdOrder RunOrder CenterPt Blocks Hold psi Barrel Temp Mold Temp Overall Length ID(these are in order of column below but too wide to fit over each column)

6 1 1 1 19000 500 165 4.52701 0.73537
7 2 1 1 15000 530 165 4.52672 0.73520
11 3 0 1 17000 515 180 4.52729 0.73543
3 4 1 1 15000 530 165 4.52642 0.73516
10 5 0 1 17000 515 180 4.52690 0.73536
9 6 0 1 17000 515 180 4.52691 0.73538
2 7 1 1 19000 500 165 4.52703 0.73545
5 8 1 1 15000 500 195 4.52462 0.73494
8 9 1 1 19000 530 195 4.52969 0.73558
1 10 1 1 15000 500 195 4.52453 0.73491
4 11 1 1 19000 530 195 4.52950 0.73557

the second to last and last columns are the Mean of the 24 data points Per run.
Is there a better way to analyze of Design of Experiments in minitab to include all individual points ??

thanks,
Barb

Barb

If you look at your variable called Block you will notice you have a single block. You can replicate the setting and for each of the 6 sample intervals, you can increment the block variable (6 blocks). For each block you can replicate the design matrix 4 times for each replicate. You should end up with 264 rows (6x4x11). There might be other ways, but this gives you the sampling interval variability and within interval variability will be part of the MSE.

[Miner]

In Reply to Parent Post by Statistical Steven

Barb

If you look at your variable called Block you will notice you have a single block. You can replicate the setting and for each of the 6 sample intervals, you can increment the block variable (6 blocks). For each block you can replicate the design matrix 4 times for each replicate. You should end up with 264 rows (6x4x11). There might be other ways, but this gives you the sampling interval variability and within interval variability will be part of the MSE.

Steve,
If these were true replicates, that would be an option, but these are repeats. The variation for repeats is typically less that that of replicates because it does not include setup variation.

The standard approach for repeats is to calculate the average and standard deviation for the within run repeats then analyze the mean and Ln(StdDev) separately.

Because these repeats were collected in subgroups, I would evaluate both short and long term variations, as well as evaluate in a control chart.

[beejkelly]

So I took the Mean of each Run (mean of the 24 samples) and looked at the Length and ID See below

not sure what the Curvature Line means???

Thanks so much for helping-
Does this look right for that data and just looking at the means
do I do same DOE but for st. Dev. (not sure why ln in front of your st.dev)

again thanks a ton!!
Barb

Welcome to Minitab, press F1 for help.

Full Factorial Design
Factors: 3 Base Design: 3, 8
Runs: 11 Replicates: 1
Blocks: 1 Center pts (total): 3

All terms are free from aliasing.

Alias Information for Terms in the Model.
Totally confounded terms were removed from the analysis.
I + Hold psi*Barrel Temp*Mold Temp
Hold psi + Barrel Temp*Mold Temp
Barrel Temp + Hold psi*Mold Temp
Mold Temp + Hold psi*Barrel Temp
* NOTE * Some of the terms requested in MEANS were removed from the analysis.

Factorial Fit: Overall Length versus Hold psi, Barrel Temp, Mold Temp
Estimated Effects and Coefficients for Overall Length (coded units)
Term Effect Coef SE Coef T P
Constant 4.52694 0.000059 76940.22 0.000
Hold psi 0.00273 0.00137 0.000059 23.24 0.000
Barrel Temp 0.00229 0.00114 0.000059 19.42 0.000
Mold Temp 0.00029 0.00015 0.000059 2.46 0.049
Ct Pt 0.00009 0.000113 0.83 0.439

S = 0.000166416 PRESS = *
R-Sq = 99.35% R-Sq(pred) = *% R-Sq(adj) = 98.92%

Analysis of Variance for Overall Length (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 0.00002557 0.00002557 0.00000852 307.78 0.000
Curvature 1 0.00000002 0.00000002 0.00000002 0.69 0.439
Residual Error 6 0.00000017 0.00000017 0.00000003
Pure Error 6 0.00000017 0.00000017 0.00000003
Total 10 0.00002576

Estimated Coefficients for Overall Length using data in uncoded units
Term Coef
Constant 4.47435
Hold psi 6.83750E-07
Barrel Temp 7.61667E-05
Mold Temp 9.66667E-06
Ct Pt 0.000093333

Least Squares Means for Overall Length
Mean SE Mean
Hold psi
15000 4.526 0.000083
19000 4.528 0.000083
Barrel Temp
500 4.526 0.000083
530 4.528 0.000083
Mold Temp
165 4.527 0.000083
195 4.527 0.000083

Mean for Center Point = 4.527

Effects Plot for Overall Length

Effects Pareto for Overall Length

Alias Structure
I + Hold psi*Barrel Temp*Mold Temp
Hold psi + Barrel Temp*Mold Temp
Barrel Temp + Hold psi*Mold Temp
Mold Temp + Hold psi*Barrel Temp

Residual Plots for Overall Length

Alias Information for Terms in the Model.
Totally confounded terms were removed from the analysis.
I + Hold psi*Barrel Temp*Mold Temp
Hold psi + Barrel Temp*Mold Temp
Barrel Temp + Hold psi*Mold Temp
Mold Temp + Hold psi*Barrel Temp

Factorial Fit: ID versus Hold psi, Barrel Temp, Mold Temp
Estimated Effects and Coefficients for ID (coded units)
Term Effect Coef SE Coef T P
Constant 0.735273 0.000012 60456.05 0.000
Hold psi 0.000440 0.000220 0.000012 18.09 0.000
Barrel Temp 0.000210 0.000105 0.000012 8.63 0.000
Mold Temp -0.000045 -0.000023 0.000012 -1.85 0.114
Ct Pt 0.000118 0.000023 5.05 0.002

S = 0.0000343996 PRESS = *
R-Sq = 98.63% R-Sq(pred) = *% R-Sq(adj) = 97.71%

Analysis of Variance for ID (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 0.00000048 0.00000048 0.00000016 135.06 0.000
Curvature 1 0.00000003 0.00000003 0.00000003 25.46 0.002
Residual Error 6 0.00000001 0.00000001 0.00000000
Pure Error 6 0.00000001 0.00000001 0.00000000
Total 10 0.00000052

Estimated Coefficients for ID using data in uncoded units
Term Coef
Constant 0.730068
Hold psi 1.10000E-07
Barrel Temp 7.00000E-06
Mold Temp -1.50000E-06
Ct Pt 0.000117500

Effects Plot for ID

Effects Pareto for ID

Alias Structure
I + Hold psi*Barrel Temp*Mold Temp
Hold psi + Barrel Temp*Mold Temp
Barrel Temp + Hold psi*Mold Temp
Mold Temp + Hold psi*Barrel Temp

Residual Plots for ID

[Miner]

The center point is used to test for curvature. In this analysis, the p-value of 0.439 indicates that there is no curvature. Rerun your analysis after removing the center point from the model.

Ln (Std Dev) = Natural log (Std Dev)

The variance of Standard Deviations changes based on the magnitude, so a Natural log transform is used to stabilize the variance. Log base 10 can also be used.

[beejkelly]

Is that what you should do - is just delete the runs with the center pts in minitab(3 runs here) and just rerun DOE???

[Miner]

In Reply to Parent Post by beejkelly

Is that what you should do - is just delete the runs with the center pts in minitab(3 runs here) and just rerun DOE???

No. If you are using Minitab, uncheck the box for Include center points in model? under the Terms menu. What software are you using?

[beejkelly]

yes minitab