1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.10. Ceramic Strength

## Background and Data

Generation The data for this case study were collected by Said Jahanmir of the NIST Ceramics Division in 1996 in connection with a NIST/industry ceramics consortium for strength optimization of ceramic strength

The motivation for studying this data set is to illustrate the analysis of multiple factors from a designed experiment

This case study will utilize only a subset of a full study that was conducted by Lisa Gill and James Filliben of the NIST Statistical Engineering Division

The response variable is a measure of the strength of the ceramic material (bonded Si nitrate). The complete data set contains the following variables:

1. Factor 1 = Observation ID, i.e., run number (1 to 960)
2. Factor 2 = Lab (1 to 8)
3. Factor 3 = Bar ID within lab (1 to 30)
4. Factor 4 = Test number (1 to 4)
5. Response Variable = Strength of Ceramic
6. Factor 5 = Table speed (2 levels: 0.025 and 0.125)
7. Factor 6 = Down feed rate (2 levels: 0.050 and 0.125)
8. Factor 7 = Wheel grit size (2 levels: 150 and 80)
9. Factor 8 = Direction (2 levels: longitudinal and transverse)
10. Factor 9 = Treatment (1 to 16)
11. Factor 10 = Set of 15 within lab (2 levels: 1 and 2)
12. Factor 11 = Replication (2 levels: 1 and 2)
13. Factor 12 = Bar Batch (1 and 2)

The four primary factors of interest are:

1. Table speed (X1)
2. Down feed rate (X2)
3. Wheel grit size (X3)
4. Direction (X4)
For this case study, we are using only half the data. Specifically, we are using the data with the direction longitudinal. Therefore, we have only three primary factors

In addition, we are interested in the nuisance factors

1. Lab
2. Batch
Purpose of Analysis The goals of this case study are:
1. Determine which of the four primary factors has the strongest effect on the strength of the ceramic material
2. Estimate the magnitude of the effects
3. Determine the optimal settings for the primary factors
4. Determine if the nuisance factors (lab and batch) have an effect on the ceramic strength

This case study is an example of a designed experiment. The Process Improvement chapter contains a detailed discussion of the construction and analysis of designed experiments. This case study is meant to complement the material in that chapter by showing how an EDA approach (emphasizing the use of graphical techniques) can be used in the analysis of designed experiments

Software The analyses used in this case study can be generated using both Dataplot code and R code. The reader can download the data as a text file.
Data The following are the data used for this case study

``` Run  Lab  Batch   Y      X1   X2   X3
1    1    1   608.781  -1   -1   -1
2    1    2   569.670  -1   -1   -1
3    1    1   689.556  -1   -1   -1
4    1    2   747.541  -1   -1   -1
5    1    1   618.134  -1   -1   -1
6    1    2   612.182  -1   -1   -1
7    1    1   680.203  -1   -1   -1
8    1    2   607.766  -1   -1   -1
9    1    1   726.232  -1   -1   -1
10    1    2   605.380  -1   -1   -1
11    1    1   518.655  -1   -1   -1
12    1    2   589.226  -1   -1   -1
13    1    1   740.447  -1   -1   -1
14    1    2   588.375  -1   -1   -1
15    1    1   666.830  -1   -1   -1
16    1    2   531.384  -1   -1   -1
17    1    1   710.272  -1   -1   -1
18    1    2   633.417  -1   -1   -1
19    1    1   751.669  -1   -1   -1
20    1    2   619.060  -1   -1   -1
21    1    1   697.979  -1   -1   -1
22    1    2   632.447  -1   -1   -1
23    1    1   708.583  -1   -1   -1
24    1    2   624.256  -1   -1   -1
25    1    1   624.972  -1   -1   -1
26    1    2   575.143  -1   -1   -1
27    1    1   695.070  -1   -1   -1
28    1    2   549.278  -1   -1   -1
29    1    1   769.391  -1   -1   -1
30    1    2   624.972  -1   -1   -1
61    1    1   720.186  -1    1    1
62    1    2   587.695  -1    1    1
63    1    1   723.657  -1    1    1
64    1    2   569.207  -1    1    1
65    1    1   703.700  -1    1    1
66    1    2   613.257  -1    1    1
67    1    1   697.626  -1    1    1
68    1    2   565.737  -1    1    1
69    1    1   714.980  -1    1    1
70    1    2   662.131  -1    1    1
71    1    1   657.712  -1    1    1
72    1    2   543.177  -1    1    1
73    1    1   609.989  -1    1    1
74    1    2   512.394  -1    1    1
75    1    1   650.771  -1    1    1
76    1    2   611.190  -1    1    1
77    1    1   707.977  -1    1    1
78    1    2   659.982  -1    1    1
79    1    1   712.199  -1    1    1
80    1    2   569.245  -1    1    1
81    1    1   709.631  -1    1    1
82    1    2   725.792  -1    1    1
83    1    1   703.160  -1    1    1
84    1    2   608.960  -1    1    1
85    1    1   744.822  -1    1    1
86    1    2   586.060  -1    1    1
87    1    1   719.217  -1    1    1
88    1    2   617.441  -1    1    1
89    1    1   619.137  -1    1    1
90    1    2   592.845  -1    1    1
151    2    1   753.333   1    1    1
152    2    2   631.754   1    1    1
153    2    1   677.933   1    1    1
154    2    2   588.113   1    1    1
155    2    1   735.919   1    1    1
156    2    2   555.724   1    1    1
157    2    1   695.274   1    1    1
158    2    2   702.411   1    1    1
159    2    1   504.167   1    1    1
160    2    2   631.754   1    1    1
161    2    1   693.333   1    1    1
162    2    2   698.254   1    1    1
163    2    1   625.000   1    1    1
164    2    2   616.791   1    1    1
165    2    1   596.667   1    1    1
166    2    2   551.953   1    1    1
167    2    1   640.898   1    1    1
168    2    2   636.738   1    1    1
169    2    1   720.506   1    1    1
170    2    2   571.551   1    1    1
171    2    1   700.748   1    1    1
172    2    2   521.667   1    1    1
173    2    1   691.604   1    1    1
174    2    2   587.451   1    1    1
175    2    1   636.738   1    1    1
176    2    2   700.422   1    1    1
177    2    1   731.667   1    1    1
178    2    2   595.819   1    1    1
179    2    1   635.079   1    1    1
180    2    2   534.236   1    1    1
181    2    1   716.926   1   -1   -1
182    2    2   606.188   1   -1   -1
183    2    1   759.581   1   -1   -1
184    2    2   575.303   1   -1   -1
185    2    1   673.903   1   -1   -1
186    2    2   590.628   1   -1   -1
187    2    1   736.648   1   -1   -1
188    2    2   729.314   1   -1   -1
189    2    1   675.957   1   -1   -1
190    2    2   619.313   1   -1   -1
191    2    1   729.230   1   -1   -1
192    2    2   624.234   1   -1   -1
193    2    1   697.239   1   -1   -1
194    2    2   651.304   1   -1   -1
195    2    1   728.499   1   -1   -1
196    2    2   724.175   1   -1   -1
197    2    1   797.662   1   -1   -1
198    2    2   583.034   1   -1   -1
199    2    1   668.530   1   -1   -1
200    2    2   620.227   1   -1   -1
201    2    1   815.754   1   -1   -1
202    2    2   584.861   1   -1   -1
203    2    1   777.392   1   -1   -1
204    2    2   565.391   1   -1   -1
205    2    1   712.140   1   -1   -1
206    2    2   622.506   1   -1   -1
207    2    1   663.622   1   -1   -1
208    2    2   628.336   1   -1   -1
209    2    1   684.181   1   -1   -1
210    2    2   587.145   1   -1   -1
271    3    1   629.012   1   -1    1
272    3    2   584.319   1   -1    1
273    3    1   640.193   1   -1    1
274    3    2   538.239   1   -1    1
275    3    1   644.156   1   -1    1
276    3    2   538.097   1   -1    1
277    3    1   642.469   1   -1    1
278    3    2   595.686   1   -1    1
279    3    1   639.090   1   -1    1
280    3    2   648.935   1   -1    1
281    3    1   439.418   1   -1    1
282    3    2   583.827   1   -1    1
283    3    1   614.664   1   -1    1
284    3    2   534.905   1   -1    1
285    3    1   537.161   1   -1    1
286    3    2   569.858   1   -1    1
287    3    1   656.773   1   -1    1
288    3    2   617.246   1   -1    1
289    3    1   659.534   1   -1    1
290    3    2   610.337   1   -1    1
291    3    1   695.278   1   -1    1
292    3    2   584.192   1   -1    1
293    3    1   734.040   1   -1    1
294    3    2   598.853   1   -1    1
295    3    1   687.665   1   -1    1
296    3    2   554.774   1   -1    1
297    3    1   710.858   1   -1    1
298    3    2   605.694   1   -1    1
299    3    1   701.716   1   -1    1
300    3    2   627.516   1   -1    1
301    3    1   382.133   1    1   -1
302    3    2   574.522   1    1   -1
303    3    1   719.744   1    1   -1
304    3    2   582.682   1    1   -1
305    3    1   756.820   1    1   -1
306    3    2   563.872   1    1   -1
307    3    1   690.978   1    1   -1
308    3    2   715.962   1    1   -1
309    3    1   670.864   1    1   -1
310    3    2   616.430   1    1   -1
311    3    1   670.308   1    1   -1
312    3    2   778.011   1    1   -1
313    3    1   660.062   1    1   -1
314    3    2   604.255   1    1   -1
315    3    1   790.382   1    1   -1
316    3    2   571.906   1    1   -1
317    3    1   714.750   1    1   -1
318    3    2   625.925   1    1   -1
319    3    1   716.959   1    1   -1
320    3    2   682.426   1    1   -1
321    3    1   603.363   1    1   -1
322    3    2   707.604   1    1   -1
323    3    1   713.796   1    1   -1
324    3    2   617.400   1    1   -1
325    3    1   444.963   1    1   -1
326    3    2   689.576   1    1   -1
327    3    1   723.276   1    1   -1
328    3    2   676.678   1    1   -1
329    3    1   745.527   1    1   -1
330    3    2   563.290   1    1   -1
361    4    1   778.333  -1   -1    1
362    4    2   581.879  -1   -1    1
363    4    1   723.349  -1   -1    1
364    4    2   447.701  -1   -1    1
365    4    1   708.229  -1   -1    1
366    4    2   557.772  -1   -1    1
367    4    1   681.667  -1   -1    1
368    4    2   593.537  -1   -1    1
369    4    1   566.085  -1   -1    1
370    4    2   632.585  -1   -1    1
371    4    1   687.448  -1   -1    1
372    4    2   671.350  -1   -1    1
373    4    1   597.500  -1   -1    1
374    4    2   569.530  -1   -1    1
375    4    1   637.410  -1   -1    1
376    4    2   581.667  -1   -1    1
377    4    1   755.864  -1   -1    1
378    4    2   643.449  -1   -1    1
379    4    1   692.945  -1   -1    1
380    4    2   581.593  -1   -1    1
381    4    1   766.532  -1   -1    1
382    4    2   494.122  -1   -1    1
383    4    1   725.663  -1   -1    1
384    4    2   620.948  -1   -1    1
385    4    1   698.818  -1   -1    1
386    4    2   615.903  -1   -1    1
387    4    1   760.000  -1   -1    1
388    4    2   606.667  -1   -1    1
389    4    1   775.272  -1   -1    1
390    4    2   579.167  -1   -1    1
421    4    1   708.885  -1    1   -1
422    4    2   662.510  -1    1   -1
423    4    1   727.201  -1    1   -1
424    4    2   436.237  -1    1   -1
425    4    1   642.560  -1    1   -1
426    4    2   644.223  -1    1   -1
427    4    1   690.773  -1    1   -1
428    4    2   586.035  -1    1   -1
429    4    1   688.333  -1    1   -1
430    4    2   620.833  -1    1   -1
431    4    1   743.973  -1    1   -1
432    4    2   652.535  -1    1   -1
433    4    1   682.461  -1    1   -1
434    4    2   593.516  -1    1   -1
435    4    1   761.430  -1    1   -1
436    4    2   587.451  -1    1   -1
437    4    1   691.542  -1    1   -1
438    4    2   570.964  -1    1   -1
439    4    1   643.392  -1    1   -1
440    4    2   645.192  -1    1   -1
441    4    1   697.075  -1    1   -1
442    4    2   540.079  -1    1   -1
443    4    1   708.229  -1    1   -1
444    4    2   707.117  -1    1   -1
445    4    1   746.467  -1    1   -1
446    4    2   621.779  -1    1   -1
447    4    1   744.819  -1    1   -1
448    4    2   585.777  -1    1   -1
449    4    1   655.029  -1    1   -1
450    4    2   703.980  -1    1   -1
541    5    1   715.224  -1   -1   -1
542    5    2   698.237  -1   -1   -1
543    5    1   614.417  -1   -1   -1
544    5    2   757.120  -1   -1   -1
545    5    1   761.363  -1   -1   -1
546    5    2   621.751  -1   -1   -1
547    5    1   716.106  -1   -1   -1
548    5    2   472.125  -1   -1   -1
549    5    1   659.502  -1   -1   -1
550    5    2   612.700  -1   -1   -1
551    5    1   730.781  -1   -1   -1
552    5    2   583.170  -1   -1   -1
553    5    1   546.928  -1   -1   -1
554    5    2   599.771  -1   -1   -1
555    5    1   734.203  -1   -1   -1
556    5    2   549.227  -1   -1   -1
557    5    1   682.051  -1   -1   -1
558    5    2   605.453  -1   -1   -1
559    5    1   701.341  -1   -1   -1
560    5    2   569.599  -1   -1   -1
561    5    1   759.729  -1   -1   -1
562    5    2   637.233  -1   -1   -1
563    5    1   689.942  -1   -1   -1
564    5    2   621.774  -1   -1   -1
565    5    1   769.424  -1   -1   -1
566    5    2   558.041  -1   -1   -1
567    5    1   715.286  -1   -1   -1
568    5    2   583.170  -1   -1   -1
569    5    1   776.197  -1   -1   -1
570    5    2   345.294  -1   -1   -1
571    5    1   547.099   1   -1    1
572    5    2   570.999   1   -1    1
573    5    1   619.942   1   -1    1
574    5    2   603.232   1   -1    1
575    5    1   696.046   1   -1    1
576    5    2   595.335   1   -1    1
577    5    1   573.109   1   -1    1
578    5    2   581.047   1   -1    1
579    5    1   638.794   1   -1    1
580    5    2   455.878   1   -1    1
581    5    1   708.193   1   -1    1
582    5    2   627.880   1   -1    1
583    5    1   502.825   1   -1    1
584    5    2   464.085   1   -1    1
585    5    1   632.633   1   -1    1
586    5    2   596.129   1   -1    1
587    5    1   683.382   1   -1    1
588    5    2   640.371   1   -1    1
589    5    1   684.812   1   -1    1
590    5    2   621.471   1   -1    1
591    5    1   738.161   1   -1    1
592    5    2   612.727   1   -1    1
593    5    1   671.492   1   -1    1
594    5    2   606.460   1   -1    1
595    5    1   709.771   1   -1    1
596    5    2   571.760   1   -1    1
597    5    1   685.199   1   -1    1
598    5    2   599.304   1   -1    1
599    5    1   624.973   1   -1    1
600    5    2   579.459   1   -1    1
601    6    1   757.363   1    1    1
602    6    2   761.511   1    1    1
603    6    1   633.417   1    1    1
604    6    2   566.969   1    1    1
605    6    1   658.754   1    1    1
606    6    2   654.397   1    1    1
607    6    1   664.666   1    1    1
608    6    2   611.719   1    1    1
609    6    1   663.009   1    1    1
610    6    2   577.409   1    1    1
611    6    1   773.226   1    1    1
612    6    2   576.731   1    1    1
613    6    1   708.261   1    1    1
614    6    2   617.441   1    1    1
615    6    1   739.086   1    1    1
616    6    2   577.409   1    1    1
617    6    1   667.786   1    1    1
618    6    2   548.957   1    1    1
619    6    1   674.481   1    1    1
620    6    2   623.315   1    1    1
621    6    1   695.688   1    1    1
622    6    2   621.761   1    1    1
623    6    1   588.288   1    1    1
624    6    2   553.978   1    1    1
625    6    1   545.610   1    1    1
626    6    2   657.157   1    1    1
627    6    1   752.305   1    1    1
628    6    2   610.882   1    1    1
629    6    1   684.523   1    1    1
630    6    2   552.304   1    1    1
631    6    1   717.159  -1    1   -1
632    6    2   545.303  -1    1   -1
633    6    1   721.343  -1    1   -1
634    6    2   651.934  -1    1   -1
635    6    1   750.623  -1    1   -1
636    6    2   635.240  -1    1   -1
637    6    1   776.488  -1    1   -1
638    6    2   641.083  -1    1   -1
639    6    1   750.623  -1    1   -1
640    6    2   645.321  -1    1   -1
641    6    1   600.840  -1    1   -1
642    6    2   566.127  -1    1   -1
643    6    1   686.196  -1    1   -1
644    6    2   647.844  -1    1   -1
645    6    1   687.870  -1    1   -1
646    6    2   554.815  -1    1   -1
647    6    1   725.527  -1    1   -1
648    6    2   620.087  -1    1   -1
649    6    1   658.796  -1    1   -1
650    6    2   711.301  -1    1   -1
651    6    1   690.380  -1    1   -1
652    6    2   644.355  -1    1   -1
653    6    1   737.144  -1    1   -1
654    6    2   713.812  -1    1   -1
655    6    1   663.851  -1    1   -1
656    6    2   696.707  -1    1   -1
657    6    1   766.630  -1    1   -1
658    6    2   589.453  -1    1   -1
659    6    1   625.922  -1    1   -1
660    6    2   634.468  -1    1   -1
721    7    1   694.430   1    1   -1
722    7    2   599.751   1    1   -1
723    7    1   730.217   1    1   -1
724    7    2   624.542   1    1   -1
725    7    1   700.770   1    1   -1
726    7    2   723.505   1    1   -1
727    7    1   722.242   1    1   -1
728    7    2   674.717   1    1   -1
729    7    1   763.828   1    1   -1
730    7    2   608.539   1    1   -1
731    7    1   695.668   1    1   -1
732    7    2   612.135   1    1   -1
733    7    1   688.887   1    1   -1
734    7    2   591.935   1    1   -1
735    7    1   531.021   1    1   -1
736    7    2   676.656   1    1   -1
737    7    1   698.915   1    1   -1
738    7    2   647.323   1    1   -1
739    7    1   735.905   1    1   -1
740    7    2   811.970   1    1   -1
741    7    1   732.039   1    1   -1
742    7    2   603.883   1    1   -1
743    7    1   751.832   1    1   -1
744    7    2   608.643   1    1   -1
745    7    1   618.663   1    1   -1
746    7    2   630.778   1    1   -1
747    7    1   744.845   1    1   -1
748    7    2   623.063   1    1   -1
749    7    1   690.826   1    1   -1
750    7    2   472.463   1    1   -1
811    7    1   666.893  -1    1    1
812    7    2   645.932  -1    1    1
813    7    1   759.860  -1    1    1
814    7    2   577.176  -1    1    1
815    7    1   683.752  -1    1    1
816    7    2   567.530  -1    1    1
817    7    1   729.591  -1    1    1
818    7    2   821.654  -1    1    1
819    7    1   730.706  -1    1    1
820    7    2   684.490  -1    1    1
821    7    1   763.124  -1    1    1
822    7    2   600.427  -1    1    1
823    7    1   724.193  -1    1    1
824    7    2   686.023  -1    1    1
825    7    1   630.352  -1    1    1
826    7    2   628.109  -1    1    1
827    7    1   750.338  -1    1    1
828    7    2   605.214  -1    1    1
829    7    1   752.417  -1    1    1
830    7    2   640.260  -1    1    1
831    7    1   707.899  -1    1    1
832    7    2   700.767  -1    1    1
833    7    1   715.582  -1    1    1
834    7    2   665.924  -1    1    1
835    7    1   728.746  -1    1    1
836    7    2   555.926  -1    1    1
837    7    1   591.193  -1    1    1
838    7    2   543.299  -1    1    1
839    7    1   592.252  -1    1    1
840    7    2   511.030  -1    1    1
901    8    1   740.833  -1   -1    1
902    8    2   583.994  -1   -1    1
903    8    1   786.367  -1   -1    1
904    8    2   611.048  -1   -1    1
905    8    1   712.386  -1   -1    1
906    8    2   623.338  -1   -1    1
907    8    1   738.333  -1   -1    1
908    8    2   679.585  -1   -1    1
909    8    1   741.480  -1   -1    1
910    8    2   665.004  -1   -1    1
911    8    1   729.167  -1   -1    1
912    8    2   655.860  -1   -1    1
913    8    1   795.833  -1   -1    1
914    8    2   715.711  -1   -1    1
915    8    1   723.502  -1   -1    1
916    8    2   611.999  -1   -1    1
917    8    1   718.333  -1   -1    1
918    8    2   577.722  -1   -1    1
919    8    1   768.080  -1   -1    1
920    8    2   615.129  -1   -1    1
921    8    1   747.500  -1   -1    1
922    8    2   540.316  -1   -1    1
923    8    1   775.000  -1   -1    1
924    8    2   711.667  -1   -1    1
925    8    1   760.599  -1   -1    1
926    8    2   639.167  -1   -1    1
927    8    1   758.333  -1   -1    1
928    8    2   549.491  -1   -1    1
929    8    1   682.500  -1   -1    1
930    8    2   684.167  -1   -1    1
931    8    1   658.116   1   -1   -1
932    8    2   672.153   1   -1   -1
933    8    1   738.213   1   -1   -1
934    8    2   594.534   1   -1   -1
935    8    1   681.236   1   -1   -1
936    8    2   627.650   1   -1   -1
937    8    1   704.904   1   -1   -1
938    8    2   551.870   1   -1   -1
939    8    1   693.623   1   -1   -1
940    8    2   594.534   1   -1   -1
941    8    1   624.993   1   -1   -1
942    8    2   602.660   1   -1   -1
943    8    1   700.228   1   -1   -1
944    8    2   585.450   1   -1   -1
945    8    1   611.874   1   -1   -1
946    8    2   555.724   1   -1   -1
947    8    1   579.167   1   -1   -1
948    8    2   574.934   1   -1   -1
949    8    1   720.872   1   -1   -1
950    8    2   584.625   1   -1   -1
951    8    1   690.320   1   -1   -1
952    8    2   555.724   1   -1   -1
953    8    1   677.933   1   -1   -1
954    8    2   611.874   1   -1   -1
955    8    1   674.600   1   -1   -1
956    8    2   698.254   1   -1   -1
957    8    1   611.999   1   -1   -1
958    8    2   748.130   1   -1   -1
959    8    1   530.680   1   -1   -1
960    8    2   689.942   1   -1   -1

```