1. Caterpillar C13 Matrix Data Analysis
Elisa Santos
Caterpillar C13 Matrix Data Analysis
Discussed at meeting on October 20th, 2005
Participants: Jim Rutherford, Elisa Santos,
Phil Scinto and John Zalar
Participants in part: Jeff Clark and Todd Dvorak
“The industry statisticians reached consensus on analyses of
the PC-10 Precision Matrices. We agreed that we have more work to do,
more details to examine, more questions to address, etc. However, we
don't expect the basic analyses to change substantially from what we
have today and we are ready to share with the industry.”

2. Outline Summary Data Source Modeling Analysis by parameter
Delta Oil Consumption: Pages
Deposits Pages
Correlations Page
Precision Page 43
Appendices
Plots by parameter Pages 44 to 56
Precision for the 1P …
Precision by cylinder for the C13
Summary statistics for 32 tests
Summary statistics for 24 tests
Follow up to the BOI meeting

3. Statistical evidence that Lab F is severe on Delta OC
Summary (1)
Statistical evidence that Lab F is severe on Delta OC
Analysis with 32 tests shows that Lab A is mild for Delta OC
Lab B is severe for TLC and TLHC
Additional Lab differences
UWD: Lab A & Lab B; Lab A & Lab G; Some indication of Lab B severity
TGC: Lab A & Lab G
TGF: Lab A & Lab F ; Lab A & Lab G

4. Summary (2)
Impact of Base Oil on Delta OC seems to vary with Technology
Delta OC increases with Base Oil (1,2,3) for Technology B
And there are no significant differences among Base Oils for Technology A
In general, Deposits for Base Oil 3 are higher compared to Base Oil 2 and Base Oil 1
Correlation of Delta OC with Deposits is very weak: ~ 0.4 or lower, most of them not significantly different from zero
Precision:
E p is greater than 1 for TLC and TLHC
~ 0.85 for TGC
~ 0.65 for Delta OC and TGF

5. Data Source
TMC file with 32 tests; 26 valid matrix tests; 5 valid mini matrix tests; 1 extra test
24 PC10 oils + 2 Oil A + 3 Oil D + 3 PG10 G
Test was eliminated from the analysis because was operationally invalid.
Test was aborted.
Observation about Test 55740: the intermediate (or second) ring was stuck
24 tests for PC10 oils

6. Modeling
24 PC10 Oils:
The model used for the analysis includes Lab, Stand(Lab), Technology Type and Basel Oil Type
PC10 Oils + mini matrix + PC10G:
The model used for the analysis includes Lab, Stand(Lab) and Oil Type
Transformations were used when deemed necessary to satisfy the assumptions of the model and to allow for performing valid tests of hypothesis.
The tests are corrected for multiple comparisons
With respect to the plots with confidence intervals: if the confidence intervals overlap then there are no significant differences between Labs (or Oils).
Precision is the residual standard error of the final model for each parameter. The estimates are given in their original scale.

7. Delta Oil Consumption

8. Delta OC: 24 tests
Lab differences: Statistical evidence that Lab F is severe relative to other labs in the matrix
No differences between Stands inside Labs
Final Model: Lab, Technology, Base Oil and interaction of Technology & Base Oil
Observations about the impact of Base Oil on Delta OC
Delta OC increases when moving from Base Oil 1 to Base Oil 2 to Base Oil 3 for Technology B. 
There is statistical evidence that Delta OC for Base Oil 3 is larger than the other Base Oils.
Delta OC decreases when moving from Base Oil 1 to Base Oil 2 to Base Oil 3 for Technology A. 
Note, however, that there is not enough statistical evidence to conclude that the Base Oils are different.
For instance, the difference between A1 and A3 is ~20, and the 95% conf interval for A1 - A3 is [ -1.68; 41.61]. For the difference to be statistically significant this interval must not include zero.

9. Details for Delta OC: 24 tests
The impact of Base Oil
on Delta OC seems to vary with Technology
Levels not connected by
same letter are significantly
different

10. Details for Delta OC: 24 tests
No transformation used
Rsquare adj: 81%
Precision: 6.5
Statistical evidence that Lab F is severe relative to the other labs
Levels not connected by same
letter are significantly different

11. LN Delta OC: 32 tests Ln transformation was used
Final model: Lab and Oil Type
Rsquare adj: 79%
Precision: 6.82
Statistical evidence that Lab F is severe
Statistical evidence that Lab A is milder than Lab G
Evidence that Lab A is milder than the other labs
Levels not connected by same letter
are significantly different

12. Details for LN Delta OC: 32 tests
Oil discrimination at 5% level
The conclusions are equivalent to the previous analysis based on 24 tests, Technology and Base Oil

13. Details for LN Delta OC: 32 tests 95% conf
Details for LN Delta OC: 32 tests 95% conf. limits to help visualize Oil differences

14. Deposits

15. Differences among cylinders by parameter

16. Outlier screened UWD (OUWD): 24 tests taking into account differences among cylinders
Similar results are obtained
for the analysis before screening
for outliers
No transformation used
Final Model: Lab and Base Oil; Rsquare adj: 66%
Precision: 8.02
No significant differences among Stands or Technologies
Lab discrimination: Lab A & Lab B; Lab A & Lab G
Some indication that Lab B may be severe compared to the other labs. Differences not significant at 5%
Levels not connected by same
letter are significantly different

17. Outlier screened UWD (OUWD): 24 tests taking into account differences among cylinders
Impact of Base Oil on OUWD
Higher values of OUWD correspond to Base Oil 3
Levels not connected by same
letter are significantly different

18. Similar results are obtained
for the analysis before screening
for outliers
Outlier screened UWD: 32 tests taking into account differences among cylinders
No transformation used
Final model: Lab and Oil type; Rsquare adj: 56%
Precision: 8.38
No significant differences among Stands inside Labs
Lab discrimination: Lab A & Lab B; Lab A & Lab G; Lab B & Lab D
Levels not connected by same
letter are significantly different

19. OUWD: 32 tests taking into account differences among cylinders
Levels not connected by same
letter are significantly different

20. Outlier screened TGC (OTGC): 24 tests taking into account differences among cylinders
No transformation used
Final model: Lab and Base Oil; Rsquare adj: 56%
Precision: 5.57
No significant differences among Stands or Technologies
Lab discrimination: Lab A & Lab G
Similar results are obtained
for the analysis before screening
for outliers
Levels not connected by same
letter are significantly different

21. Outlier screened TGC (OTGC): 24 tests taking into account differences among cylinders
Impact of Base Oil on OTGC
Higher values of OTGC correspond to Base Oil 3;
Difference between Base oil 1 and Base oil 3 is borderline significant

22. Outlier screened TGC (OTGC): 32 tests taking into account differences among cylinders
No transformation used
Final Model: Lab and Oil Type; Rsquare adj: 55%
Precision: 5.46
No significant differences among Stands inside Labs
Lab discrimination: Lab A & Lab G
Similar results are obtained
for the analysis before screening
for outliers
Levels not connected by same letter are significantly different

23. Outlier screened TGC (OTGC):32 tests taking into account differences among cylinders
No Oil differences; borderline discrimination Oil D & PC10 F

24. Outlier screened TLC (scrnd TLC): 24 tests
No transformation used
Final Model: Lab, Technology, Base Oil and interaction of Technology & Base Oil
Rsquare adj: 63%
Precision: 4.02
No significant differences among Stands
Statistical evidence that Lab B is severe
Similar results are obtained
for the analysis before screening
for outliers

25. Outlier screened TLC (scrnd TLC): 24 tests
Impact of Base Oil on scrnd TLC depends upon Technology
Technology B/Base oil 3 seems significantly higher than the other Technology/ Base Oil combinations, except for Technology A/Base oil 3
Levels not connected by same
letter are significantly different

26. Outlier screened TLC (scrnd TLC): 32 tests
No transformation used
Final model: Lab and Oil Type
Rsquare adj: 52%
Precision: 4.25
No significant differences among Stands inside Labs
Statistical evidence that Lab B is severe
Similar results are obtained
for the analysis before screening
for outliers

27. Outlier screened TLC (scrnd TLC): 32 tests
Oil discrimination:
PC10 F & all the other oils, except for oil A & PC10 C
Oil A & PC10 A

28. Outlier screened TGF (OTGF): 24 tests taking into account differences among cylinders
No transformation used
Final Model: Lab; Rsquare adj: 47%
Precision: 7.22
No significant differences among Stands, Technologies or Base Oil
Lab discrimination: Lab A & Lab F; Lab A & Lab G;
Similar results are obtained
for the analysis before screening
for outliers
Levels not connected by same
letter are significantly different

29. Outlier screened TGF (OTGF): 32 tests taking into account differences among cylinders
Similar results are obtained
for the analysis before screening
for outliers
No transformation used
Final model: Lab and Oil Type; Rsquare adj: 47.5%
Precision: 6.96
No significant differences among Stands or Oil types
Lab discrimination: Lab A & Lab F; Lab A & Lab G

30. Outlier screened TGF (OTGF): 32 tests taking into account differences among cylinders
No Oil Discrimination

31. Outlier screened TLHC (scrnd TLHC): 24 tests
No transformation used
Final Model: Lab, Technology, Base Oil and interaction of Technology & Base Oil
Rsquare adj: 80%
Precision: 3.05
No significant differences among Stands
Statistical evidence that Lab B is severe
Similar results are obtained
for the analysis before screening
for outliers

32. Outlier screened TLHC (scrnd TLHC):24 tests
Impact of Base Oil on scrnd TLHC depends upon Technology
Technology B/Base oil 3 seems significantly higher than the other Technology/ Base Oil combinations
Levels not connected by same
letter are significantly different

33. Outlier screened TLHC (scrnd TLHC):32 tests
No transformation used
Final Model: Lab, Oil Type; Rsquare adj: 69%
Precision: 3.45
No significant differences among Stands
Some indication that Lab B is severe

34. scrnd TLHC:32 tests Oil discrimination:

35. Correlations:
24 tests
taking into account the final model for each parameter

36. Pairwise Correlations 24 tests: taking into account the final model for each parameter

37. Correlations 24 tests: raw data

38. Pairwise Correlations 24 tests: raw data

39. Correlations 32 tests: taking into account Lab and Oil Type

40. Pairwise Correlations 32 tests: taking into account Lab and Oil Type

41. Correlations 32 tests: raw data

42. Pairwise Correlations 32 tests: raw data

43. Precision based on the model
Desirable values for E p are greater than 1
E p is greater than 1 for TLC and TLHC
Precision based on the model
Median of MAD survey
E p1
E p2
Parameter
24 tests
32 tests
Delta OC
6.5
6.82
4.5
0.6923
0.6598
OUWD
8.15
8.5
OTGC
5.85
5.74 5
0.8547
0.8711
OTGF
7.22
6.96
0.6233
0.6466
scrnd TLC
4.02
4.25
1.1194
1.0588
scrnd TLHC
3.05
3.45 4
1.3115
1.1594
MAD survey indicates the maximum acceptable difference between
two test results on the same formulation

44. Appendix 1 Plots of the performance measures by Oil

57. Appendix 2: Precision for 1P
ASTM TMC requirements for Engine Test
Stand/Lab Calibration (Page 12-1)
Calculated from all data: 103 tests: Chart = Yes
WD: There seems to be Lab differences for WD
OC-g/h: There seems to be Lab differences and Oil differences

58. Appendix 3: C13 Precision by cylinder based on 24 tests
The numbers below may be compared to the precision for the 1P
TGC:
TGC1=10.36 TGC2= 9.04 TGC3= 9.95
TGC4= 7.73 TGC5= 9.21 TGC6= 7.7
TLC:
TLC1=10.24 TLC2=9.23 TLC3= 7.47
TLC4= 8.9 TLC5=8.71 TLC6= 9.16

59. Appendix 4: Summary statistics - 32 tests

60. Appendix 5: Summary statistics - 24 tests
Area under construction
Appendix 5: Summary statistics - 24 tests

61. Appendix 6: Additional plots Follow up to the BOI meeting

62. Delta OC versus Base Oil

63. Parameter versus Tech/Base Oil Combination

64. OTGC versus Base Oil

65. scrnd TLC versus Base Oil

66. OTGF versus Base Oil

67. OUWD versus Base Oil

68. Base Oil Effect Summary from the BOI presentation (10/21/05)
Prmter
Tchnlgy
Base Oil Effect Observed
Statistically Significant? OC A
Higher Sats/BOVI=Lower OC No B
Higher Sats/BOVI=Higher OC
Group III
UWD
A & B
Group III=Higher UWD
Yes
TLC
Higher Sats/BOVI=Higher TLC
Group III=Higher TLC
TLHC
Higher Sats/BOVI=Higher TLHC
Group III=Higher TLHC
TGF
NONE NA
TGC
Group III=Higher TGC