Cummins ISB LTMS2 This package contains charts and figures that supplement the LTMS2 template put forth by Statistics Task Group. LTMS2 Template document name: “Cummins ISB LTMS Version 2 Proposal.docx” The LTMS2 template contains possible values for the various chart limits. Page 2 of this document summarizes these values. Pages 3-11 show the control charts and alarms of LTMS1 and proposed LTMS2. Pages 12-14 contain some comments on Excessive Influence calculations and alarms in LTMS1&2. Art Andrews November 30, 2010

LTMS1 LTMS2 lambda=0.2 No Fast start Fast start with three reference oil results No e alarms Level 1 e limit = 1.351 (e.g. hardware change) Level 2 e limit = 1.734 (reduced interval) Level 3 e limit = 2.066 (immediate re-reference) No Z alarms Level 1 Z limit = 0 (dead band) ACWS Level 2 Z limit = +/- 1.5 (immediate re-reference) ATWL Level 2 Z limit = +2/-1.5 (immediate re-reference) Shewhart severity (Y) limit = +/-1.96 (immediate re-reference) No Y Alarms No Excessive Influence calculation Excessive Influence calculation; uses Level 3 e limit as its tolerance No extended reference intervals Ee = 1.05 Ez = 0.66 (eligible for +20% and +40% reference intervals)

focus: Shewhart severity (Y) alarms LTMS1 focus: Shewhart severity (Y) alarms

ACSW

ATWL

LTMS2 focus: e alarms

ACSW

ATWL

Comparisons LTMS1 / LTMS2 focus: number of reference interval extensions and reductions

Reference Interval Extensions and Reductions 37 total reference oil results 12 were calibration tests 37-12=25 tests were eligible for extended intervals 9/25 (36%) received extended intervals in LTMS2 7/37 (18.9%) failed in LTMS2

RMSE overall for all labs RMSE by lab

Comments on Excessive Influence and Alarms Appendix Comments on Excessive Influence and Alarms

Tappet weight loss severity charts showing Excessive Influence calculation Excessive Influence calculation adjusted Y results from green filled circle to cyan circle.

The dotted line is Level 2 e alarm, and solid line Level 3 e alarm Tappet weight loss precision charts showing e These are examples of results that trigger alarms in LTMS2 but not LTMS1. While their Y results are not excessive, their e values are high (~1.1) because they outlie the lab’s Z baseline (~-0.9). This is an example of a result that would trigger alarm in either LTMS1 and LTMS2. It has a high Y value that exceeds LTMS1 limit. It has a high e value because its result (~2.8) outlies the lab’s Z baseline (~0.1). The dotted line is Level 2 e alarm, and solid line Level 3 e alarm