# Title 40

## SECTION 90.708

### 90.708 Cumulative Sum (CumSum) procedure.

§ 90.708 Cumulative Sum (CumSum) procedure.(a) (1) Manufacturers must construct separate CumSum Equations for each regulated pollutant (HC + NOX (NMHC + NOX) and CO) for each engine family. Test results used to calculate the variables in the CumSum Equations must be final deteriorated test results as defined in § 90.709(c). The CumSum Equation is constructed as follows:

*C*i = max[0 0

*R*(

*C*i−1 +

*X*i−(

*FEL + F))*] Where: Ci = The current CumSum statistic. Ci-1 = The previous CumSum statistic. Prior to any testing, the CumSum statistic = 0 (i.e. C0 = 0). Xi = The current emission test result for an individual engine. FEL = Family Emission Limit (the standard if no FEL). F = .25 × σ.

(2) After each test pursuant to paragraph (a)(1) of this section, Ci is compared to the action limit, H, the quantity which the CumSum statistic must exceed, in two consecutive tests, before the engine family may be determined to be in noncompliance for a regulated pollutant for purposes of § 90.710.

Where: H = The Action Limit. It is 5.0 × σ, and is a function of the standard deviation, σ. σ = is the sample standard deviation and is recalculated after each test.(b) After each engine is tested, the CumSum statistic shall be promptly updated according to the CumSum Equation in paragraph (a) of this section.

(c)(1) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in § 90.122(a) by performing an engine family modification (i.e. a change such as a running change involving a physical modification to an engine, a change in specification or setting, the addition of a new configuration, or the use of a different deterioration factor) with no changes to the FEL (where applicable), all previous sample size and CumSum statistic calculations for the model year will remain unchanged.

(2) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in § 90.122 (a) by modifying its FEL (where applicable) for future production, as a result of an engine family modification, the manufacturer must continue its calculations by inserting the new FEL into the sample size equation as specified in § 90.706(b)(1) and into the CumSum equation in paragraph (a) of this section. All previous calculations remain unchanged. If the sample size calculation indicates that additional tests are required, then those tests must be performed. CumSum statistic calculations must not indicate that the family has exceeded the action limit for two consecutive tests. Where applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that result from each FEL and corresponding CumSum analysis for the set of engines built to each FEL.

(3) If, at any time during the model year, a manufacturer amends the application for certification for an engine family as specified in § 90.122 (a) (or for an affected part of the year's production in cases where there were one or more mid-year engine family modifications), by modifying its FEL (where applicable) for past and/or future production, without performing an engine modification, all previous sample size and CumSum statistic calculations for the model year must be recalculated using the new FEL. If the sample size calculation indicates that additional tests are required, then those tests must be performed. The CumSum statistic recalculation must not indicate that the family has exceeded the action limit for two consecutive tests. Where applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that result from each FEL and corresponding CumSum analysis for the set of engines built to each FEL.