NRC 95-95, Interpretation

8/16/2019 NRC 95-95, Interpretation

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NRC Staff Interpretation of

95/95 Tolerance Limitsin Safety System Setpoint AnalysisNRC Public Meeting with GE-Hitachi

September 28, 2010NRC Headquarters

6003 Executive Boulevard, Rockville, MD 20852

David Rahn, Sr. Electronics Engineer, NRR/DE/EICB

[email protected]


2/17

Disclaimer

• The following slides summarize the collective opinions of

several members of the NRC staff concerning the

interpretation of statistical representations used in theanalysis of instrument channel performance. This

information is being considered for use in establishing

acceptance review criteria pertinent to the review of

proposed instrument setpoint methodologies. The

information herein represents work in progress, and

does not necessarily represent the concurrence of all

cognizant staff members or a final decision in this matter.

2


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Regulatory Guide 1.105

• Regulatory Position C.1 of Rev. 3 (1999) of Reg

Guide 1.105 states:

– “Section 4 of ISA-S67.04-1994 specifies the

methods, but not the criterion, for combining

uncertainties in determining a trip setpoint and its

allowable values. The 95/95 tolerance limit is an

acceptable criterion for uncertainties. That is, thereis a 95% probability that the constructed limits

contain 95% of the population of interest for the

surveillance interval selected.”

3


4/17

Regulatory Guide 1.105 (continued)

• Revision 2 (1986) of Reg. Guide 1.105 stated:

– “Paragraph 4.3 of the standard specifies the methods

for combining uncertainties in determining a tripsetpoint and its allowable values. Typically, the NRC

staff has accepted 95% as a probability limit for

errors. That is, of the observed distribution of values

for a particular error component in the empirical database, 95% of the data points will be bounded by the

value selected. If the data base follows a normal

distribution, this corresponds to an error distribution

approximately equal to a "two sigma" value.”4


5/17

Further Clarification Planned

• The NRC staff has recognized that these definitions

and statements in the previous and current versions

of RG 1.105 could be enhanced with furtherclarification to ensure that all licensees and NRC

reviewers of safety-related instrument setpoints have

a clear, common understanding of the NRC staff’s

concerns. The following slides represent a proposed

way of providing such clarification.

5


6/17

Confidence Interval Estimation• When the magnitude of a particular performance

characteristic, (such as “power supply effect” or “drift”) of

an instrument population is to be estimated, sampling of

that population is performed, and the characteristic ofinterest is measured for each sample. The mean and

standard deviation of the sample are then determined.

• One is usually interested in finding an interval around the

sample mean such that there is a high probability thatthe actual population mean falls inside of this

interval. This interval is called a confidence interval and

the high probability is called the confidence level.

6


7/17

Confidence Interval Estimation• The NRC staff position is that an acceptable confidence level to use

for such estimates of instrument performance characteristics is

±1.96 σ, which is the confidence interval that is large enough to

ensure, with a 95% confidence, that the true population meanactually lies within this interval.

• If the raw data sample size is not sufficiently large, (e.g., there has

not been an appropriate number of tests or measurements of the

characteristic of interest to support statistical test methods) the

interval should be determined through best-estimate means, such asbounding assumptions supported by adequate technical justification,

(e.g., documented historical operating experience) or through use of

appropriate statistical means (e.g., Student’s t-factors)

7


8/17

Tolerance Intervals• Used to specify with a certain degree of confidence

that a specified proportion of a population lies within a

certain interval.

• The “level of confidence” of a tolerance interval is a

measure of the likelihood that the calculated interval of

interest does, in fact, cover at least the specified

proportion of the population of interest.

• The tolerance interval that covers 95% of a population

of interest with 95% confidence is used by the NRC

staff as an acceptance criterion when reviewing

several types of nuclear safety-related analyses.

8


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95% Tolerance Intervals of Interest

0

0.005

0.01

0.015

0.02

0.025

-100.00 -80.00 -60.00 -40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00

-1.96 σ +1.96 σ

95% of Probabili ty Distribution2.5% of

Distribution

2.5% ofDistribution

Lower and Lower Probability

Areas

Population Area

of lower interest

(Population area of highest interest)

Highest Probability of Trip

Occurrence

9

Population Area

of lower interest


10/17

Assumptions:• Sufficient data exists to support statistical analyses

• Data representing random error is normally distributed

• Data represents random and independent terms

• Central limit theorem/SRSS methods can be used to

combine like units of standard deviations of random error

• Setpoint errors are disposed symmetrically about the

mean, resulting in the highest probability of a channel trip

being closest to, and symmetric about, the mean

• The highest probabilities of trip occurrence are centered

close to the mean, and lower probabilities are symmetric,

but further away the mean

10


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95% Tolerance Interval• If the endpoints of the interval are being estimated based

on random variables, then the level of confidence

associated with a particular tolerance interval is a

measure of the likelihood that the calculated intervaldoes, in fact, cover at least the specified portion of the

population.

• If the tolerance limits have been based on a statistically

sufficient quantity of sample data, the confidence that theinterval contains 95% of the population of interest

increases.

• The NRC staff uses a confidence level of 95% as an

acceptance criterion for this likelihood. 11


12/17

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

-100.00 -80.00 -60.00 -40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00

-1.96σ+1.96σ

-1.96σ +1.96σ (for the yellow curve)

(for the red curve)

95% Tolerance Intervals of Interest

for Various Probabil ity Distributions

For each of these curves, 95% of the

population of interest lies between the

interval beginning with -1.96 σ and

ending with + 1.96 σ. The population of

interest is centered about (or, symmetric

with respect to) the mean.

12


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0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

-12 -7 -2 3 8

-1.96 σ +1.96 σ

+1.645 σ-∞

95% 97.5%

2.5% 5%

Tolerance Interval

of Interest

NEDC-31336P

Tolerance

Interval

Setpoint

5%

2.5%

Cumulative Probabil ity –Interval of

Interest

13


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Cumulative Probability

The NRC staff understanding of the tolerance intervalassociated with the cumulative probability of interest is

that portion of the probability distribution encompassing

the interval from 2.5% of the population to 97.5% of the

population, totaling 95% of the population of interest.

The NRC staff understanding of the 95% tolerance

limits is such that those limits are symmetric with

respect to the mean. In Reg Guide 1.105 Revision 3,

the NRC staff intended that the term “95/95 tolerancelimit” referred to those limits reflecting a 95% confidence

that the limits contain 95% of the population of interest,

which is that centered around the mean, containing the

highest probabilities of occurrence. 14


15/17

Probabil ity of Failure to Trip before

AL is exceeded

• Ignoring instrument channel performance bias terms, an

instrument channel set at 1.96-σ away from the analytical

limit, assuming the 95/95 tolerance interval definition thatincludes the “symmetric about the mean” criterion, has a

probability of failing to trip before the analytical limit is

exceeded of 2.5%.

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0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

-12 -7 -2 3 8

-1.96 σ +1.96 σ

+1.645 σ-∞

95% 97.5%

2.5% 5%

Tolerance Interval

of Interest

NEDC-31336P

Tolerance

Interval

Setpoint

5%

2.5%

AL1 AL2

Instrument Channel Probabil ity of

Failure to Trip before AL: 2.5%

16

Total Loop

Uncertainty

(TLU)

(ignoring

bias terms)


17/17

Other Acceptable Approaches are Possible• Reg Guide 1.105 represents one method of ensuring

that the instrument channel will trip with a 95/95

tolerance limit before the analytical limit is exceeded.

• Other methods are also possible.

• The NRC staff would consider an instrument setpoint

determination method to be adequate where it can be

shown that the instrument channel will trip before the

analytical limit is exceeded, and provided it can beadequately demonstrated that the “95/95 tolerance limit”

is applied to ensure, with 95% confidence, that the

appropriate tolerance interval contains 95% of the

population of interest. 17

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NRC 95-95, Interpretation

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