Estimation of uncertainty in the single burning item test

The measuring technique of the SBI (single burning item) test instrument is based on the observation that, in general, the heats of combustion per unit mass of oxygen consumed are approximately the same for most fuels commonly encountered in fires (Huggett [12]). The mass flow, together with the oxygen concentration in the extraction system, suffices to continuously calculate the amount of heat released. Some corrections can be introduced if CO2, CO and/or H2O are additionally measured.

Messunsicherheit - Thermische Beanspruchung durch einen einzelnen brennenden Gegenstand (SBI)

Ocena negotovosti s preskusom enega samega gorečega predmeta

Merilna tehnika instrumenta za preskušanje gorljivosti posameznega predmeta (SBI) temelji na ugotovitvi, da je toplota zgorevanja na enoto mase porabljenega kisika na splošno približno enaka za večino goriv, ki so običajna pri požarih (Huggett [12]). Masni pretok skupaj s koncentracijo kisika v sistemu za odvajanje zadostuje za neprekinjeno izračunavanje količine sproščene toplote. Nekateri popravki se lahko uporabijo, če se dodatno izmerijo vrednosti CO2, CO in/ali H2O.

General Information

Status
Published
Publication Date
26-Jul-2016
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
27-Jul-2016
Completion Date
27-Jul-2016

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SLOVENSKI STANDARD
SIST-TP CEN/TR 16988:2016
01-november-2016
2FHQDQHJRWRYRVWLVSUHVNXVRPHQHJDVDPHJDJRUHþHJDSUHGPHWD
Estimation of uncertainty in the single burning item test
Messunsicherheit - Thermische Beanspruchung durch einen einzelnen brennenden
Gegenstand (SBI)
Ta slovenski standard je istoveten z: CEN/TR 16988:2016
ICS:
13.220.40 Sposobnost vžiga in Ignitability and burning
obnašanje materialov in behaviour of materials and
proizvodov pri gorenju products
SIST-TP CEN/TR 16988:2016 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/TR 16988:2016
CEN/TR 16988
TECHNICAL REPORT
RAPPORT TECHNIQUE
July 2016
TECHNISCHER BERICHT
ICS 17.200.01
English Version
Estimation of uncertainty in the single burning item test
Messunsicherheit - Thermische Beanspruchung durch
einen einzelnen brennenden Gegenstand (SBI)

This Technical Report was approved by CEN on 4 July 2016. It has been drawn up by the Technical Committee CEN/TC 127.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,

Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels

© 2016 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 16988:2016 E

worldwide for CEN national Members.
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Contents Page

European foreword ....................................................................................................................................................... 4

1 Scope .................................................................................................................................................................... 5

1.1 General ................................................................................................................................................................ 5

1.2 Calculation procedure ................................................................................................................................... 5

1.2.1 Introduction ...................................................................................................................................................... 5

1.2.2 Synchronization of data ................................................................................................................................ 5

1.2.3 Heat output ........................................................................................................................................................ 5

2 Uncertainty ........................................................................................................................................................ 9

2.1 Introduction ...................................................................................................................................................... 9

2.2 Elaboration of terms and concepts ........................................................................................................ 11

2.2.1 Mean and variance ....................................................................................................................................... 11

2.2.2 Estimation of the confidence interval for the population mean ................................................. 12

2.2.3 Sources of uncertainty ................................................................................................................................ 12

2.2.4 Standard uncertainties for different distributions .......................................................................... 12

2.2.5 Combined uncertainty ................................................................................................................................ 15

2.2.6 Expanded uncertainty ................................................................................................................................ 16

2.2.7 Uncorrected bias .......................................................................................................................................... 16

2.3 Combined standard uncertainties ......................................................................................................... 17

2.3.1 Combined standard uncertainty on sums ........................................................................................... 17

2.3.2 Combined standard uncertainty on averages .................................................................................... 18

2.3.3 Combined standard uncertainty of a product and a division ....................................................... 19

2.3.4 Combined standard uncertainty on the heat release rate (Q) ..................................................... 20

2.3.5 Combined standard uncertainty on the depletion factor (ϕ) ...................................................... 22

2.3.6 Combined standard uncertainty on the initial O -concentration (X ) ................................. 22

2 O2

2.3.7 Combined standard uncertainty on the volume flow rate (V ) .............................................. 23

D298

2.3.8 Combined standard uncertainty on the air density (ρ ) .............................................................. 24

air

2.3.9 Combined standard uncertainty on specimen heat release rate (Qspecimen) ............................ 24

2.3.10 Combined standard uncertainty on the average heat release rate (Q ) ................................. 24

2.3.11 Combined standard uncertainty on FIGRA ......................................................................................... 25

2.3.12 Combined standard uncertainty on THR600s ................................................................................... 25

2.3.13 Combined standard uncertainty on the volume flow (V(t)) ......................................................... 25

2.3.14 Combined standard uncertainty on the smoke production rate (SPR) .................................... 25

2.3.15 Combined standard uncertainty on specimen smoke production rate (SPR) ....................... 26

2.3.16 Combined standard uncertainty on the average smoke production rate (SPR ) ................ 26

2.3.17 Combined standard uncertainty on SMOGRA .................................................................................... 26

2.3.18 Combined standard uncertainty on TSP600s .................................................................................... 27

2.4 Confidence interval classification parameters .................................................................................. 27

2.5 Standard uncertainty on the different components ........................................................................ 28

2.5.1 Uncertainty on the data acquisition (DAQ)......................................................................................... 28

2.5.2 Transient error ............................................................................................................................................. 28

2.5.3 Aliasing error ................................................................................................................................................. 28

2.5.4 Uncertainty on data synchronicity ........................................................................................................ 29

2.5.5 Uncertainty on the component E and E’ ............................................................................................... 30

2.5.6 Uncertainty on the component φ ........................................................................................................... 36

2.5.7 Uncertainty on the component p ....................................................................................................... 36

atm

2.5.8 Uncertainty on the component T ..................................................................................................... 36

room

2.5.9 Uncertainty on the component α ............................................................................................................ 38

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2.5.10 Uncertainty on the component c ............................................................................................................. 38

2.5.11 Uncertainty on the component A and L ................................................................................................ 39

2.5.12 Uncertainty on the component q ........................................................................................................ 40

gas

2.5.13 Uncertainty on the component k ............................................................................................................ 40

2.5.14 Uncertainty on the component k ........................................................................................................... 43

2.5.15 Uncertainty on the component Δp .......................................................................................................... 44

2.5.16 Uncertainty on the component T ......................................................................................................... 44

2.5.17 Uncertainty on the component I .............................................................................................................. 46

Annex A (informative) List of symbols and abbreviations ......................................................................... 48

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European foreword

This document (CEN/TR 16988:2016) has been prepared by Technical Committee CEN/TC 127 “Fire

Safety in Buildings”, the secretariat of which is held by BSI.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document has been prepared under a mandate given to CEN by the European Commission and the

European Free Trade Association.
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1 Scope
1.1 General

The measuring technique of the SBI (single burning item) test instrument is based on the observation

that, in general, the heats of combustion per unit mass of oxygen consumed are approximately the same

for most fuels commonly encountered in fires (Huggett [12]). The mass flow, together with the oxygen

concentration in the extraction system, suffices to continuously calculate the amount of heat released.

Some corrections can be introduced if CO , CO and/or H O are additionally measured.

2 2
1.2 Calculation procedure
1.2.1 Introduction

The main calculation procedures for obtaining the HRR and its derived parameters are summarized

here for convenience. The formulas will be used in the following clauses and especially in the clause on

uncertainty.

The calculations and procedures can be found in full detail in the SBI standard [1].

1.2.2 Synchronization of data

The measured data are synchronized making use of the dips and peaks that occur in the data due to the

switch from ‘primary’ to ‘main’ burner around t = 300 s, i.e. at the start of the thermal attack to the test

specimen. Synchronization is necessary due to the delayed response of the oxygen and carbon dioxide

analysers. The filters, long transport lines, the cooler, etc. in between the gas sample probe and the

analyser unit, cause this shift in time.

After synchronization, all data are shifted so that the ‘main’ burner ignites – by definition – at time

t = 300 s.
1.2.3 Heat output
1.2.3.1 Average heat release rate of the specimen (HRR )
30s

A first step in the calculation of the HRR contribution of the specimen is the calculation of the global

HRR. The global HRR is constituted of the HRR contribution of both the specimen and the burner and is

defined as
 φ(t) 
HRR (t)= EV (t)x   (1)
total D298 a_O2
 
1+ 0,105φ(t)
 
where
is the total heat release rate of the specimen and burner (kW);
HRR (t)
total

′ is the heat release per unit volume of oxygen consumed at 298 K, = 17 200 (kJ/m3);

 is the volume flow rate of the exhaust system, normalized at 298 K (m3/s);
Vt()
D298
is the mole fraction of oxygen in the ambient air including water vapour;
a_O2
is the oxygen depletion factor.
ϕ()t
 φ(t) 

The last two terms x and   express the amount of moles of oxygen, per unit volume,

a_O2
 
1+ 0,105φ(t)
 

that have chemically reacted into some combustion gases. Multiplication with the volume flow gives the

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amount of moles of oxygen that have reacted away. Finally this value is multiplied with the ‘Huggett’

factor. Huggett stated that regardless of the fuel burnt roughly a same amount of heat is released.

The volume flow of the exhaust system, normalized at 298 K, V (t) is given by
D298
k Dp(t)
V (t)=cA (2)
D298
k T (t)
ρ ms
where
0,5 1,5 −0,5
(2T /ρ ) 22, 4 [K⋅ m ⋅ kg ]
A is the area of the exhaust duct at the general measurement section (m2);

is the flow profile correction factor; converts the velocity at the height of the bi-directional

probe in the axis of the duct to the mean velocity over the cross section of the duct;

is the Reynolds number correction for the bidirectional probe, taken as 1,08;
Dpt() is the pressure difference over the bi-directional probe (Pa);
is the temperature in the measurement section (K).
Tt()
The oxygen depletion factor ϕ()t is defined as
xO (30s...90s){1−xCO (t)}−xO (t){1−xCO (30s...90s)}
2 2 2 2
φ(t)= (3)
xO (30s...90s){1−xCO (t)−xO (t)}
2 2 2
where
is the oxygen concentration in mole fraction;
xtO ()
is the carbon dioxide concentration in mole fraction;
xtCO ( )
Ys...Zs mean taken over interval Y s to Z s.

The mole fraction of oxygen in ambient air, taking into account the moisture content, is given by

 
 
H 3816
x = xO (30s...90s) 1− exp 23,2− (4)
  
a_O2 2
100p T (30s...90s)− 46
 ms 
 
where
is the oxygen concentration in mole fraction;
xtO ()
H is the relative humidity (%);
p is the ambient pressure (Pa);
Tms(t) is the temperature in the general measurement section (K).

Since we are interested in the HRR contribution of the specimen only, the HRR contribution of the

burner should be subtracted. An estimate of the burner contribution HRR (t) is taken as the

burner

HRR (t) during the base line period preceding the thermal attack to the specimen. A mass flow

total

controller ensures an identical HRR through the burners before and after switching from primary to the

main burner. The average HRR of the burner is calculated as the average HRR (t) during the base line

total
period with the primary burner on (210 s ≤ t ≤ 270 s):
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HRR = HRR total (210s...270s) (5)
av_burner
where
HRRav_burner is the average heat release rate of the burner (kW);
HRRtotal(t) is the total heat release rate of specimen and burner (kW).
HRR of the specimen

In general, the HRR of the specimen is taken as the global HRR, HRR (t), minus the average HRR of the

total
burner, HRR :
av_burner
For t > 312 s:
HRR(t)= HRR (t)− HRR (6)
total av_burner
where:
HRR(t) is the heat release rate of the specimen (kW);
HRRtotal(t) is the global heat release rate of specimen and burner (kW);
HRRav_burner is the average heat release rate of the burner (kW).

During the switch from the primary to the main burner at the start of the exposure period, the total heat

output of the two burners is less than HRR (it takes some time for the gas to be directed from one

av_burner

burner to the other). Formula (24) gives negative values for HRR(t) for at most 12 s (burner switch

response time). Such negative values and the value for t = 300 s are set to zero, as follows:

For t = 300 s:
HRR(300)= 0 kW (7)
For 300 s < t ≤ 312 s:
HRR(t)= max.{0 kW, HRR (t)− HRR } (8)
total av_burner
where
max.[a, b] is the maximum of two values a and b.
Calculation of HRR
30s

In view of the calculation of the FIGRA index, the HRR data are smoothened with a ‘flat’ 30 s running

average filter using 11 consecutive measurements:
0,5HRR(t−15)+ HRR(t−12 )+ ...+ HRR(t+12)+ 0,5HRR(t+15)
(9)
HRR (t)=
30s
where
HRR (t) is the average of HRR(t) over 30 s (kW);
30s
HRR(t) is the heat release rate at time t (kW).
1.2.3.2 Calculation of THR(t) and THR
600s

The total heat release of the specimen THR(t) and the total heat release of the specimen in the first

600 s of the exposure period (300 s ≤ t ≤ 900 s), THR , are calculated as follows:

600s
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THR(t )= HRR(t)×3 (10)
a ∑
1000
300s
900s
THR = HRR(t)×3 (11)
600s ∑
1000
300s

whereby the factor 1 000 is introduced to convert the result from kJ into MJ and the factor 3 stands for

the time interval in-between 2 consecutive measurements,
and where

THR(t ) is the total heat release of the specimen during the period 300 s ≤ t ≤ t (MJ);

a a
HRR(t) is the heat release rate of the specimen (kW);

THR is the total heat release of the specimen during the period 300 s ≤ t ≤ 900 s (MJ);

600s
(equal to THR(900)).
1.2.3.3 Calculation of FIGRA and FIGRA (Fire growth rate indices)
0.2MJ 0.4MJ

The FIGRA is defined as the maximum of the ratio HRR (t)/(t − 300), multiplied by 1 000. The ratio is

calculated only for that part of the exposure period in which the threshold levels for HRR and THR

have been exceeded. If one or both threshold values are not exceeded during the exposure period,

FIGRA is equal to zero. Two combinations of threshold values are used, resulting in FIGRA and

0,2MJ
FIGRA .
0,4MJ

a) The average of HRR, HRR , used to calculate the FIGRA is equal to HRR , with the exception of the

av 30s

first 12 s of the exposure period. For data points in the first 12 s, the average is taken only over the

widest possible symmetrical range of data points within the exposure period:
For t 300 s: HRR (300 s) 0 (12)
For t 303 s: HRR (303 s) HRR(300 s306 s) (13)
For t 306 s: HRR (306 s) HRR(300 s312 s) (14)
For t 309 s: HRR (309 s) HRR(300 s318 s) (15)
For t 312 s: HRR (312 s) HRR(300 s324 s) (16)
For t≥=315 s: HRR (tt) HRR ( ) (17)
av 30s
b) Calculate FIGRA for all t where:
0,2MJ
(HRR (t) > 3 kW) and (THR(t) > 0,2 MJ) and (300 s < t ≤ 1 500 s);
and calculate FIGRA for all t where:
0,4MJ
(HRRav(t) > 3 kW) and (THR(t) > 0,4 MJ) and (300 s < t ≤ 1 500 s);
both using:
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HRR (t)
 
FIGRA=1000× max. (18)
 
t− 300
 
where:
FIGRA is the fire growth rate index
HRR (t) is the average of HRR(t) as specified in a) (kW);

As a consequence, specimens with a HRR not exceeding 3 kW during the total test have FIGRA values

FIGRA and FIGRA equal to zero. Specimens with a THR not exceeding 0,2 MJ over the total test

0,2MJ 0,4MJ

period have a FIGRA equal to zero and specimen with a THR not exceeding 0,4 MJ over the total test

0,2MJ
period have a FIGRA equal to zero.
0,4MJ
2 Uncertainty
2.1 Introduction

According to EN ISO/IEC 17025 [3], which sets out the general requirements for the competence of

testing and calibration laboratories, and EN ISO 10012 [7], which sets out the requirements for assuring

the quality of measuring equipment, uncertainties shall be reported in both testing and calibration

reports.

The general principles for evaluating and reporting uncertainties are given in the ISO Guide to the

Expression of Uncertainty in Measurement (GUM) [6], but need to be applied to the specific case of fire

testing. Due to the harmonization of fire testing in the European Community (EUROCLASSES;

EN 13501-1 [21]) and the pressure on testing laboratories to operate under accreditation, this is

becoming even more important.

It is of common knowledge that measurement results are never perfectly accurate. In practice the

sources of systematic and random errors which can affect the results of measurement are numerous,

even for the most careful operators. To describe this lack of perfection, the term 'uncertainty' is used.

Although the concept of uncertainty may be related to a 'doubt', in the real sense the knowledge of

uncertainty implies increased confidence in the validity of results.

The qualitative concept of accuracy is quantified by the uncertainty which varies inversely

‘proportioned’ to it. Accuracy consists of both trueness and precision as shown in Figure 1. A numerical

measure for precision is the standard deviation, while trueness is expressed numerically by the

systematic error or the bias.

It is considered good practice to eliminate any systematic errors. However, if the value of a systematic

error is unknown it may be regarded as a random error. Random errors result in a spread of the values

and can usually be reduced by increasing the number of observations. Its expectation or expected value

is zero.
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high precision low precision
high
trueness
(high accuracy)
low
trueness

Figure 1 — Concepts of accuracy (uncertainty), precision (standard deviation) and trueness

(bias)

In general, the result of a measurement is only an approximation or estimate of the value of the specific

quantity subject to measurement, that is, the measurand, and so the result is complete only when

accompanied by a quantitative statement of its uncertainty.

Without knowledge of the accuracy (trueness and precision) of measurement methods and/or the

uncertainty of measurement results, it can appear very easy to make decisions. But, in practice, these

decisions might be incorrect and sometimes lead to serious consequences, if the measurement

uncertainty is not taken into account.

For example, in fire testing, when rejecting instead of accepting a good product during a certification

process or, conversely, when accepting a bad product by error. So, it is vital to quantify the reliability of

the measurement results to greatly reduce any disputes and adverse consequences of legal proceedings.

This is of particular importance if the growing number of cases of litigation in Europe and the liability

problems of manufacturers in case of accidents are considered.

The difference between error and uncertainty should always be borne in mind. For example, the result

of a measurement after correction can unknowably be very close to the unknown value of the

measurand, and thus have negligible error, even though it might have a large uncertainty.

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Key
X value
Y frequency
1 bias
2 repeated measurements would give values with this frequency curve
3 standard deviation (σ)
4 true value
5 expected value

Figure 2 — Concepts of accuracy (uncertainty), precision (standard deviation) and trueness

(bias)
2.2 Elaboration of terms and concepts
2.2.1 Mean and variance

A population with a ‘normal’ probability density function is characterized by its mean value μ and its

2 2 2

variance σ : N(μ,σ ). When both μ and σ are unknown, they can be estimated by taking a number n of

samples and by calculating the estimated mean x , the estimated variance s and the estimated

standard deviation s.
(19)
x= x
i=1
( ) (20)
s = x−x
n−1
i=1
If a covariance exists between two variables x and y, it is given by
s = (x−x)(y− y) (21)
ij ∑ i i
n−1
i=1
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2.2.2 Estimation of the confidence interval for the population mean

Often the standard deviation σ is unknown. To evaluate the confidence interval, some estimate of σ shall

be made. The most obvious candidate is the sample standard deviation s. But the use of s introduces an

additional source of unreliability, especially if the sample is small. To retain the confidence interval, the

interval shall therefore be widened. This is done by using the t distribution instead of the standard

normal distribution. For a sample size larger than 100, the t-distribution approaches the normal

distribution. For a 95 % (two tails of 2,5 %) confidence interval – which we strive for – the uncertainty

is estimated by
t (22)
0.025

The value t depends on the amount of information used in calculating s , i.e. on the degrees of

0.025

freedom. For large sample sizes, t approaches 1,96 which is the value for a normal distribution. For a

0.025

normal distribution, a coverage factor 2 (1,96) corresponds to a 95 % confidence interval (see 2.2.6).

2.2.3 Sources of uncertainty

According to GUM [6] any detailed report of the uncertainty should consist of a complete list of the

components, specifying for each the method used to obtain its numerical value. The components may be

grouped into two categories based on their method of evaluation:

Type A The components in category A are characterized by the estimated variances s

or by the estimated standard deviation s derived from data by statistical
methods. Where appropriate the covariance s should be given.
For such a component, the standard uncertainty is ui = si.
Type B The standard uncertainty of a Type B evaluation is approximated based on
specifications, calibrations, handbooks, experience, judgements etc. and is
represented by a quantity uj. It is obtained from an assumed probability
distribution based on all the available information.
Where appropriate the covariance should be given and should be treated in a
similar way.

The ‘type’ classification does not indicate any difference in the nature of the components resulting from

the two types of evaluation. Both are based on probability distributions, and the uncertainty

components resulting from either type are quantified by standard deviations. It should be recognized

that a Type B evaluation of standard uncertainty can be as reliable as a Type A evaluation.

The standard deviation of a Type B evaluation is based on the shape of the distribution. Distributions

used in this dcoument are the rectangular, the triangular, the trapezoidal and the normal distribution.

For the rectangular and triangular also asymmetric distributions are discussed.
2.2.4 Standard uncertainties for different distributions
Normal distribution

Often calibration certificates, handbooks, manufacturer’s specifications, etc. state a particular multiple

of a standard deviation. In this case, a normal distribution is assumed to obtain the standard

uncertainty.
Rectangular distribution

In other cases the probability that the value of X lies within the interval a- to a+ for all practical

purposes is equal to one and the probability that X lies outside this interval is essentially zero. If there

is no specific knowledge about the possible values of X within the interval, a uniform or rectangular

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distribution of values is assumed. The associated standard deviation is function of the width of the

distribution as:
(23)
u =
rect

Indeed, for a rectangular distribution, the variance is obtained as in 24. Given the probability function of

the rectangular distribution
0 x Vitryalice1P(x)= a< x b−a
0 x>b
This can be written in terms of the Heaviside step function H(x) as
H (x−a)−H (x−b)
P(x)= (25)
b−a

This makes that the variance σ with population mean μ for an asymmetric distribution becomes

∞ b
x b+a
µ= P(x)xdx= dx= (26)
∫ ∫
(b−a) 2
−∞ a
2 2
σ = P(x)(x−µ) dx (27)
H (x−a)−H (x−b) a+b
2 2
(28)
σ = (x− ) dx
b−a 2
a+b
b (x− ) 2
(a+b)
σ = dx= (29)
b−a 12
So for a symmetric rectangular interval a- to a+, the variance reduces to
σ = . (30)
The sample estimate of the standard deviation thus is:
u = . (31)
rect
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The rectangular distribution is a reasonable default model in the absence of any other information. But

if it is known that values of the quantity in question near the centre of the limits are more likely than

values close to the limits, a triangular or a normal distribution migth be a better model.

Triangular and trapezoidal distribution

In many cases it is more realistic to expect that values near the bounds are less likely than those near

the midpoint. It is then reasonable to replace the symmetric rectangular distribution by a symmetric

trapezoidal distribution having
...

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