ISO/DIS 14451-2:2026(en)

ISO/TC 22/SC 36

Secretariat: AFNOR

Date: 2025-11-18

Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 2: Test methods

© ISO 2026

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Contents

Foreword v

1 Scope 7

2 Normative references 7

3 Terms and definitions 7

4 Test methods 7

4.1 Verification of design and documentation 7

4.2 Drop test 8

4.2.1 Purpose 8

4.2.2 Equipment 8

4.2.3 Test conditions 8

4.2.4 Test procedure 8

4.3 Vibration and temperature test 9

4.3.1 Purpose 9

4.3.2 Equipment 9

4.3.3 Test conditions 9

4.3.4 Test procedure 9

4.4 Thermal humidity cycling test 10

4.4.1 Purpose 10

4.4.2 Equipment 10

4.4.3 Test condition 10

4.4.4 Test procedure 10

4.5 Electrostatic discharge (ESD) test 11

4.5.1 Purpose 11

4.5.2 Equipment 11

4.5.3 Test conditions 12

4.5.4 Test procedure 12

4.6 Fire test 14

4.6.1 Purpose 14

4.6.2 Equipment 14

4.6.3 Test conditions 15

4.6.4 Test procedure 16

4.7 Igniter test 16

4.7.1 Purpose 16

4.7.2 Test procedure 16

4.8 Tank test 16

4.8.1 Purpose 16

4.8.2 Equipment 16

4.8.3 Test conditions 16

4.8.4 Test procedure 17

4.9 Functioning test (regular) 17

4.9.1 Purpose 17

4.9.2 Equipment 17

4.9.3 Test conditions 17

4.9.4 Test procedure 17

4.10 Functioning test with height measurement 17

4.10.1 Purpose 17

4.10.2 Equipment 17

4.10.3 Test procedure 18

4.11 Sensitivity test 20

4.11.1 Purpose 20

4.11.2 Equipment 20

4.11.3 Test procedure 20

Annex A (normative) Definition of temperature build-up time, t_e 22

Annex B (normative) Probit test (PBBS test) 24

B.1 General 24

B.2 Symbols 24

B.3 Calculation of the frequencies 25

B.4 Calculation of intermediate statistical parameters 25

B.5 Calculation of the no-fire and all-fire values 26

B.6 Example 1: Calculation of relative frequencies 27

B.7 Example 2: Calculation of a no-fire current and an all-fire current 28

Annex C (normative) Bruceton method 30

C.1 General 30

C.2 Procedure 30

C.3 Calculation of results 30

Annex D (informative) Guideline for the vibration test 34

Bibliography 35

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

ISO draws attention to the possibility that the implementation of this document may involve the use of (a) patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a) patent(s) which may be required to implement this document. However, implementers are cautioned that this may not represent the latest information, which may be obtained from the patent database available at www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.

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For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO's adherence to the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 36, Safety and impact testing.

This second edition cancels and replaces the first edition (ISO 14451-2:2013), which has been technically revised.

The main changes are as follows:

— The new test method 4.10 “Functioning test with height measurement” was added.

— Wording and equipment were homogenised between 4.9 “Functioning test” and 4.10 “Functioning test with height measurement”.

— The new test method 4.11 “Sensitivity test” was added.

— The vibration spectra and its specifications were moved as an informative annex.

A list of all parts in the ISO 14451 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A complete listing of these bodies can be found at www.iso.org/members.html.

Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 2: Test methods

This document establishes uniform test methods for pyrotechnic articles for vehicles.

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ISO/DIS 14451‑1:2025,^[1] Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 1: Vocabulary

ISO/DIS 14451‑3:2025¹⁾ Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 3: Labelling

ISO/DIS 14451‑5:2025¹⁾, Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 5: Requirements and categorization for airbag gas generators

ISO/DIS 14451‑6:2025¹⁾, Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 6: Requirements and categorization for airbag modules

ISO/DIS 14451‑7:2025¹⁾, Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 7: Requirements and categorization for seatbelt pretensioners

ISO/DIS 14451‑9:2025¹⁾, Pyrotechnic articles — Pyrotechnic articles for vehicles — Part 9: Requirements and categorization for actuators

For the purposes of this document, the terms and definitions given in ISO/DIS 14451-1:2025 apply.

NOTE Wherever reference is made to pyrotechnic article(s) only pyrotechnic articles for vehicles are meant.

The manufacturer shall supply a document which describes the pyrotechnic article. The typical content of the document shall include the following information:

— description of the purpose of the pyrotechnic article;

— sketch with external dimensions;

— total mass of the pyrotechnic article;

— cross section and part list;

— mass and pyrotechnic composition(s) contained in the article;

— description of intended behaviour;

— description of foreseeable behaviour during fire test if applicable;

— proposed labelling in accordance with ISO/DIS 14451‑3:2025;

— safety data sheet/handling instructions, including electrical characteristics (e.g. all-fire current, no-fire current, resistance, etc.) which shall be provided with the pyrotechnic article.

This shall be verified by visual inspection by the naked eye.

The purpose of this test is to determine whether the pyrotechnic article experiences any detrimental effect when dropped from a specified height and at specified orientations.

A steel impact plate of a minimum of 1 m x 1 m with at least 10 mm thickness, resting on a solid floor, with a fixture that supports the pyrotechnic article at the specified height, shall be used.

The drop height shall be  m.

The test shall be done with the pyrotechnic article at ambient temperature.

Mount one pyrotechnic article into the support fixture at the specified height above the impact plate and oriented such that it will fall in one of the six directions indicated in Figure 1. Disarm the trigger device, if included in the pyrotechnic article.

Release the pyrotechnic article, allowing it to free fall onto the impact plate. Repeat the test using the same pyrotechnic article oriented to fall in the opposite direction.

Repeat the test twice more, once using a second pyrotechnic article and once using a third pyrotechnic article, each time along one of the remaining directions indicated in Figure 1.

Figure 1 — Definition of main axes

The purpose of this test is to determine the ability of the pyrotechnic article to withstand vibration and temperature conditions. The test may be performed simultaneously or sequentially.

The equipment shall consist of a vibration table capable of producing the vibration loads as characterized in Figure D.1 and a climatic chamber capable of controlling the temperature during the test in accordance with Figure 2. In case the test is being performed simultaneously the vibration table shall be mounted within the climatic chamber.

The temperature tolerance shall be ±2,5 °C.

Fix the pyrotechnic article to the vibration table by an appropriate method insuring correct transmission of the vibration load. Apply random vibration (refer to Annex D for typical specifications) along each of the three main axes (see Figure 1) of each pyrotechnic article for 24 h.

Place the pyrotechnic article in the climatic chamber. The temperature shall be changed in accordance with Figure 2. It may be changed simultaneously with application of the vibration load.

Key

X time, expressed in hours

Y temperature, expressed in degrees Celsius

^a Duration of one cycle: 24 h.

Figure 2 — Temperature cycle

The purpose of this test is to determine the ability of the pyrotechnic article to withstand high humidity and temperature variations.

A climatic chamber with recirculating air shall be used.

The temperature tolerance shall be ±2,5 °C.

Place the pyrotechnic article in the climatic chamber and subject it to 30 thermal humidity cycles in accordance with Figure 3.

NOTE 1 The temperature reference point is within the propelling media.

Key

X time, expressed in hours

Y₁ relative air humidity, expressed as a percentage

Y₂ temperature, expressed in degrees Celsius

^a Lead time.

^b Duration of one cycle: 24 h, or less using t_e.

^c Or: reference temperature build-up time, t_e.

NOTE 2 The relevant temperature build-up times, t_e, may be used instead of the given hours; if t_e is used, it shall be determined prior to the test according to the procedure in Annex A.

Figure 3 — Thermal humidity cycle

The purpose of this test is to prove the ability of the pyrotechnic article to withstand electrostatic discharges without unintended ignition.

An ESD generator capable of producing the test pulse, adjustable within the limits given in 4.5.3, shall be used consisting in its main parts of the following and meeting the respective requirements:

— charging resistor: resistance, R_ch, between 50 MΩ and 100 MΩ;

— energy-storage capacitor: capacitance, C_s; (C_s + C_d) 150 pF ± 10 %;

— distributed capacitance, C_d;

— hand capacitor: capacitance, C_h of 10 pF ± 10 %;

— discharge resistor: resistance, R_d, of 330 Ω ± 10 %;

— voltage indicator: tolerance of the output voltage indication, ±5 %;

— output voltage (see Note 1 of Figure 4), up to 8 kV (nominal) for contact discharge;

— polarity of the output voltage: positive and negative;

— discharge switch;

— discharge return cable;

— holding time: at least 5 s;

— discharge, mode of operation: single discharge; the generator should be able to generate at a rate of at least 20 discharges per second for exploratory purposes only;

— time between successive discharges: at least 1 s;

— power supply unit.

NOTE Open circuit voltage is measured at the energy storage capacitor.

The generator shall be provided with a means of preventing unintended radiated or conducted emissions, of either pulse or continuous type, so that the pyrotechnic article and auxiliary test equipment are not disturbed by these effects.

The discharge return cable of the test generator shall be constructed to allow the generator to meet the waveform specification. It shall be sufficiently insulated to prevent the flow, during the ESD test, of the discharge current to personnel or conducting surfaces other than via its termination.

Figure 4 presents a simplified diagram of the ESD generator. Construction details are not given.

Key

1 DC HV supply

2 charging resistor (R_ch)

3 discharge resistor (R_d)

4 discharge switch

5 discharge contact

6 energy-storage capacitor (C_s)

7 hand capacitor (C_h)

8 discharge return connection

NOTE 1 C_d, omitted from Figure 4, is a distributed capacitance existing between generator and the pyrotechnic article, ground reference planes and coupling planes.

NOTE 2 Because the capacitance is distributed over the whole generator, it is not possible to show this in the circuit.

Figure 4 — Simplified diagram of the ESD generator

General

The pyrotechnic article shall be at ambient temperature.

Calibration of the test set-up for contact discharge

The calibration shall be done in such a way that the impulse shown in Figure 5 and given in Table 1 is measured by a suitable device connected to the ESD-simulator in accordance with the wiring diagram in Figure 6.

The values of the parameters of the discharge current shall be verified with 1 000 MHz bandwidth-measuring instrumentation.

A lower bandwidth implies limitations in the measurement of rise time and amplitude of the first current peak.

Electrostatic discharge shall be applied in accordance with Figure 5.

Place the pyrotechnic article under test on a conductive bench.

The bench ESD simulator and power source shall be grounded to earth.

Identify specific test points on the pyrotechnic article prior to conducting the test.

If an igniter is present, apply the discharge to the igniter from pin to pin and from each pin to all those other areas of the casing accessible to personnel in normal use.

Perform the test with contact discharges and with positive and negative voltages. Subject each discharge point to a minimum of three positive and three negative discharges at the voltage level as shown in Figure 5. The time duration between discharges shall be at least 5 s.

Key

X time, expressed in nanoseconds

Y current intensity, expressed in amperes

^a Risetime, t_r, with discharge switch.

Figure 5 — Typical waveform of the output current of the ESD generator

Table 1 — Characteristics of output current of ESD generator

Key

1 ESD simulator (330 Ω)

2 50 Ω

3 20 dB attenuator

4 purpose input

5 coaxial target

6 2 Ω

Figure 6 — ESD simulator calibration set-up schematic

The purpose of this test is to determine the behaviour of the pyrotechnic article when exposed to fire.

The following equipment shall be used when carrying out a fire test:

— gas cylinder, containing, for example, propane gas with gas-cylinder valve and hose assembly;

— gas burner(s), 60 mm in diameter;

— support made of mild steel according to Figure 7;

— grid, an expanded metal made of mild steel as specified in Figure 8 that shall cover the entire support surface;

— gas lighter;

— stop watch.

The vertical distance between mouth of the burner(s) and top of the grid shall be 400 ± 10 mm.

Dimensions in millimetres

Key

1 fixture for user

Figure 7 — Support

Key

L_l long diagonal length, equal to 43 mm

L_c short diagonal length, equal to13 mm

l strip width, equal to 2 mm

e thickness, equal to 2 mm

Figure 8 — Grid

General

The test shall be performed with the pyrotechnic article at ambient temperature. Standard positions and heating rate of the pyrotechnic article shall be considered according to the requirement specified in ISO/DIS 14451‑5:2025, ISO/DIS 14451‑6:2025, ISO/DIS 14451‑7:2025 or ISO/DIS 14451‑9:2025.

The number of burner(s) shall be chosen such that the whole cross-section of the pyrotechnic article (projection to the grid) shall be completely engulfed in the flames.

The pyrotechnic article shall be fixed to the grid during the test by an appropriate method (e.g. hose clamps, clamps, etc.) to ensure very low thermal loss through fixation contacts.

Each pyrotechnic article shall be filmed during the test with a minimum of 25 frames per second. Each test shall be recorded.

Calibration of the fire test set-up

Calibration as described below shall be ensured for each individual burner while all burners being used for the test are ignited.

For calibration of the test installation, the heating rate shall be measured with a steel cube of 50 mm side length made of mild steel and with a mass of 975 g ± 10 g. The cube shall be placed on the grid (as described in 4.6.2) so that heat losses through fixation contact are minimized. A hole with diameter of maximum 3 mm and 25 mm depth to accommodate the thermocouple shall be machined in the centre of one face. The diameter at the bottom of the hole shall be adjusted to fit the thermocouple as to allow good heat contact.

The calibration shall take place between 50 °C and 200 °C with the heating rate as defined for each individual article in ISO/DIS 14451‑5:2025, ISO/DIS 14451‑6:2025, ISO/DIS 14451‑7:2025 and ISO/DIS 14451‑9:2025. The tolerance for the heat rate is ±5 K/min. Maintain the testing conditions constant (especially gas flow rate and possible air movement) in order to guarantee that the pyrotechnic article experiences the same heating rate as set during calibration.

This calibration shall be repeated prior to each test series in order to guarantee constant heating rate and the calibration shall be documented.

Position the pyrotechnic article in the intended path of the fire before lighting. Heat the pyrotechnic article until all pyrotechnic content is consumed or for a time period of 20 min when no further reaction has been observed.

The purpose of this test is to establish the function and reliability of the igniter using appropriate statistical tests.

For an electrical igniter, the Probit Bayes test (see Annex B)^[1] or the Bruceton test (see Annex C)^[1] shall be used.

The test procedure proves the all-fire and no-fire values. These values, together with reliability and confidence levels, shall be specified.

The purpose of this test is to assess the performance of the pyrotechnic article by firing it into a closed volume container at a given temperature level.

A tank suited to the performance of the pyrotechnic article shall be used.

Each pyrotechnic article shall be tested at ambient temperature.

General

The pyrotechnic article tightly fixed to the appropriate tank shall, if applicable, be ignited with a pulse not lower than the all-fire value.

Electrical connection

Measure the igniter resistance to ensure electrical connection before ignition of the pyrotechnic article.

Tank pressure

Measure the tank pressure versus time, using a pressure transducer with the following specifications:

— appropriate calibration range;

— linearity and hysteresis error ≤ 1 %.

Do not place the pressure transducer in the direct gas flow from the exit ports of the pyrotechnic article.

The purpose of this test is to assess the behaviour of the pyrotechnic article by firing it without fixation into an open air volume.

For the execution of this test the following equipment is necessary:

— Test area sufficient to accommodate a 15 m diameter from the placement point of the pyrotechnic article for ignition. If a low displacement is excepted from the functioning of the pyrotechnic article, the test area can have a smaller diameter than 15 m. The chosen surface shall be similar in hardness to concrete.

— At least one camera with at least a standard framerate of 24 fps and a pixel resolution suitable for distinguishing individual fragments.

Each pyrotechnic article shall be tested at ambient temperature.

The pyrotechnic article shall be ignited with a pulse not less than the all-fire value and filmed during the whole test from the ignition until the end of the effect or the fallout of debris.

The purpose of this test is to observe if after initiation, the pyrotechnic article or any ejected debris exceeds a height of 15 m. This additional test shall only be carried out, if such article or projection heights are witnessed or anticipated to occur when tested in accordance with 4.9.

For the execution of this test the following equipment is necessary:

— Test area sufficient to accommodate a 15 m diameter from the placement point of the pyrotechnic article for ignition. The chosen surface shall be similar in hardness to concrete.

— Two cameras with at least a standard framerate of 24 fps and a pixel resolution suitable for distinguishing individual fragments. Camera lenses can be used.

— Two vertical viewing devices with an adjustable horizontal mark at the top, such as a string, a rod, or a marking on a transparent sheet, 0,5 m width and near 0,5 m height: the height of the mark shall be adjusted with the camera placed at 0,5 m ± 5 cm from the viewing device, so that the top of the mark as recorded by the camera correlates with a height of 15 m ± 3 cm at 15 m ± 2 cm of the lens of the camera, as illustrated in Figure 9. The viewing devices can have a specific support for mounting the camera in order to maintain fixed distances and orientations of the camera toward the mark. Any change of camera or camera lens requires the adjustment to performed again.

The equipment shall be installed in accordance with the drawing shown in Figure 9.

Place the pyrotechnic article in the centre of the test ground without additional support: the orientation shall allow a maximal vertical movement after initiation.

Each adjusted viewing device shall be placed with their camera used for its adjustment such:

that the camera is directed toward the vertical axis at the centre of the test area,

that the lens of the camera is at a horizontal distance of 15 m ± 2 cm from the vertical axis at the centre of the test area,

and that the middle of the mark as filmed by the camera is nearly aligned with the vertical axis at the centre of the test area.

The angle between axe of the cameras shall be 90° ± 5 °C.

The field of view of the camera shall be set to capture the adjustable horizontal mark and the centre of the test area, while keeping enough space above the mark to see the article or fragment clearly exceeding the mark ; but, if additional accuracy is needed near the mark, a camera lens providing additional zoom can be used and the field of view of the camera shall be centred near the centre of the mark without the centre of the test area in the field of view.

Then, pyrotechnic article shall be ignited with a pulse not less than the all-fire value and filmed with both cameras during the whole test from the ignition until the end of the effect or the fallout of debris.

After the functioning, the video recording is assessed as follows: if the pyrotechnic article or one of its fragments exceeded totally the 15 m mark at the top of the viewing devices, it indicates a vertical movement of more than 15 m.

Key

1 centre of the test area

2 vertical axis at the centre of the test area

3 viewing device

4 adjustable horizontal mark

5 camera (may include a camera lens)

6 point where the top of the mark as recorded by the camera correlates with a height of 15 m ± 3 cm at 15 m ± 2 cm of the lens of the camera

Figure 9 — Test setup for measuring the height (second viewing device omitted for clarity in subfigures a) and b))

The purpose of this test is to check that the tested articles cannot detonate the booster specified in 4.11.2 if this booster is initiated and detonates, the article has the capacity to detonate secondary explosives.

The test is carried out at 20 °C ± 5 °C.

The equipment and material needed for the test is composed of:

3 articles have to be tested under the conditions described here below.

Place the article at one end of the booster in such a way that it touches the flat surface. As a rule, the known or anticipated effect is orientated towards the centre of the booster. If these conditions cannot be kept (e.g. due to its shape), the article shall be placed in the best possible way as if it was intended to initiate the booster.

Then place the other end of the booster into contact with the steel plate in the anticipated direction of the possible detonation.

Fire the article.

After the initiation and functioning of the article, the result of the test is considered to be a detonation of the booster if a clean hole is punched through the steel plate. In the other case, no detonation has occurred although the explosive of the booster was dispersed or partly reacted.

Repeat the test on two other articles.

The test result is recorded in the following way:

— “capacity to detonate secondary explosives” is reported for the article, if at least one detonation of boosters occurred during the test;

— if not, the article has “no capacity to detonate secondary explosives”.

Recording

All measured parameters in tests under Clause 4 shall be recorded.

1. 
   (normative)
   
   Definition of temperature build-up time, t_e

The temperature build-up time t_e is the time required, after a change in the surrounding temperature from T₁ to T₂, for a defined reference point of the test sample to reach the temperature T₂, as follows:

— within 3 °C, in the case of │T₂ − T₁│ ≥ 60 °C;

— within 5 % of the temperature difference │T₂ − T₁│, in the case of │T₂ − T₁│ < 60 °C.

The temperature build-up time begins at the point where the desired target value curve reaches the surrounding temperature T₂ (see Figure A.1 and A.2). The temperature build-up times shall be determined in the apparatus for the relevant test. The test sample temperature shall be measured at the prescribed reference point.

Key

X time, expressed in hours

Y temperature, expressed in degrees Celsius

^a Target temperature, T_targ.

^b Actual temperature, T_act.

Figure A.1 — Temperature build-up time t_e for │T₂ − T₁│ ≥ 60 °C

Key

X time, expressed in hours

Y temperature, expressed in degrees Celsius

^a Target temperature, T_targ.

^b Actual temperature, T_act.

Figure A.2 — Temperature build-up time t_e for │T2 − T1│ < 60 °C

1. 
   (normative)
   
   Probit test (PBBS test)
   1. General

The aim of this annex is to describe the statistical model used to estimate the value of a specific quantity with a probability level of “no-fire” equal to 0,01 % and of “all-fire” equal to 99,99 %, within a confidence interval equal to 95 %. Typical estimated quantities are fire currents and fire impulses.

• 1. Symbols

• 1. Calculation of the frequencies

The relative frequency, p_k, is estimated by the general Formula (B.1):

(B.1)

Difficulties arise when the value of the frequency is 0 or 1, i.e. when the number of occurrences at test level y_k is equal to 0 or N. In these cases, the corresponding values for φ_k are theoretically equal to -∞ or to +∞. Appropriate values of φ_k are in these cases estimate by using the Bayes estimator as follows.

Let the test level values, y_k, be ordered such that: y₁ < y₂ ………… < y_K

Let u be the smallest index such that i_u > 0 and o be the largest index such that all i_o < N. Calculate the frequency p_k in the interval u ≤ k ≤ o using the set of equations given in Formulae (B.2):

if i_k ≠ 0 and N

if i_k = 0 (B.2)

if i_k = N

When u > 1, calculate p_u-1 from Formula (B.3):

(B.3)

When o < K, calculate p_o+1 from Formula (B.4):

(B.4)

If u −1 > 1 or o +1 < K still holds, repeat the procedure, that is, according to Formulae (B.5) and (B.6):

(B.5)

or

(B.6)

and so forth.

• 1. Calculation of intermediate statistical parameters

The following equations apply:

(B.7)

(B.8)

(B.9)

(B.10)

(B.11)

(B.12)

(B.13)

(B.14)

(B.15)

(B.16)

(B.17)

(B.18)

(B.19)

• 1. Calculation of the no-fire and all-fire values

The theoretical model gives Formula (B.20):

(B.20)

where the parameters a and b are estimated by

(B.21)

(B.22)

From these values, the mean and the standard deviation of the underlying normal distribution may be calculated:

(B.23)

(B.24)

The following functions are obtained as limiting curves for the corresponding confidence interval:

and using Formula (B.22):

(B.25)

Estimate the no-fire and all-fire values by solving the following quadratic equation, respectively:

(B.26)

(B.27)

From Formulae (B.21) and (B.22), calculate the values y_0,000 1 and y_0,999 9 from Formulae (B.28) and (B.29):

(B.28)

(B.29)

From the resolution of Formulae (B.26) and (B.27), the estimated no-fire and all-fire values, with a confidence level of 95 %, are given in Formulae (B.30) and (B.31), respectively:

(B.30)

(B.31)

• 1. Example 1: Calculation of relative frequencies

An example of experimentally tested quantity y (for example, fire current), with its respective number of fires i_k at a given level y_k (current level in milliamperes) is given in Table B.1. The y_k values are ordered by increasing values.

Table B.1 — Example of experimental results for
the calculation of the frequencies

From Table B.1, we have: u = 3 and o = 6.

Calculate the frequencies for 3 ≤ k ≤ 6 [Formula (B.1)]:

p₃ = 0,5 p₄ = 0,7 p₅ = 0,8 p₆ = 0,95

Using the Bayes estimator, calculate the other relative frequencies [Formulae (B.3), (B.4) and (B.5)]:

p₂ = 0,045 p₁ = 0,019 3 p₇ = 0,979 2

• 1. Example 2: Calculation of a no-fire current and an all-fire current

Typical results for determining the no-fire and all-fire currents are reported in Table B.2. The number of tests is equal to 20 for each level (N = 20). The relative frequencies are calculated according to the procedure described above and example 1. For each frequency, the φ_k value is calculated using the inverse of the standard normal distribution, Φ⁻¹.

The result of the calculation of the statistical parameters is collected in Table B.3.

Table B.2 — Example of values for calculation of the no-fire and all-fire currents

Table B.3 — Calculated statistical parameters

The estimated no-fire and all-fire currents, with probability 0,000 1 and 0,999 9 respectively, are as follows [see Formulae (B.28) and (B.29)]:

 mA

and

 mA

Finally, calculate the no-fire and all-fire currents with a confidence level of 95 % using Formulae (B.30) and (B.31):

1. 
   (normative)
   
   Bruceton method
   1. General

The Bruceton method is used to determine the level of stimulus at which there is a 50 % probability of obtaining a positive result.

• 1. Procedure

The method involves the application of different levels of stimulus and determining whether or not a positive reaction occurs. The performance of the trials is concentrated around the critical region. It takes place by decreasing the stimulus in one level at the next trial if a positive result is obtained and by increasing the stimulus in one level if a negative result is obtained. Usually about five preliminary trials are performed to find a starting level in approximately the right region and then at least 25 trials are performed to provide the data for the calculations.

• 1. Calculation of results

In determining the level at which the probability of obtaining a positive result is 50 % (H₅₀), only the positive results (+) or only the negative results (-) are used, depending on which has the smaller amount. If the numbers are equal, either may be used. The data are recorded in a table (e.g. as in Table C.1) and summarized as shown in Table C.2. Column 1 of Table C.2 contains the drop heights, in ascending order, starting with the lowest level for which a test result is recorded. In column 2, ‘i’ is a number corresponding to the number of equal increments above the base or zero line. Column 3 contains the number of positive results [n(-)] for each drop height. The fourth column tabulates the result of multiplying ‘i’ times ‘n’ and the fifth column tabulates the results of multiplying the square of ‘i’ times ‘n’. A mean is calculated from Formula (C.1):

(C.1)

where

;

;

If negative results are used, the sign inside the brackets is positive; it is negative if positive results are used. The standard deviation, s, may be estimated using Formula (C.2):

(C.2)

where

EXAMPLE Using the following data from Tables C.1 and C.2: lowest drop height 10 cm; height level interval 5 cm; sum of i·n(-)16; sum of i²·n(-)12:

The mean height from Formula (C.1) is given as:

The standard deviation from Formula (C.2) is given as:

Table C.1 — Recording data

Table C.2 — Summarizing data

1. 
   (informative)
   
   Guideline for the vibration test

The typical specifications for a vibration test, as per 4.3, are given in Table D.1.

Table D.1 — Frequency characteristics at RMS of 1,34 g

Key

X frequency, expressed in hertz

Y power spectral density, expressed in g² per hertz

Figure D.1 — Vibration test

With the following parameters:

Number of lines: 400;

Range of analysis (filter bandwidth 1,25 Hz): 500 Hz;

Degree of freedom (DOF): 154;

Abort limits lines: ±5 dB;

Abort limits g RMS: ±5 dB.

Bibliography

[1] EN 13763‑1, Explosives for civil uses — Detonators and relays — Part 1: Requirements

1. Under Preparation at DIS stage ↑