ISO/TR 16194:2017

Pneumatic fluid power - Assessment of component reliability by accelerated life testing - General guidelines and procedures

ISO/TR 16194:2017 provides general procedures for assessing the reliability of pneumatic fluid power components using accelerated life testing and the method for reporting the results. These procedures apply to directional control valves, cylinders with piston rods, pressure regulators, and accessory devices ? the same components covered by the ISO 19973 series of standards. ISO/TR 16194:2017 does not provide specific procedures for accelerated life testing of components. Instead, it explains the variability among methods and provides guidelines for developing an accelerated test method. The methods specified in this document apply to the first failure, without repairs.

Transmissions pneumatiques — Évaluation de la fiabilité du composant par essai de durée de vie accélérée — Lignes directrices générales et modes opératoires

General Information

• Status: Published
• Publication Date: 26-Apr-2017
• ICS: 23.100.01 - Fluid power systems in general
• Technical Committee: ISO/TC 131 - Fluid power systems
• Drafting Committee: ISO/TC 131 - Fluid power systems
• Parallel Committee: ISO/TC 20/SC 10/WG 1 - Joint ISO/TC 20/SC 10 - ISO/TC 131/SC 7 WG: Seals and seal retainers
• Current Stage: 6060 - International Standard published
• Start Date: 27-Apr-2017
• Due Date: 04-Nov-2017
• Completion Date: 04-Nov-2017

Overview

ISO/TR 16194:2017 - "Pneumatic fluid power - Assessment of component reliability by accelerated life testing - General guidelines and procedures" - is a technical report from ISO that provides general guidelines for assessing the reliability of pneumatic components using accelerated life testing (ALT). It applies to directional control valves, cylinders with piston rods, pressure regulators, and accessory devices (the same component family covered by the ISO 19973 series). ISO/TR 16194:2017 explains variability among ALT methods and guides development of test methods and reporting; it does not prescribe specific test procedures. The methods in this TR apply to first-failure analysis (no repairs).

Key topics

• Concepts and terminology: definitions such as B‑life, acceleration factor (AF), failure rate, ALT and HALT, destruct limits, failure mode and mechanism.
• Failure analysis: guidance to ensure accelerated test failure modes match those in normal use.
• Test strategy: planning ALT programs including identification of field failure types, use of FMEA, FTA, QFD, and differentiation between qualitative HALT and quantitative ALT.
• Test design elements: defining normal-use conditions, preliminary tests, accelerated stress levels, sample size, types of stress loading, data observation and measurement, and end-of-test criteria (minimum failures, termination cycle count, censored units).
• Statistical analysis: life distributions (Weibull, lognormal, exponential), life–stress relationship models (Arrhenius, Eyring, inverse power law), parameter estimation, censored data handling and reliability characteristic extraction (e.g., B‑life, MTTF).
• Reporting: standardized content for ALT test reports and informative annexes with worked examples (life-stress models, Weibull slope verification, censored data calculations, industrial examples).

Practical applications

• Develop and validate accelerated life-test programs to estimate pneumatic component life under normal use from accelerated data.
• Compare designs or suppliers by quantifying first-failure reliability metrics.
• Support reliability claims, product development, qualification testing, and risk analysis.
• Provide laboratory test templates, statistical analysis approaches, and reporting formats for ALT results.

Who should use this standard

• Test and certification laboratories
• Pneumatic component manufacturers (design, R&D, quality engineering)
• Reliability engineers and test planners
• Standards committees and conformity assessment bodies

Related standards

• ISO 19973 series (pneumatic component test methods and reliability assessment)
• ISO 5598 (fluid power - vocabulary) - referenced terminology
• Relevant statistical and measurement standards (e.g., life distribution and censoring methods) as used in ALT analysis

Keywords: ISO/TR 16194:2017, accelerated life testing, ALT, pneumatic fluid power, component reliability, HALT, Weibull, life‑stress models, ISO 19973.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 16194
First edition
2017-04
Pneumatic fluid power — Assessment
of component reliability by
accelerated life testing — General
guidelines and procedures
Transmissions pneumatiques — Évaluation de la fiabilité du
composant par essai de durée de vie accélérée — Lignes directrices
générales et modes opératoires
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and units . 3
5 Concepts of reliability and accelerated life testing . 3
6 Failure mechanism and mode . 4
7 Strategy of conducting accelerated life testing . 4
8 Design of accelerated life testing . 5
8.1 Normal use conditions . 5
8.2 Preliminary tests . 5
8.3 Levels of accelerated stress . 6
8.4 Sample size . 7
8.5 Data observation and measurement . 7
8.6 Types of stress loading . 7
9 End of test . 8
9.1 Minimum number of failures required . 8
9.2 Termination cycle count. 8
9.3 Suspended or censored test units . 8
10 Statistical analysis . 9
10.1 Analysis of failure data . 9
10.2 Life distribution. 9
10.3 Accelerated life testing model .10
10.4 Data analysis and parameter estimation .10
11 Reliability characteristics from the test data .11
12 Test report .12
Annex A (informative) Determining stress levels when stress is time-dependent .13
Annex B (informative) Life-stress relationship models .17
Annex C (informative) Verification of compromise Weibull slopes .26
Annex D (informative) Calculation procedures for censored data .32
Annex E (informative) Examples of using accelerated life testing in industrial applications .35
Annex F (informative) Palmgren-Miner’s rule .37
Annex G (informative) ALT experimental results for pneumatic cylinder .39
Bibliography .59
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).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on 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 the following
URL: w w w . i s o .org/ iso/ foreword .html
ISO/TR 16194 was prepared by Technical Committee ISO/TC 131, Fluid power systems.
iv © ISO 2017 – All rights reserved

Introduction
This document is being released to document progress that the working group has developed for
accelerated testing. It is a new method with which the working group members have very little
experience, but has been used by institutional laboratories and taught at academic levels.
Some experimentation on air cylinders has been done at the Korean Institute of Machinery and
Materials (KIMM), but the application to pneumatic components in general has not been evaluated.
This document is offered to members as a reference and model procedure, so that they can develop
experience with its use in their own laboratories.
TECHNICAL REPORT ISO/TR 16194:2017(E)
Pneumatic fluid power — Assessment of component
reliability by accelerated life testing — General guidelines
and procedures
1 Scope
This document provides general procedures for assessing the reliability of pneumatic fluid power
components using accelerated life testing and the method for reporting the results. These procedures
apply to directional control valves, cylinders with piston rods, pressure regulators, and accessory
devices – the same components covered by the ISO 19973 series of standards.
This document does not provide specific procedures for accelerated life testing of components.
Instead, it explains the variability among methods and provides guidelines for developing an
accelerated test method.
The methods specified in this document apply to the first failure, without repairs.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5598, ISO 19973-1 and
the following apply. ISO and IEC maintain terminological databases for use in standardization at the
following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1
B life
x
life of a component or assembly that has not been altered since its production, where its reliability is (
100− x) %; or the time at which (100− x) % of the population has survived
Note 1 to entry: The cumulative failure fraction is x %. For example, if x = 10, the B life has a cumulative failure
probability of 10 %.
3.2
acceleration factor
AF
ratio between the life at the normal use stress level and the life at the accelerated stress level
3.3
accelerated life test
ALT
process in which a component is forced to fail more quickly that it would have under normal use
conditions and which provides information about the component’s life characteristics
3.4
destruct limit
stress level at which one or more of the component’s operating characteristics is no longer within
specification or the component is damaged and cannot recover when the stress is reduced
Note 1 to entry: Destruct limits are classified as a lower destruct limit and upper destruct limit.
3.5
failure mechanism
physical or chemical process that produces instantaneous or cumulative damage to the materials from
which the component is made
3.6
failure mode
manifestation of the failure mechanism resulting from component failure or degradation
Note 1 to entry: The failure mode is the symptom of the aggressive activity of the failure mechanism in the
component’s areas of weakness, where stress exceeds strength.
3.7
failure rate
λ
frequency at which a failure occurs instantaneously at time t, given that no failure has occurred before t
3.8
highly accelerated life test
HALT
process in which components are subjected to accelerated environments to find weaknesses in the
design and/or manufacturing process
Note 1 to entry: The primary accelerated environments include pressure and heat.
3.9
model for accelerated life testing
model that consists of a life distribution that represents the scatter in component life and a relationship
between life and stress
Note 1 to entry: Life distribution examples: Weibull, Lognormal, Exponential, etc.
Note 2 to entry: Life and stress examples: Arrhenius, Eyring, Inverse Power Law, etc.
3.10
normal use conditions
test conditions at which a component is commonly used in the field, which can be less strenuous than
rated conditions
3.11
termination cycle count
number of cycles on a test item when it reaches a threshold level for the first time
2 © ISO 2017 – All rights reserved

4 Symbols and units
a
Symbol Definition
B Time at which 10 % of the population is estimated to fail
η Scale parameter (characteristic life) of the Weibull distribution
F(t) Probability of failure of a component up to time t
β Shape parameter (slope) of the Weibull distribution
R(t) Reliability of a component at time t; R(t) = 1 – F(t)
λ(t) Failures per unit time
a
Other symbols could be used in other documents and software.
Units of measurements are in accordance with ISO 80000-1.
5 Concepts of reliability and accelerated life testing
Reliability is the probability (a percentage) that a component does not fail (for example, exceed the
threshold level or experience catastrophic failure) for a specified interval of time or number of cycles
when it operates under stated conditions. This reliability can be assessed by test methods described in
the ISO 19973 series.
Generally, reliability analysis involves analysing time to failure of a component, obtained under normal
use conditions in order to quantify its life characteristics. Obtaining such life data is often difficult.
The reasons for this difficulty can include the typically long life times of components, the small time
period between design and product release, and the necessity for testing components under normal use
conditions. Given this difficulty and the need to observe failures of components to better understand
their life characteristics, procedures have been devised to accelerate their failures by overstress,
thus forcing components to fail more quickly than they would under normal use conditions. The term
accelerated life testing (ALT) is used to describe such procedures.
However, a relationship between the reliability of a component determined by ALT, and its reliability
at normal use conditions, is necessary. This can be assessed by extrapolating the test results obtained
from an accelerated life test and comparing it to that obtained from testing at normal use conditions.
Figure 1 shows the graphical concept for this relationship.
Figure 1 — Graphical explanation of relationship between S-N curve and accelerated life testing
NOTE Distributions in this concept Figure 1 are not defined.
In Figure 1, failures under normal use conditions are represented by the distribution S , and the
accelerated conditions are distributions S and S . Their relationship is shown by the connecting line(s).
1 2
6 Failure mechanism and mode
The failure mechanism is the physical or chemical process that produces instantaneous or cumulative
damage to the materials from which the component is made. The failure mode is the manifestation
of the failure mechanism resulting from component failure or degradation. The failure mode is the
symptom of the aggressive activity of the failure mechanism in areas of component weakness where
the stress exceeds the strength.
It is necessary that the failure modes observed in accelerated life test conditions are identical to those
defined for normal use conditions.
7 Strategy of conducting accelerated life testing
Before starting an accelerated life test, it is important to identify the types of failures that might occur
in service; especially any feedback from the field. Several methods are available to assist in this effort:
design analysis and review using the quality function deployment (QFD), fault tree analysis (FTA), and
failure modes and effect analysis (FMEA). Another method is a qualitative test like highly accelerated
life testing (HALT). Qualitative tests are used primarily to reveal probable failure modes, but they do
not quantify the life (or reliability) of the component under normal use conditions.
4 © ISO 2017 – All rights reserved

Accelerated life testing involves acceleration of failures with the single purpose of quantification of the
life characteristics of the component at normal use conditions.
Therefore, accelerated life testing can be divided into two areas: qualitative accelerated testing (HALT)
and quantitative accelerated life testing. In qualitative accelerated testing, the objective is to identify
failures and failure modes without attempting to make any predictions as to the component’s life under
normal use conditions. In quantitative accelerated life testing, the objective is predicting the life of the
component (life characteristics such as MTTF, B life, etc.) at normal use conditions from data obtained
in an accelerated life test.
The strategy for effectively conducting an accelerated life testing program includes the following:
— establishing a stress level that can be referred to as normal use conditions;
— determining the stress levels to use for accelerated testing; and
— determining the number of components to be tested at each stress level.
8 Design of accelerated life testing
8.1 Normal use conditions
Normal use conditions can often be defined from the ratings of the component’s characteristics, for
example: pressure, temperature, voltage, duty cycle, lubrication requirements, etc. However, these
ratings often represent a maximum condition that is above commonly used conditions. Therefore, a
definition for normal use conditions needs to be established from these characteristics before starting
an accelerated test. An example definition for a pneumatic valve is shown in Table 1.
Table 1 — Definition of normal use conditions for a pneumatic valve
Common use applica- Proposed normal use
Characteristic Typical rating value
tion value value for testing
Pressure 1 000 kPa (10 bar) 630 kPa (6,3 bar) 630 kPa (6,3 bar)
Temperature 50 °C 25 °C 25 °C
Voltage 24 VDC 24 VDC 24 VDC
Duty cycle Continuous On-off varies 10 % on / 90 % off
Lubrication Sometimes required Sometimes applied Not used
Air dryness Dew point < 0 °C Dew point ≤ 10 °C Dew point = 10 °C
It is necessary to define this normal use conditions before starting an ALT program.
8.2 Preliminary tests
It is also necessary to determine the highest stress to be tested that does not result in failure modes
different from those that occur under normal use conditions. Typically, these stresses or limits are
unknown, so qualitative tests (HALT) with small sample sizes can be performed in order to determine
the appropriate stress levels for use in the accelerated life test. Design of Experiments (DOE)
methodology is a useful technique at this step.
The following steps can be taken to determine three stress levels:
a) Propose the highest possible stress that might yield failure in less than 1 day of testing
(approximately).
b) Reduce this stress level to 90% of that value and test at least two test units to failure at this
stress level, using the test procedures of one of the parts of the ISO 19973 series (modified for the
conditions of the stress level).
c) Examine the failure mode to determine if it is the same type of failure as would be experienced
under normal use conditions. If it is not, reduce the level of stress and repeat steps b) and c) until
failures are the same as would be experienced under normal use conditions. Identify this as stress
level S .
d) Reduce the stress level by another 10% to 20% from step b) and test at least two more test units to
failure. Again, examine the failure mode to determine if it is the same type of failure as would be
experienced under normal use conditions. If it is not, modify the stress conditions and repeat the
test. Identify this as stress level S . See Figure 2.
e) Identify a third, yet lower stress level S that results in failures within the project timing constraints.
This third level of stress is identified by extrapolating from the previous pairs of failures as shown
in Figure 2. As an alternative, S can be estimated by using an average value of S and S , so that
3 1 2
S = ½ (S – S ).
3 2 1
f) Test at least two more test units to failure at this third level of stress S . Again, examine the failure
mode to determine if it is the same type of failure as would be experienced under normal use
conditions. If it is not, modify the stress conditions and repeat the test.
Figure 2 — Graphical explanation of determining stress levels during preliminary tests
These preliminary tests might have to be conducted several times before the necessary stress levels
are determined.
8.3 Levels of accelerated stress
The levels of stress identified from 8.2 are used to conduct a series of accelerated tests on randomly
selected test units, in accordance with one of the parts of ISO 19973. Generally, these stress levels
6 © ISO 2017 – All rights reserved

fall outside of the limits of the component’s specification. It is important, therefore, to constantly
examine the types of failures obtained to be sure they are the same as those experienced at normal
use conditions. If they are not, the test units would be designated as suspensions, or the test conditions
would be modified and the testing restarted.
Conduct the tests at each of the selected stress levels. It is also helpful to conduct at least one test at a
stress level that is as close as possible to the normal use conditions.
At the higher levels of stress in an accelerated test, the required test duration decreases, and the
uncertainty in the extrapolation increases. Confidence intervals provide a measure of the uncertainty
in extrapolation.
The most common stresses for pneumatic fluid power components are pressure and temperature.
Testing can be conducted either at one set of stress conditions on a sample lot, or two stresses on
different sample lots. Cylinder speed, and cycle rate of valves and regulators are other possibilities.
Temperature of the process air used to test components is usually heated (or cooled) to approximately
equal the environmental test temperature.
When conducting an accelerated life test, arrangements are made to ensure that the failures of the
components are independent of each other (e.g. so that failures due to temperature do not influence the
failures due to pressure).
8.4 Sample size
Ideally, at least seven test units are subjected to each stress level for the accelerated life test. However,
the number of test units allocated to each stress level is usually inversely proportional to the level of
applied stress; that is, more test units are subjected to lower stress levels than to higher stress levels
because of the higher proportion of failures expected at the higher stress levels. A good ratio for the
number of test units among the stress levels, from highest to lowest, is 1:2:4. If test units are expensive,
four test units each at stress levels S and S would be tested; and five or more test units would be
1 2
tested at stress level S . As an option, the number of test units could be two if time is limited, but the
estimation uncertainty at the normal use condition will increase.
8.5 Data observation and measurement
No repairs are made to the test units during accelerated life testing.
The test operator determines the intervals between measurements to obtain data during accelerated
life testing. Short intervals between measurements give better statistical results and are conducted
during testing at the high stress level. At the low stress levels, longer intervals between measurements
are adequate.
8.6 Types of stress loading
There are two possible stress loading schemes: loading in which the stress is time-independent (where
the stress does not vary over time), and loading in which the stress is time-dependent (where the stress
does vary over time). This document uses constant time-independent stress loading, which is the most
common type used in an accelerated life test; see Figure 3. However, non-constant stress loads, such as
step stress, cycling stress, random stress, etc., can be used. These types of loads are classified according
to their dependence on time and are described in Annex A. The method specified in Annex A is used
where a time-dependent analysis is required.
Figure 3 — Constant stress model
Time-independent stress loading has many advantages over time-dependent stress loading. Specifically:
— most components are assumed to operate at a constant stress under normal use conditions;
— it is far easier to run a constant stress test;
— it is far easier to quantify a constant stress test;
— models for data analysis are widely publicized and are empirically verified; and
— extrapolation from a well-executed constant stress test is more accurate than extrapolation from a
time-dependent stress test.
9 End of test
9.1 Minimum number of failures required
Confidence levels are generated when at least four test units have failed (which includes their reaching
a threshold level) at each stress level.
9.2 Termination cycle count
When a test unit fails between consecutive observations, the data collected is referred to as left-
censored or interval data. In this case, both the last cycle count at which the test unit was operating
properly and the cycle count at which the test unit was observed to have failed, are recorded. This data
is usually processed in accordance with ISO 19973-1:2015, 10.2.
9.3 Suspended or censored test units
Individual test units on which testing was stopped before failure occurred are known as suspensions.
Some examples of suspensions include:
— the test unit needed to be disassembled for inspection;
— the test unit experienced a failure mode different than the type being considered; and
— the test unit was accidentally damaged from a source not related to the test.
Because these test units had achieved a number of cycles before the point of suspension, the data has a
positive influence on the calculation of the statistical parameters. However, they cannot be returned to
the testing program.
If the minimum number of failures has been reached, but some test units have not failed (reached a
threshold level), the test can be stopped. The remaining test units are designated as censored.
8 © ISO 2017 – All rights reserved

Data from suspended test units is considered the same as data from censored test units. The method
specified in Annex D allows calculation of the statistical parameters for these types of data
10 Statistical analysis
10.1 Analysis of failure data
The failure data from testing at all stress levels is analysed in accordance with 10.2, 10.3 and 10.4.
10.2 Life distribution
Select an initial life distribution (it can be changed later, if necessary). For pneumatic components, the
Weibull distribution is commonly used, and its scale parameter,η , is selected to be the life characteristic
that is stress-dependent; while the slope β is assumed to remain constant across different stress levels.
Plot the raw data from all stress levels on one graph and obtain a best fit straight line to the data from
each stress level (see Figure 4 for an example). If the slopes β from each stress level are not parallel,
consider a compromise slope for each set of stress levels (see Figure 5). A judgment is necessary as to
whether the compromise slope is statistically acceptable (see example in Annex C), and if it is judged
not acceptable, the testing program is restarted with improved data collection methods. It is necessary
to have a constant value of the slope β for each stress level.
Figure 4 — Best fit slope to raw data
Figure 5 — Compromised equal slope lines
The resulting distribution is verified by statistical analysis as described in Annex C. If the lines fitted
from the plotted data at each accelerating stress level are parallel, it implies that the failure mechanism
at each stress level is the same, and the selected stress levels for the accelerated testing are appropriate.
10.3 Accelerated life testing model
Select or create a model of accelerated life testing that describes a life characteristic of the distribution
from one stress level to another; this is also called a life-stress relationship model. Examples of these
models include the Arrhenius, Eyring, Inverse Power Law, etc., and are described in Annex B.
10.4 Data analysis and parameter estimation
Using the selected life-stress relationship model, estimate the parameters of the life-stress distribution
using either a graphical method, a least squares method, or the maximum likelihood estimation (MLE)
method. An example using the Arrhenius model with a graphical estimation method is shown in
Figure 6.
10 © ISO 2017 – All rights reserved

Figure 6 — Arrhenius plot of data from Figure 5
In Figure 6, the individual dots are the raw data points, and the connecting line joins the characteristic
life η from each stress level. The example curves in Figures 4, 5 and 6 used a Weibull distribution.
NOTE Commercial software can be helpful in developing all of these plots.
The acceleration factor (AF) can now be determined from a simple proportion of lives at the normal
use life to those at any accelerated condition. Methods of calculating acceleration factors are given in
Annex B of this document and an example is shown in Annex C.
11 Reliability characteristics from the test data
To improve the interpretation of the calculation results, the failure mode for each test unit is recorded.
Calculations are made from the test data at each stress level to determine:
— characteristic life η ;
— Weibull shape parameter β , slope of the straight line in the Weibull plot;
— the mean life, which provides a measure of the average time of operation to failure;
— B life, which is the time by which X% of the components are estimated to fail; and
X
— the confidence intervals of the B life at the 95% confidence level using Fisher information matrix,
X
Calculations are made from the life-stress analysis to determine:
— model parameters and acceleration factor; and
— B life and confidence intervals of B life at the normal use conditions.
X x
12 Test report
The test report includes at least the following data:
a) the number of this document, including the component-specific part number;
b) date of the test report;
c) component description (manufacturer, type designation, series number, date code);
d) sample size;
e) test conditions (types of stress, number of stress levels, stress loading, etc.);
f) threshold levels;
g) shape parameter (β );
h) types of failures for each test unit;
i) B life and confidence intervals of B life at 95% confidence level under normal use conditions;
10 10
j) characteristic life η under normal use conditions;
k) number of failures considered;
l) method used to calculate the Weibull data (Maximum likelihood, etc.);
m) model for accelerated life testing (Arrhenius-Weibull, Eyring-Weibull, Inverse power law-
Weibull, etc.);
n) acceleration factor;
o) parameters of the selected acceleration model;
p) other remarks, as necessary.
12 © ISO 2017 – All rights reserved

Annex A
(informative)
Determining stress levels when stress is time-dependent
When the stress is time-dependent, the component is subjected to a stress level that varies with time.
Components subjected to time-dependent stress loadings yield failures more quickly, and models that
fit them are valuable methods of accelerated life testing.
The step-stress model and the related ramp-stress model are typical cases of time-dependent stress
tests. In these cases, the stress load remains constant for a period of time and then is stepped/ramped
into a different stress level where it remains constant for another time interval until it is stepped/ramped
again. There are numerous variations of this concept as shown in Figures A.1 to A.4:
Figure A.1 — Step stress model Figure A.2 — Ramp stress model
Figure A.3 — Increasing stress model Figure A.4 — Complete time-dependent stress
model
There are some cases where the stress in a field operating condition is variable. In that case, the
following steps are helpful to process the accelerated life test:
a) First, identify the field operating condition for a related component. The result using histogram is
shown in Figure A.5.
b) Calculate equivalent load needed for accelerated life testing using Palmgren-Miner’s rule (see
Annex F). Figure A.6 represents the equivalent load for the resulting accelerated life test.
Figure A.5 — Field operating condition Figure A.6 — Equivalent damage effect cal-
culation
c) Decide upon a step-stress loading method to determine a destruct limit and yield point for the
accelerated life testing. Figure A.7 shows step-stress loading method.
d) Determine the appropriate stress range using destruct limit, operating limit (or elastic limit), and
specification limit (proportional limit) of a strain-stress curve as shown in Figure A.8.
e) Find the accelerated stress level using an accelerated life test curve as shown in Figure A.9. In the
field of mechanical engineering, overstress levels commonly used in industry are 120 %, 133 %,
and 150 %.
f) Determine the stress levels using a step by step process (see Figure A.10) and the procedure given
in 8.2. Accelerated life testing at the three accelerating stress levels can then be performed.
14 © ISO 2017 – All rights reserved

Figure A.7 — Step-stress loading method Figure A.8 —Strain-stress curve
Figure A.9 — Accelerated life test curve Figure A.10 — Decision method of stress levels
g) Before estimating the reliability characteristics, check on the validation of accelerated test using
probability plot in Figure A.11. If the fitted lines of the plotted data at each accelerating stress levels
are parallel, it means that assumed lifetime distribution is appropriate and the accelerating stress
is effective.
h) Check the error between the estimates of the considered model and real test results. First, check
that the shape parameters acquired from the considered model, and tested results in normal use
conditions, are the same. Second, check if the scale parameter of the considered model resides in the
confidence intervals of scale parameter from the test results. Finally, if the scale parameter of the
considered model is within the confidence intervals, it could be judged that both the characteristic
life of the considered model and test result are not statistically different. Figure A.12 shows the
graphical explanation of the error between estimate of the considered model and test result.
Figure A.11 — Validation and verification of Figure A.12 — Graphical explanation of the
accelerated test error between test estimate of the considered
model and test result
16 © ISO 2017 – All rights reserved

Annex B
(informative)
Life-stress relationship models
B.1 Acceleration factor
The acceleration factor is a unitless number that relates a component’s life at an accelerated stress level
to the life at the normal use stress level. It is defined by;
L
U
AF = (B.1)
L
A
where
is the life at the normal use stress level
L
U
is the life at the accelerated stress level
L
A
As it can be seen in Formula (B.1), the acceleration factor depends on the life-stress model and is thus a
function of stress.
B.2 Arrhenius life-stress model
The Arrhenius life-stress model (or relationship) is probably the most common life-stress model utilized
in accelerated life testing. It has been widely used when the stimulus or accelerated stress is thermal
(i.e. temperature).
The Arrhenius life-stress model is formulated by assuming that life is proportional to the inverse
reaction rate of the process, thus the Arrhenius life-stress model is given by;
B
V
LV()=⋅Ce (B.2)
where
L is the quantifiable life measure (mean life, characteristic life, median life, B life, etc.)
X
V is the stress level (temperature values in degrees Kelvin)
C and B are the model parameter (C>0, B>0)
The choice of the Arrhenius model is justified by the fact that this is a physics-based model derived for
temperature dependence.
The Arrhenius model is linearized by taking the natural logarithm of both sides in Formula (B.2).
B
ln()LV() =ln(C)+ (B.3)
V
Depending on the application (and where the stress is exclusively thermal), the parameter B can be
replaced by;
E activation energy activation ennergy
A
B== = (B.4)
−−51
K Boltzman's constant
8,623×10 eVK
The activation energy is meant to be known a priori. If the activation energy is known, then only
model parameter C remains. Because this is rarely the case in most real-life situations, all subsequent
formulations can assume that this activation energy is unknown and treat B as one of the model
parameters. B is a measure of the effect that the stress (i.e. temperature) has on the life. The larger the
value of B, the higher the dependency of the life on the specific stress.
Most practitioners use the term acceleration factor to refer to the ratio of the life (or acceleration
characteristic) between the normal use level and a higher test stress level. For the Arrhenius model,
acceleration factor is;
B
 
B B
−
V  
U
 
L
Ce⋅
V V
USE
 UA 
AF == =e. (B.5)
B
L
Accelerated
V
A
Ce⋅
The probability density function for 2-parameter Weibull distribution is given by;
β
 
t
β−1
−
 
 
β t
η
 
ft()= e (B.6)
 
ηη
 
The scale parameter (or characteristic life) of the Weibull distribution is η. The Arrhenius-Weibull
model’s probability density function at a stress level V can then be obtained by setting η = L(V) in
Formula (B.2);
B
V
η ==LV() Ce⋅ (B.7)
and substituting for η in Formula (B.6);
β
 
 
t
β−1
− 
 
B
 
   
β t
V
Ce⋅ 
ft(;V )= e (B.8)
 
B B
 
V V
Ce⋅⋅Ce 
The mean time to failure (MTTF) of the Arrhenius-Weibull model is given by;
B
 1 
V
MTTF =⋅Ce ⋅+Γ 1 (B.9)
 
β
 
where Γ⋅ is the gamma function.
()
18 © ISO 2017 – All rights reserved

The Arrhenius-Weibull reliability function at stress level V is given by;
β
 
 
t
− 
B
 
 
V
Ce⋅ 
Rt(;Ve)= (B.10)
B.3 Inverse power law life-stress model
The inverse power law (IPL) model is commonly used for non-thermal accelerated stresses and is
given by;
LV()= (B.11)
n
KV
where
L is the quantifiable life measure (mean life, characteristic life, median life, B life, etc.)
X
V is the stress level
K and n are model parameters (K>0, n>0)
The inverse power law appears as a straight line when plotted on a log-log paper. The equation of the
line is given by;
ln()LK=-ln()-lnVn( ) (B.12)
The parameter η in the inverse power model is a measure of the effect of the stress on the life, i.e. the
larger the value of n, the greater the effect of the stress. A value of n approaching 0 indicates small effect
of the stress on the life, with no effect (constant life with stress) when n = 0.
For the inverse power law model, the acceleration factor is given by;
n
n
 
L KV V
USE U A
AF == = (B.13)
 
L V
Accelerated U
 
n
KV
A
The inverse power law Weibull model can be derived by setting η = L(V), yielding the following IPL-
Weibull probability density function at stress level V;
β
n
β−1
−⋅KV ⋅t
)
(
nn
ft(;VK)=⋅β ⋅⋅VK Vt⋅ e (B.14)
()
The mean time to failure (MTTF) of the IPL-Weibull model is given by;
11 
MTTF =⋅Γ +1 (B.15)
 
n
β
KV  
The IPL-Weibull reliability function at stress level V is given by;
β
n
−⋅KV ⋅t
( )
Rt(;Ve)= (B.16)
B.4 Eyring life-stress model
The Eyring life-stress model was formulated from quantum mechanics principles and is most often
used when thermal stress (temperature) is the acceleration variable. However, the Eyring model is also
often used for stress variables other than temperature, such as humidity. The model is given by;
B
−−()A
V
LV()= e (B.17)
V
where
L is the quantifiable life measure (mean life, characteristic life, median life, B life, etc.)
X
V is the stress level
A and B are model parameters
For the Eyring model the acceleration factor is given by;
 
B
−−A
 
 
V
 u   
e
B −
 
 
L V V
VV
USE u AA
 UA 
AF == = e (B.18)
 
L B V
Accelerated U
−−A
 
 
V
 A 
e
V
A
The Eyring-Weibull model can be derived by setting η = L(V), yielding the following Eyring-Weibull
probability density function at stress level V;
β
  B  
A−−
 
 
V
 
β−1
−⋅tV⋅e
 
 B   B 
 
A− A−  
   
 
V V
     
ft(;VV)=⋅β ⋅⋅et Ve⋅ e (B.19)
 
 
 
The mean time to failure (MTTF) of the Eyring-Weibull model is given by;
B
 
−−A
 
 
V
 
MTTF =⋅e ⋅+Γ 1 (B.20)
 
V β
 
The Eyrin-Weibull reliability function at stress level V is given by;
β
  B  
A−
 
 
V
 
−⋅Vt⋅e
 
 
 
Rt(;Ve)= (B.21)
20 © ISO 2017 – All rights reserved

B.5 Temperature-humidity combination model
The temperature-h
...