ISO/TR 19972-1:2009

Hydraulic fluid power - Methods to assess the reliability of hydraulic components - Part 1: General procedures and calculation method

ISO/TR 19972-1:2009 provides a means for determining the reliability of hydraulic fluid power components using: estimates from a design analysis; analysis of laboratory testing to failure or suspension; analysis of field data; analysis of a substantiation test. These methods apply to the first failures without repairs, but exclude certain infant mortality failures. Specific component test procedures and exclusions are provided in subsequent parts of ISO/TR 19972. ISO/TR 19972-1:2009 also provides calculation methods, reporting descriptions and examples of reliability calculations.

Transmissions hydrauliques — Méthodes d'évaluation de la fiabilité des composants hydrauliques — Partie 1: Modes opératoires généraux et méthode de calcul

General Information

• Status: Published
• Publication Date: 08-Feb-2009
• ICS: 23.100.01 - Fluid power systems in general
• Technical Committee: ISO/TC 131/SC 8 - Product testing
• Drafting Committee: ISO/TC 131/SC 8/WG 11 - Pressure rating
• Current Stage: 9093 - International Standard confirmed
• Start Date: 26-Mar-2019
• Completion Date: 13-Dec-2025

Overview

ISO/TR 19972-1:2009 - "Hydraulic fluid power - Methods to assess the reliability of hydraulic components - Part 1" describes general procedures and calculation methods for assessing the reliability of hydraulic components. The Technical Report defines approaches for estimating reliability from a design analysis, laboratory testing to failure or suspension, field data, and substantiation tests. It applies to first failures (no repairs) while excluding certain infant‑mortality failures. The document also provides calculation methods, reporting guidance and worked examples (Annexes A–D).

Key topics and requirements

• Reliability concepts and metrics
  • Definitions for reliability, failure, MTTF (mean time to failure), MCTF (mean cycles to failure) and B10 life (90 % survival).
  • Need to associate confidence bounds with reliability estimates.
• Methods for determining reliability
  • Design analysis: engineering calculation procedures and combining component‑level predictions when test/field data are absent.
  • Laboratory testing: guidance on test planning, acceleration, test‑stand integrity, measurement accuracy and preserving failure mechanisms under accelerated conditions.
  • Field data collection: structured data capture, product identification, operating environment and bias minimization.
  • Substantiation testing: procedures and equations for proving reliability claims.
• Statistical and calculation tools
  • Use of statistical distributions (e.g., Weibull) and symbols (β, η) for life modeling.
  • Examples and worked calculations are provided in informative annexes.
• Test and reporting requirements
  • Define threshold levels for performance characteristics (leakage, flow, response time, electrical parameters) that constitute failure.
  • Record assumptions, environmental conditions and measurement tolerances to ensure repeatability and traceability.
• Scope limits
  • Applies to first failures without repair; specific component exclusions and test procedures appear in later parts of ISO/TR 19972.

Practical applications and users

ISO/TR 19972-1:2009 is useful for:

• Hydraulic system designers and OEMs - to predict component reliability during design and to inform design improvements.
• Test engineers and reliability analysts - to plan laboratory tests, accelerated tests and substantiation programs.
• Field service, maintenance planners and spare‑parts managers - to derive service intervals and spare stocking strategies based on component life metrics.
• Warranty and quality teams - to evaluate field failure data and establish confidence in reliability claims. Practical outcomes include improved product life estimation, optimized test programs, validated warranty policies and better-informed maintenance schedules.

Related standards

• ISO 1000 - SI units and recommendations
• ISO 5598 - Fluid power vocabulary
• ISO 9110-1 - Measurement techniques (general principles)
• Subsequent parts of ISO/TR 19972 - specific component test procedures and exclusions

Keywords: ISO/TR 19972-1:2009, hydraulic fluid power reliability, hydraulic components reliability, reliability assessment, laboratory testing to failure, design analysis, field data collection, Weibull analysis, MTTF, B10 life.

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 19972-1
First edition
2009-02-15
Hydraulic fluid power — Methods to
assess the reliability of hydraulic
components —
Part 1:
General procedures and calculation
method
Transmissions hydrauliques — Méthodes d'évaluation de la fiabilité des
composants hydrauliques —
Partie 1: Modes opératoires généraux et méthode de calcul

Reference number
©
ISO 2009
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ii © ISO 2009 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Units of measurement and symbols. 2
5 Reliability concept . 2
6 Means for determining reliability . 3
7 Procedures for analysing a design concept . 5
8 Procedures for laboratory testing to failure or suspension. 8
9 Procedures for collecting field data. 9
10 Procedure for a substantiation test . 10
Annex A (informative) Example calculation for analysing a design concept . 13
Annex B (informative) Calculation examples for laboratory test to failure data analysis . 19
Annex C (informative) Example calculation for collecting field data. 27
Annex D (informative) Equation development and example calculations for substantiation testing . 33
Annex E (informative) Reference material . 38
Bibliography . 40

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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
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.
ISO/TR 19972-1 was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee
SC 8, Product testing.
ISO/TR 19972 consists of the following parts, under the general title Hydraulic fluid power — Methods to
assess the reliability of hydraulic components:
⎯ Part 1: General procedures and calculation method
It is possible that other parts will be developed in the future.
iv © ISO 2009 – All rights reserved

Introduction
In hydraulic fluid power systems, power is transmitted and controlled through a liquid or gas under pressure
within an enclosed circuit. Fluid power systems are composed of components, and are an integral part of
various types of machines and equipment. Efficient and economical production requires highly reliable
machines and equipment.
Machine producers need to know the reliability of the components that comprise their machine’s fluid power
system. Once they know the reliability characteristic of the component, the producers can model the system
and make decisions on service intervals, spare parts inventory and areas for future improvement.
There are different methods used to investigate component reliability.
A preliminary design analysis is useful to identify potential failure modes and to reduce their effect on reliability.
In addition, calculation of failure rates is possible. When prototypes are available, in-house laboratory
reliability tests are run and initial reliability can be determined. Reliability testing is often continued into the
initial production run and throughout the production lifetime as a continuing evaluation of the component.
Collection of field data is possible when products are operating and data on their failures are available. This, in
turn, can be utilized for reduced lab testing on improvements to the products or similar, new products. These
methods also offer the user an opportunity to choose the most economical and practical procedure to
measure reliability for a given application.
TECHNICAL REPORT ISO/TR 19972-1:2009(E)

Hydraulic fluid power — Methods to assess the reliability of
hydraulic components —
Part 1:
General procedures and calculation method
1 Scope
This part of ISO/TR 19972 provides a means for determining the reliability of hydraulic fluid power
components using:
a) estimates from a design analysis;
b) analysis of laboratory testing to failure or suspension;
c) analysis of field data;
d) analysis of a substantiation test.
These methods apply to the first failures without repairs, but exclude certain infant mortality failures. Specific
component test procedures and exclusions will be provided in subsequent parts of ISO/TR 19972.
This part of ISO/TR 19972 also provides calculation methods, reporting descriptions and examples of
reliability calculations.
2 Normative references
The following referenced documents are indispensable for the application 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 1000, SI units and recommendations for the use of their multiples and of certain other units
ISO 5598, Fluid power systems and components — Vocabulary
ISO 9110-1, Hydraulic fluid power — Measurement techniques — Part 1: General measurement principles
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 5598 and the following apply.
3.1
B life
L life
life of the component or assembly that has not been altered since its production, where its reliability is 90 %;
or time at which 90 % of the population has survived
NOTE The cumulative failure percentage is 10 %.
3.2
component
individual unit (e.g. cylinder, motor, valve, filter, but excluding piping) comprising one or more parts designed
to be a functional part of a fluid power system
3.3
mean time to failure
MTTF
mean lifetime of a component that has not been repaired since its production, based on a statistical mean,
using times to failure as the definition of failure
3.4
mean cycles to failure
MCTF
mean life, expressed as number of cycles, of a component that has not been repaired since its production,
based on a statistical mean, using cycles to failure as the definition of failure
3.5
reliability
probability that a component can perform continuously, without failure, for a specified interval of time when
operating under stated conditions
3.6
failure
state at which a component reaches the threshold level or terminates its ability to perform a required function
3.7
termination cycle count
number of cycles on a specimen when it reaches any threshold level for the first time
3.8
threshold level
the value of a performance characteristic (e.g. leakage, flow and current) against which the component’s test
data is compared
NOTE This is an arbitrary value defined by the experts as the critical value for performance comparisons, but not
necessarily indicative of the end of component operation.
4 Units of measurement and symbols
Units of measurement are in accordance with ISO 1000, except for Clause 7 and Annex A, which are based
[9]
on The Handbook of Reliability Prediction Procedures for Mechanical Equipment and use imperial units.
Symbols for the Weibull parameters: β = Slope
η = Characteristic life
t or x = Minimum life
0 0
5 Reliability concept
Reliability is the probability (a percentage) that a component will not exceed the threshold level for a specified
interval of time or number of cycles when it operates under stated conditions. This probability can be
determined by any of the methods described in Clause 6. There are many different statistical distributions that
describe the population of failures that result from these methods. Mean time to failure and B life are
common terms used for expressing reliability.
2 © ISO 2009 – All rights reserved

It is also necessary to associate some confidence with a reliability result. This takes into account the fact that
results will vary if the process is repeated many times, and the confidence describes probability bounds to the
distribution of failures.
To determine reliability scientifically, it is necessary to define failure. This can be evident in field failures, but
for the other methods the concept of threshold levels is defined for various performance characteristics. This
is necessary because the value of some of these characteristics (e.g. leakage) might not represent a total
failure of the component.
Examples of analytical methods and test parameters for which threshold levels might need to be established
include:
a) dynamic leakage, both internal and external;
b) static leakage, both internal and external;
c) changes in performance characteristics (e.g. loss of stability, increase in minimum operating pressure,
deterioration of flow rate, increase in response time, change in electrical characteristics, performance
degradation due to contamination and breakdown of accessory functions).
In addition to these threshold levels, failure can also occur from catastrophic events such as burst, breakage,
fatigue or loss of function.
6 Means for determining reliability
6.1 General
Environmental aspects for any of the methods discussed in this part of ISO/TR 19972 will have an influence
on the results. Therefore, it is important to record the assumptions used in 6.2, follow the requirements
specified for 6.3, record the observations obtained in 6.4, and use the original historical conditions in 6.5.
6.2 Design analysis
Calculation methods can be used to quantify the reliability of hydraulic components. In cases where neither
field data or test data are available or tests cannot be carried out economically, calculation methods are
recommended to estimate component reliability.
Predicting the reliability of mechanical equipment requires consideration of its exposure to the environment
and subjection to a wide range of stress levels (e.g. impact loading). The approach to predicting reliability of
mechanical equipment considers the intended operation environment, and determines the effect of that
environment at the lowest part level where the material properties can also be considered. The combination of
these factors permits the use of engineering design parameters to determine the design life of the equipment
in its intended operating environment, and the rate and pattern of failures during design life.
An analysis of a design for reliability and maintenance (R and M) can identify critical failure modes and causes
of unreliability as well as providing an effective tool for predicting equipment behaviour. The design evaluation
programme includes a methodology for evaluating a design for R and M that considers the material properties,
operating environment and critical failure modes at component level. In The Handbook of Reliability Prediction
[9]
Procedures for Mechanical Equipment , 19 mechanical components have been identified for which reliability
prediction equations have been developed. If a hydraulic component includes more than one mechanical
component, the individual mechanical component reliabilities can be combined to establish the total
equipment reliability.
A great advantage of this method is that the influence of parameters on the life of a component can be
determined. This allows the engineer to improve the design in an early phase of development.
6.3 Laboratory test to failure or suspension
One of the major difficulties encountered in specifying a reliability test is the time it takes to cause a failure
without accelerating the test. Accelerated testing, with environmental conditions above those for which the
component is rated, is sometimes necessary in order to keep the test time at a reasonable length. The goals
and objectives of the test method should be clearly defined.
The primary criterion for determining test acceleration factors is that the failure mode or failure mechanism
should not change or be different from that expected from a non-accelerated test.
Two other important factors are the test stand and measurement of parameters. The test stand should be
designed to operate reliably within the planned environmental conditions. Its configuration should not affect
the results of the test being run on the component. Evaluation and maintenance of the test stand during the
reliability test programme is critical. The accuracy of parameter measurement and control of parameter values
should be within the specified tolerances to assure accurate and repeatable test results.
Proper test planning is essential in order to have results that accurately predict the component’s reliability
under specified conditions. The goals and objectives of the test programme should be clearly defined if a
supplier and user agree to apply this part of ISO/TR 19972.
6.4 Collection of field data
Collection of field reliability data is an essential element of an effective product reliability programme. It is one
of the most valuable sources of data since it represents actual customer/user product experience under
working conditions.
Failures occur as a result of manufacturing and material deviations, product overstress in use, design
deficiencies, cumulative wear and degradation, and random occurrences. Factors such as product
misapplication, operating environment, installation and maintenance practices directly impact product life.
Hence the collection of field data is necessary to assess these factors. Therefore, it is very important that
details such as product lot identification, date codes and the specific operating environment be recorded.
Communication of objectives and the qualifications of personnel involved in the reporting process are crucial
to the success of the data collection effort. It should be recognized that information to be extracted can only be
obtained from the data collected. It is essential to be clear about objectives.
Since field data collection relies on people, it is subject to errors, personal biases, omissions and
misunderstandings. It is therefore critically important to collect all data using a formal structured procedure
and format.
The importance that appropriately trained qualified operations and maintenance personnel can contribute to
the completeness and correctness of the data should not be underestimated. However, the design of the data
collection system should minimize any bias that could be introduced by the personnel involved.
NOTE It is important to consider the individual’s position, experience and objectivity when developing the collection
procedures.
Selection of the data to be collected depends on the kind of performance metrics to be evaluated or estimated.
The data collection system should provide at least
a) basic product identification information, including total number of units in service,
b) equipment environmental class,
c) environmental conditions,
d) operating conditions,
e) performance measurements,
4 © ISO 2009 – All rights reserved

f) maintenance support conditions,
g) failure description,
h) system changes implemented following occurrence of failure,
i) corrective action and specific details of replacement or repair, and
j) date, time and/or cycles to each failure.
6.5 Substantiation testing
Substantiation testing, based on statistical methods, is an efficient means used to validate the reliability of
small sample test populations using historical data to define a population failure distribution.
NOTE This is also known as the Weibayes method.
This method validates a minimum level of reliability for a new population similar to an existing one, but does
not result in an explicit value for its reliability. Instead, the testing validates that the reliability of the new
population is greater than, or equal to, the reliability target of the test.
The procedure consists of selecting a Weibull shape or distribution factor, β, and calculating the test length
required to support substantiation (historical data has shown that β tends to be consistent for a specific failure
mode criterion). A test programme is then conducted on a sample of the new population. If the test is
successful, the minimum level of reliability is substantiated.
7 Procedures for analysing a design concept
7.1 General
Based on handbooks for mechanical and electronic equipment, failure rates can be calculated for all critical
parts of a hydraulic component that can fail in service (see Figure 1). For mechanical equipment, failure rates
are calculated with reliability prediction equations that consider material properties, operating environment and
design parameters. To predict the reliability of a complete component, the single failure rates are simply
added to a component failure rate. The MTTF is the reciprocal of the failure rate.

Figure 1 — Flow chart for calculating failure rates

Where integrated electronics are part of a hydraulic component, the failure rate of the electronics can be
[7] [6]
calculated by using MIL-STD-756B , MIL-HDBK-217F or the Telcordia Technologies Special
[8]
Report SR332 data bank .
[9]
The Handbook of Reliability Prediction Procedures for Mechanical Equipment is recommended for
mechanical parts. This reference is a summary of experiments that have led to an analytical method based on
empirical values obtained from that source.
7.2 Design evaluation
Critical components can be identified by simply comparing the parts of the design with the components listed
[9]
in The Handbook of Reliability Prediction Procedures for Mechanical Equipment , for example:
a) seals and gaskets;
b) springs;
c) solenoids;
d) valve assembles;
e) bearings;
f) gears and splines;
g) actuators;
h) pumps;
i) filters;
j) brakes and clutches;
k) compressors;
l) electric motors;
m) accumulators and reservoirs;
n) threaded fasteners;
o) mechanical couplings;
p) slider-crank mechanisms;
q) sensors and transducers.
Typical failure modes and failure rate models are defined for each component. The part list should identify all
components and the number of parts in a design for the calculation of failure rates.
7.3 Threshold levels
For some components, threshold levels (e.g. allowable leakage) have to be defined in order to calculate the
failure rate.
6 © ISO 2009 – All rights reserved

7.4 Operational conditions
Operational conditions have an important influence on the life of a component. All parameters (e.g. fluid
pressure, fluid viscosity, temperature, contamination and externally applied loads) are needed to calculate the
failure rate of a component.
7.5 Failure rate calculation
For each component there exists a characteristic equation to calculate the failure rate. Also, a base failure rate
is given for each component. A generalized equation that adjusts the base failure rate can be established.
These characteristics and equations are given in the reference used for the analysis.
[8]
For electronic parts, the Telcordia Technologies Special Report SR332 can be used to calculate the failure
rate.
The failure rate of the total assembly is the sum of the failure rates calculated for each individual component.
Then, the MTTF or MCTF is the reciprocal of the failure rate, λ. An example calculation is given in Annex A.
7.6 Validation statement
Several test programmes were conducted during the development of The Handbook of Reliability Prediction
[9]
Procedures for Mechanical Equipment to verify the identity of failure modes and validate the engineering
approach being taken to develop the reliability equations. For example, valve assemblies were procured and
tested at the Belvoir Research, Development and Engineering Center in Ft. Belvoir, Virginia. The number of
failures for each test was predicted using the equations presented in the Handbook. Failure rate tests were
performed for several combinations of stress levels and results compared to predictions. Typical results are
shown in Table 1.
Table 1 — Sample test data for validation of reliability
a b
Test Valve Test cycles Actual Average Predicted Failure
series number to failure failures/ failures/ failures/ mode no.
6 6 6
10 cycles 10 cycles 10 cycles
15 11 68 322 14,64 14,64 18,02 3
24 8 257 827 — — — 1
24 9 131 126 7,63 10,15 10,82 1
24 10 81 113 12,33 — — 1
24 11 104 — — — 2
24 12 110 488 9,05 — — 1
24 13 86 285 11,59 — — 1
25 14 46 879 21,33 19,67 8,45 2
25 15 300 — — — 3
25 18 55 545 18,00 — — 1
a
Test parameters: System pressure: 3 500 psi
Fluid flow: 100 % rated
Fluid temperature: 90 °C
Hydraulic fluid: MIL-H-83282.
b
Failure modes: 1 Spring fatigue;
2 No apparent failure mode;
3 Accumulated debris.
8 Procedures for laboratory testing to failure or suspension
8.1 Minimum testing requirements
Testing should be carried out in accordance with the provisions of the relevant part of ISO/TR 19972
applicable to the component to be evaluated, and should include:
a) the statistical analysis method to be employed;
b) the test parameters to be measured in a reliability test and the threshold level for each parameter.
Several parameters can be selected for any component and threshold levels can also be classified in
groups;
c) the class of measurement accuracy in accordance with ISO 9110-1;
d) the number of specimens to be tested. This can be determined by practical methods (e.g. experience or
cost) or by statistical (e.g. analytical) methods. The specimens should be representative of the population
and should be selected randomly;
e) any preliminary measurements or bench tests that can be necessary to establish baseline
measurements;
f) a determination of whether production assembly testing is permissible or necessary before starting a
reliability test;
g) the conditions for the reliability test (e.g. supply pressure, cycle rate, loads, duty cycle, environmental
conditions and component orientation);
h) the frequency of test parameter measurement (e.g. at specific intervals or continuous monitoring).
i) any repairs permitted on the samples during the reliability test;
j) a disposition if the samples experience a failure that is not defined by one of the parameters being
measured;
k) the minimum number of specimens that should reach a termination cycle count (e.g. 50 %);
l) the maximum number of specimen suspensions allowed before the test is ended and to define whether a
minimum number of cycles is necessary before a specimen can be classified as a suspension or
discounted as a specimen;
m) any final examinations that are to be performed on the specimens, and on the test instruments at the end
of the test and any influence these examinations can have on the test data. Confirm the validity of the
data and any pass or fail conclusions (e.g. a failed solenoid might not be observed during a cycling test
until it is separately examined or a hairline crack might not be observed unless separately examined).
8.2 Data analysis
The resulting data shall be evaluated for estimating the reliability. One of the most commonly used methods is
the Weibull analysis because of its versatility in modelling various statistical distributions. Other methods are
possible if the distribution can be determined, or if an assumption for a distribution can be justified.
Typically, the following steps are performed during data analysis.
a) Record the cycle count at which a specimen reaches the threshold level for any parameter; this is the
termination cycle count for that specimen. The specimen may continue to be tested if there is interest for
other parameters, but it will not be counted any further in the analysis;
8 © ISO 2009 – All rights reserved

b) Plot a statistical distribution from the test data. If a Weibull analysis is employed, use median ranks. If
suspensions are included, use the modified Johnson formula and Bernard’s equation for the plotting
positions. See the example data analysis shown in Annex B;
c) Using a best-fit plot of the data, determine the characteristic values of the distribution. If a Weibull
analysis is used, this includes the minimum life, t or x , the slope, β, and characteristic life, η. In addition,
0 0
the desired level of confidence specified for the design is to be plotted using a type 1 Fisher Matrix;
NOTE Commercial software can be helpful for this purpose.
d) If a Weibull analysis is used, determine the B life at the confidence level for which the reliability values
i
will be determined.
9 Procedures for collecting field data
9.1 General
Reliability data collection can be based on events or on monitoring/inspection time intervals. Both methods are
established practice. Statistical methods are available to analyse data for either method used. A structured
approach should be adopted for assigning responsibilities, identifying data needed and developing procedures
for data collection methods for analysis and reporting.
Recording of the data can be manual, but automated and interactive data collection systems are
recommended. Reporting should include information on the conditions of use. Where the items are under
multiple usage (e.g. operation, configuration, standby, storage, transportation, test), it is necessary to collect
data on each usage type.
A fully relational database is recommended to permit storage and retrieval of required data, and facilitate data
analysis. The database includes records on all reported failures, failure analysis and failure resolution.
Analysis capabilities for efficient retrieval and analysis of the data to produce failure trends, failure summary
and status reports, failure history and corrective action should be incorporated. Any database needs an in-
depth study of its specific requirements, in order to define the most suitable methods of data checking, error
correction and updating.
Regardless of the design of the data collection procedure and the method of data storage, checks should be
made on the validity of data before entry. Data accepted for inclusion in the database should be validated and
checked for consistency. Validation depends on a clear definition of acceptable data. At a basic level, this can
be a check on whether or not a numeric value falls within a permitted range. However, data, unless erroneous,
should be retained even if outside a predetermined range.
Data stored for retrieval should be structured to maintain confidentiality of the source. Data should be
distributed only in composite form.
The goal of the data collection system is to convert large amounts of data into useable knowledge. Obviously
the nature of the product and marketplace needs will be a major consideration in deciding how extensive the
data collection and analysis system should be.
Frequently, one of a number of types of statistical distribution will underlie the collected data. Three principal
methods are available to identify a particular distribution:
a) engineering judgement, based on an analysis of the physical process generating the data;
b) graphical methods using special charts, leading to the construction of nomographs (e.g. see
[1]
ISO 8258 );
c) statistical tests providing a measure of the deviations between the sample and the assumed distributions;
[3]
such a test is given for the exponential distribution in IEC 60605-6 ; for other distributions, where there
are no international standards, information can be found in the technical literature;
Unfortunately, no single standard method or system for the analysis of field reliability data exists. Often, the
interpretation and analysis of field data require combining technical expertise, intuition and knowledge based
upon experience in order to achieve meaningful results.
The technical literature provides numerous methods for both graphical and analytical methods of presenting
field reliability data. A combination of graphical and analytic methods is often most informative. However,
graphical methods are the simplest, while analytic methods are generally mathematically rigorous in statistical
techniques. Some of the methods employed for data analysis are:
a) Pareto plots;
b) pie charts;
c) histograms;
d) time series plots;
e) custom charts;
f) non-parametric statistical techniques;
g) cumulative probability plots;
h) statistical methods and probability distribution functions;
i) Weibull analysis;
j) extreme value probability methods.
There are a number of commercially available software packages that support the analysis of field reliability
data and include many of the preceding analysis methods.
9.2 Methods for estimating reliability from field survey data
The MTTF, or the MCTF, for field data can be calculated in the same manner as for laboratory data. Use the
methods described in 8.2, with examples shown in Annex B. Supplementary information is given in Annex C.
10 Procedure for a substantiation test
10.1 General
Substantiation test procedures such as zero failure and zero/one failure test plans are derived from statistical
distribution procedures using a null hypothesis for the reliability of a component that is less than or equal to
the specification requirement, with zero failures (or one failure) in a binomial distribution. These test
procedures are particularly applicable for small sample test programmes.
In a zero failure test procedure, a specified B life is demonstrated if no failures occur during the test.
i
The zero/one failure test plan is similar to a zero failure test plan, except that one failure is allowed during the
test programme. A zero/one failure test accepts a higher cost (due to more testing) for a reduced risk of
rejecting an acceptable design. One advantage of the zero/one failure plan occurs when specimens are tested
in groups (e.g. due to test capacity restrictions). If all of the specimens up to the last specimen do not fail, then
the last specimen does not need to be tested. This is a basic part of the assumption that accounts for one
failure to occur while still validating the reliability requirement.
For the following analysis, the Weibull distribution method is assumed.
10 © ISO 2009 – All rights reserved

10.2 Zero failure method
10.2.1 Select a Weibull slope value for the component to be tested, based on known historical data. Then,
determine either the test duration or the number of samples from Equation (1) (see Annex D for its
development):
β
⎡⎤β
ln 1− C ⎡⎤β
() ⎛⎞t
⎛⎞1ln(1−CA) ⎛ ⎞β
i
tt==t =t or nA= (1)
⎢⎥
⎢⎥ ⎜⎟
ii⎜⎟ i⎜ ⎟
nR× ln n lnR n t
() ⎝⎠ ⎝ ⎠
⎢⎥ ⎝⎠
ii⎣⎦
⎣⎦
where
t is the test duration expressed in time, cycles, or distance;
t is the reliability objective in time, cycles, or distance;
i
β is the Weibull slope, obtained from historical data;
R is the reliability goal (100 − i)/100;
i
i is the variable index for % cumulative failure (e.g. i = 10 for B life);
n is the number of specimens;
C is the test confidence level;
A is obtained from Table 2 or calculated from Equation (1).
Table 2 — Values of A
R
i
C
R R R R R
1 5 10 20 30
95 % 298,1 58,40 28,43 13,425 8,399
90 % 229,1 44,89 21,85 10,319 6,456
80 % 160,1 31,38 15,28 7,213 4,512
70 % 119,8 23,47 11,43 5,396 3,376
60 % 91,2 17,86 8,70 4,106 2,569

10.2.2 Conduct a test on the samples using procedures in other parts of ISO/TR 19972. The test duration will
be t as defined above, and all samples shall survive the test.
10.2.3 If the test is successful, the reliability can be stated as follows.
The B life of (component) has been substantiation tested to demonstrate a minimum life of at least t (e.g.
i i
cycles, hours or kilometres) at a confidence level of C based on a zero failure Weibayes method.
10.3 Zero/one failure method
10.3.1 Select a Weibull slope value for the component to be tested, based on known historical data.
10.3.2 Determine the test duration from Equation (2) (see Annex D).
⎛⎞β
ln R
tt=⎜⎟ (2)
0 j
⎜⎟
ln R
j
⎝⎠
where:
t is the test duration expressed in time, cycles, or distance;
t is the reliability objective in time, cycles, or distance;
j
β is the Weibull slope obtained from historical data;
R is the reliability goal (100 − i)/100;
j
R is the reliability root value for zero/one failures (see Table 3);
j is the variable index percent cumulative failure (e.g. j = 10 for B life);
n is the number of specimens;
C is the confidence level.
Table 3 — Values of R
n
C
2 3 4 5 6 7 8 9 10
95 % 0,025 3 0,135 3 0,248 6 0,342 5 0,418 2 0,479 3 0,529 3 0,570 8 0,605 8
90 % 0,051 3 0,195 8 0,320 5 0,416 1 0,489 7 0,547 4 0,593 8 0,631 6 0,663 1
80 % 0,105 6 0,287 1 0,417 6 0,509 8 0,577 5 0,629 1 0,669 6 0,702 2 0,729 0
70 % 0,163 4 0,363 2 0,491 6 0,578 0 0,639 7 0,685 7 0,721 4 0,749 8 0,773 0
60 % 0,225 4 0,432 9 0,555 5 0,635 0 0,690 5 0,731 5 0,762 9 0,787 7 0,807 9

10.3.3 Conduct a test on the specimens using procedures in other parts of ISO/TR 19972. The test duration
will be t as determined using Equation (2) and no more than one specimen may fail the test. If all specimens
cannot be tested at one time, the last specimen need not be tested if all of the other specimens survive the
test.
10.3.4 If the test is successful, the reliability can be stated as follows.
The B life of (component) has been substantiation tested to demonstrate a minimum life of at least t (e.g.
j j
cycles, hours, kilometres) at a confidence level of C, based on a zero/one failure Weibayes method.
12 © ISO 2009 – All rights reserved

Annex A
(informative)
Example calculation for analysing a design concept
A.1 Example design evaluation procedure
A hydraulic valve assembly will be used to illustrate an approach to predicting the reliability of mechanical
1)
equipment. Developing reliability equations for all the different types of hydraulic valve available would be
an impossible task. For example, some valves are named after the function they perform (e.g. check valve,
regulator valve and unloader valve). Others are named after a distinguishing design feature (e.g. globe valve,
needle valve and solenoid valve). From a reliability standpoint, dropping down one indenture level provides
two basic types of valve assembly, poppet valves and sliding action valves.
The assembly chosen for this analysis example is a poppet valve consisting of a poppet assembly, spring,
seals and housing.
A.2 Poppet assembly
The functions of a poppet valve would indicate the primary failure mode to be incomplete closure of the valve
resulting in leakage around the poppet seat. This failure mode can be caused by contaminants being wedged
between the poppet and seat, wear of the poppet seat and corrosion of the poppet/seat combination. External
seal leakage, sticking valve stem and damaged poppet return spring are other failure modes which should be
considered in the design of the valve.
A new poppet assembly can be expected to have a sufficiently smooth surface for the valve to meet internal
leakage specifications. However, after a period of time, contaminants will cause wear of the poppet assembly
until the leakage rate is beyond tolerance. The leakage rate at which the valve is considered to have failed will
depend on the application and to what extent leakage can be tolerated.
The failure rate of a poppet assembly can be calculated using Equation (A.1).
−232 2
21xD0 f P −P
MS()1 2
λλ= K (A.1)
PP,B 1
1.5
QLν S
()
fa w s
where:
λ is the failure rate of the poppet assembly, expressed in the number of failures per million cycles;
P
λ is the base failure rate for poppet assembly, expressed in the number of failures per million cycles;
P,B
D is the mean seat diameter, expressed in inches;
MS
f is the mean surface finish of opposing surfaces, expressed in inches;
P is the upstream pressure, expressed in pounds per square inch;
1) As stated in Clause 4, units of measurement are in accordance with ISO 1000, except for Annex A and Clause 7,
[9]
which are based on The Handbook of Reliability Prediction Procedures for Mechanical Equipment and use imperial
units.
P is the downstream pressure, expressed in pounds per square inch;
Q is the leakage rate considered to be a valve failure expressed in cubic inches per minute;
f
ν is the absolute fluid viscosity expressed as pound minute per square inch;
a
L is the radial seat land width expressed in inches;
w
S is the apparent seat stress expressed in pounds per square inch;
s
K is a constant which considers the impact of contaminant size, hardness and quantity of particles.
Values used to determine the failure rates for the parts used in this example are listed in Table A.1.
Failure rate equations for each component and part are then translated into a base failure rate using a series
of multiplying factors to modify the base failure rate to match the operating environment being considered. For
example, Equation (A.1) can be rewritten as shown in Equation (A.2).
λ = λ × C × C × C × C × C × C × C × C × C (A.2)
PO PO,B P Q F ν N S DT SW W
where:
λ is the failure rate of the poppet assembly expressed in the number of failures per million
PO
operations;
λ is the base failure rate of the poppet assembly expressed in the number of failures per million
PO,B
operations;
C is the multiplying factor which takes into account the effect of fluid pressure on the base failure
P
rate;
C is the multiplying factor which takes into account the effect of allowable leakage on the base
Q
failure rate;
C is the multiplying factor which takes into account the effect of surface finish on the base failure
F
rate;
C is the multiplying factor which takes into account the effect of fluid viscosity on the base failure
ν
rate;
C is the multiplying factor which takes into account the effect of contaminants on the base failure
N
rate;
C is the multiplying factor which takes into account the effect of seat stress on the base failure rate;
S
C is the multiplying factor which takes into account the effect of seat diameter on the base failure
DT
rate;
C is the multiplying factor which takes into account the effect of seat land width on the base failure
SW
rate;
C is the multiplying factor which takes into account the effect of fluid flow rate on the base failure
W
rate.
The parameters in the failure rate equation can be located on an engineering drawing, through knowledge of
design standards or by actual measurement. Other design parameters which have a minor effect on reliability
are included in the base failure rate as determined from field performance data.
14 © ISO 2009 – All rights reserved

A.3 Spring assembly
Depending
...