The r asons for this diff iculty can inclu e the ty ical y long lfe times of comp nent , the smal time pe iod betwe n design an prod ct r lease, and the ne es ity for t es ing comp nent
Normal use conditions
Normal use conditions for components can be determined by their characteristic ratings, such as pressure, temperature, voltage, duty cycle, and lubrication needs However, these ratings typically indicate maximum conditions that exceed standard usage Thus, it is essential to define normal use conditions based on these characteristics prior to conducting accelerated tests An example of this definition for a pneumatic valve is provided in Table 1.
Table 1 — Definition o f normal use conditions f or a pneumatic valve
Characteristic Typical rating value Common use applica- tion value Proposed normal use value f or testing Pressure 1 000 kPa (10 bar) 630 kPa (6,3 bar) 630 kPa (6,3 bar)
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.
Preliminary tests
To identify the maximum stress levels for testing without inducing failure modes different from normal usage, qualitative tests such as Highly Accelerated Life Testing (HALT) are often conducted with small sample sizes These tests help establish appropriate stress limits for accelerated life testing, and employing Design of Experiments (DOE) methodology can enhance the effectiveness of this process.
To determine three stress levels, follow these steps: First, propose the maximum stress that could lead to failure in under one day of testing Next, reduce this stress to 90% and test at least two units to failure, adhering to ISO 19973 procedures modified for the specific stress conditions Analyze the failure mode to ensure it aligns with typical use conditions; if not, lower the stress and repeat until the failures match normal use scenarios, designating this as stress level S1 Then, decrease the stress by an additional 10% to 20% and conduct further tests on at least two more units, again examining the failure mode for consistency with normal use If discrepancies arise, adjust the stress conditions and retest, labeling this as stress level S2 Finally, identify a third stress level, S3, that yields failures within project timelines, which can be determined by extrapolating from previous failure data or averaging S1 and S2.
To ensure reliability, conduct tests on at least two additional units at the third stress level, S 3, defined as \$S_3 = ẵ (S_2 - S_1)\$ Carefully analyze the failure modes to confirm they align with those expected under normal usage If discrepancies arise, adjust the stress conditions and repeat the testing Continuous monitoring of failure types is crucial to ensure they remain within the component's specifications; otherwise, the units may be classified as suspensions, necessitating a restart of the testing process.
Conduct tests at each chosen stress level, ensuring to include at least one test that closely simulates normal usage conditions.
In accelerated testing, higher stress levels lead to shorter required test durations, which in turn increases the uncertainty of extrapolation Confidence intervals serve as a valuable tool for quantifying this uncertainty in the extrapolation process.
The most common stresses for pneumatic fluid power components are pressure and temperature
Testing can be performed under a single set of stress conditions on a sample lot or under two different stress conditions on separate sample lots Additionally, factors such as cylinder speed and the cycle rate of valves and regulators can also be evaluated Typically, the temperature of the process air used for testing components is adjusted to closely match the environmental test temperature.
In an accelerated life test, it is essential to organize the testing conditions to guarantee that the failures of components remain independent This means that failures caused by temperature should not affect those caused by pressure.
For an effective accelerated life test, it is recommended to use at least seven test units per stress level, with the allocation of units inversely proportional to the applied stress This means that lower stress levels should have more test units due to the higher failure rates expected at elevated stress levels A suggested ratio for test units across stress levels is 1:2:4 In cases where test units are costly, testing four units at stress levels S1 and S2, and five or more at stress level S3 is advisable Alternatively, if time constraints exist, testing two units may be considered, although this will increase estimation uncertainty under normal use conditions.
No repairs are made to the test units during accelerated life testing.
The test operator establishes measurement intervals for accelerated life testing, where shorter intervals yield more accurate statistical results, particularly under high stress levels Conversely, at low stress levels, longer measurement intervals are sufficient.
There are two main types of stress loading schemes: time-independent stress, which remains constant over time, and time-dependent stress, which varies This document focuses on constant time-independent stress loading, the most common approach in accelerated life testing However, other non-constant stress loads, such as step stress, cycling stress, and random stress, can also be utilized These loads are categorized based on their time dependence and are detailed in Annex A, which outlines the method for time-dependent analysis.
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.
Confidence levels are generated when at least four test units have failed (which includes their reaching a threshold level) at each stress level.
When a test unit fails between observations, the collected data is classified as left-censored or interval data This involves recording both the last cycle count during proper operation and the cycle count at which the failure occurred Such data is typically processed following the guidelines of ISO 19973-1:2015, section 10.2.
9.3 Suspended or censored test units
Individual test units on which testing was stopped before failure occurred are known as suspensions
Data from suspended test units is treated equivalently to data from censored test units The procedure outlined in Annex D facilitates the calculation of statistical parameters for these data types.
The failure data from testing at all stress levels is analysed in accordance with 10.2 , 10.3 and 10.4
Select an initial life distribution, which can be adjusted later; the Weibull distribution is often used for pneumatic components, with the scale parameter, η, representing a stress-dependent life characteristic, while the slope, β, is assumed constant across stress levels Plot the raw data from all stress levels on a single graph and determine the best fit straight line for each stress level If the slopes, β, are not parallel, consider a compromise slope for the sets of stress levels, ensuring that this compromise slope is statistically acceptable If deemed unacceptable, restart the testing program with improved data collection methods, maintaining 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
Statistical analysis, as outlined in Annex C, confirms the resulting distribution If the fitted lines from the plotted data at each accelerating stress level are parallel, it indicates a consistent failure mechanism across these stress levels, validating the appropriateness of the selected stress levels for accelerated testing.
Choose or develop an accelerated life testing model that illustrates the life characteristics of a distribution across varying stress levels, known as a life-stress relationship model Notable examples of these models include the Arrhenius, Eyring, and Inverse Power Law, which are detailed in Annex B.
10.4 Data analysis and parameter estimation
Sample size
For an effective accelerated life test, it is recommended to use at least seven test units for each stress level The allocation of test units is typically inversely proportional to the applied stress level, meaning that more units are tested at lower stress levels due to the higher failure rates expected at higher stress levels A suggested ratio for test units across stress levels is 1:2:4 In cases where test units are costly, four units should be tested at stress levels S1 and S2, while five or more units are advisable for stress level S3 If time constraints exist, testing with two units may be considered, although this will increase estimation uncertainty under normal use conditions.
Data observation and measurement
No repairs are made to the test units during accelerated life testing.
The test operator establishes measurement intervals for accelerated life testing, where shorter intervals yield more accurate statistical results under high stress levels, while longer intervals are sufficient for low stress levels.
Types of stress loading
There are two main types of stress loading schemes: time-independent stress, which remains constant over time, and time-dependent stress, which varies This document focuses on constant time-independent stress loading, the most prevalent method in accelerated life testing However, other non-constant stress loads, including step stress, cycling stress, and random stress, can also be utilized These loads are categorized based on their time dependence, with further details provided in Annex A, which outlines the method for time-dependent analysis.
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.
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.
Termination cycle count
When a test unit fails between observations, the collected data is classified as left-censored or interval data This involves recording both the last successful cycle count and the cycle count at which the failure occurred Such data is typically processed following the guidelines of ISO 19973-1:2015, section 10.2.
Suspended or censored test units
Individual test units on which testing was stopped before failure occurred are known as suspensions
Data from suspended test units is treated equivalently to data from censored test units The procedure outlined in Annex D facilitates the calculation of statistical parameters for these data types.
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.
Life distribution
Begin by selecting an initial life distribution, which can be adjusted later if needed The Weibull distribution is often utilized for pneumatic components, with the scale parameter, \$\eta\$, representing the stress-dependent life characteristic, while the slope, \$\beta\$, is assumed to be constant across various stress levels Plot the raw data from all stress levels on a single graph and determine the best fit straight line for each stress level If the slopes, \$\beta\$, from different stress levels are not parallel, consider using a compromise slope for the sets of stress levels It is crucial to assess whether this compromise slope is statistically acceptable; if not, the testing program should be restarted with enhanced data collection methods Maintaining a constant value of the slope, \$\beta\$, for each stress level is essential.
Figure 4 — Best fit slope to raw data
Figure 5 — Compromised equal slope lines
Statistical analysis, detailed in Annex C, confirms the resulting distribution If the fitted lines from the plotted data at each accelerating stress level are parallel, it indicates a consistent failure mechanism across these stress levels, validating the appropriateness of the selected stress levels for accelerated testing.
Accelerated life testing model
To establish a life-stress relationship model for accelerated life testing, select or develop a model that effectively represents the life characteristics across varying stress levels Notable examples of such models include the Arrhenius, Eyring, and Inverse Power Law, which are detailed in Annex B.
Data analysis and parameter estimation
Utilizing the chosen life-stress relationship model, estimate the parameters of the life-stress distribution through graphical methods, least squares methods, or maximum likelihood estimation (MLE) An illustrative example employing the Arrhenius model with a graphical estimation technique is presented in Figure 6.
Figure 6 — Arrhenius plot o f data f rom Figure 5
Figure 6 illustrates the raw data points represented by individual dots, with a connecting line that links the characteristic life η at each stress level The curves depicted in Figures 4, 5, and 6 are based on a Weibull distribution Additionally, utilizing commercial software can facilitate the creation of these plots.
The acceleration factor (AF) can be calculated by comparing the number of lives at normal usage conditions to those under accelerated conditions Various methods for determining acceleration factors are available.
Annex B of this document and an example is shown in Annex C
11 Reliability characteristics f rom the test data
To enhance the understanding of calculation outcomes, the failure mode for each test unit is documented Calculations are performed on the test data at various stress levels to ascertain the results.
— 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 X life, which is the time by which X% of the components are estimated to fail; and
— the confidence intervals of the BX life at the 95% confidence level using Fisher information matrix, Calculations are made from the life-stress analysis to determine:
— model parameters and acceleration factor; and
— B X life and confidence intervals of Bx life at the normal use conditions.
The test report must include essential data such as the document number and component-specific part number, the date of the report, and a detailed component description including the manufacturer, type designation, series number, and date code It should also specify the sample size, test conditions (including types of stress, number of stress levels, and stress loading), and threshold levels Additionally, the report must present the shape parameter (β), types of failures for each test unit, B10 life with 95% confidence intervals under normal use conditions, and the characteristic life (η) under the same conditions Furthermore, it should indicate the number of failures considered, the method used to calculate the Weibull data (such as Maximum likelihood), and the model for accelerated life testing (including Arrhenius-Weibull, Eyring-Weibull, and Inverse power law).
Weibull, etc.); n) acceleration factor; o) parameters of the selected acceleration model; p) other remarks, as necessary.
Annex A (informative) Determining stress levels when stress is time-dependent
Time-dependent stress causes components to experience varying stress levels over time, leading to quicker failures Consequently, models that accurately represent these conditions are essential for effective accelerated life testing.
The step-stress and ramp-stress models are common examples of time-dependent stress tests, where the stress load is held constant for a specific duration before being increased to a new level, which is then maintained for another period Various adaptations of this concept are illustrated 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
In variable stress conditions during field operations, it is essential to follow specific steps for conducting accelerated life tests First, identify the relevant field operating conditions for the component, as illustrated in Figure A.5 Next, calculate the equivalent load required for accelerated life testing using Palmgren-Miner’s rule, with the results depicted in Figure A.6.
To determine the destruct limit and yield point for accelerated life testing, a step-stress loading method should be employed, as illustrated in Figure A.7 The appropriate stress range must be established by considering the destruct limit, operating limit (or elastic limit), and specification limit (proportional limit) from the strain-stress curve shown in Figure A.8 The accelerated stress level can then be identified using the accelerated life test curve depicted in Figure A.9, with common overstress levels in mechanical engineering being 120%, 133%, and 150% Finally, a systematic approach to determine the stress levels is outlined in Figure A.10 and the procedure in section 8.2, allowing for accelerated life testing at the three specified stress levels.
Figure A.7 — Step-stress loading method Figure A.8 —Strain-stress curve
Before estimating reliability characteristics, validate the accelerated test using the probability plot in Figure A.11 If the fitted lines for each accelerating stress level are parallel, the assumed lifetime distribution is appropriate, indicating effective accelerating stress Next, assess the error between the model estimates and actual test results First, ensure that the shape parameters from the model align with those from normal use conditions Second, verify that the scale parameter of the model falls within the confidence intervals of the test results If the scale parameter is within these intervals, it can be concluded that the characteristic life of the model and the test results are statistically similar, as illustrated in Figure A.12.
Figure A.11 — Validation and verification o f accelerated test Figure A.12 — Graphical explanation o f the error between test estimate o f the considered model and test result
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 is the life at the normal use stress level
L A is the life at the accelerated stress level
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.
The Arrhenius life-stress model is the most widely used framework in accelerated life testing, particularly for scenarios involving thermal stress as the primary stimulus.
The Arrhenius life-stress model posits that the lifespan of a system is inversely related to the reaction rate of the underlying process This relationship is mathematically represented by the Arrhenius life-stress equation.
L is the quantifiable life measure (mean life, characteristic life, median life, BX life, etc.)
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) ln ( ) = ln( ) + L V C B
Depending on the application (and where the stress is exclusively thermal), the parameter B can be replaced by;
= A = activation energy Boltzman's constant activation ennergy
Activation energy is typically required to be known in advance; however, in most real-life scenarios, it is often unknown When the activation energy is not available, model parameter B can be treated as a variable Parameter B quantifies the influence of stress, such as temperature, on the lifespan of a system A higher value of B indicates a greater sensitivity of lifespan to specific stress conditions.
The acceleration factor is commonly defined by practitioners as the ratio of the lifespan or acceleration characteristic between normal usage conditions and elevated test stress levels In the context of the Arrhenius model, the acceleration factor is a key concept.
The probability density function for 2-parameter Weibull distribution is given by; f t t e t
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
( ) V (B.7) and substituting for η in Formula (B.6) ; f t V t
The Arrhenius-Weibull reliability function at stress level V is given by;
B.3 Inverse power law li f e-stress model
The inverse power law (IPL) model is commonly used for non-thermal accelerated stresses and is given by;
L is the quantifiable life measure (mean life, characteristic life, median life, BX life, etc.)
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( ) = -ln( ) - ln( ) L K n V (B.12)
In the inverse power model, the parameter η quantifies the impact of stress on lifespan; a higher value of n signifies a more significant effect of stress Conversely, an n value nearing 0 suggests a minimal influence of stress on lifespan, with no effect observed when n equals 0, indicating a constant lifespan regardless of stress.
For the inverse power law model, the acceleration factor is given by;
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 ; f t V K V K V t n n e K V t n
The mean time to failure (MTTF) of the IPL-Weibull model is given by;
The IPL-Weibull reliability function at stress level V is given by;