NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Step-Stress Accelerated 

Degradation Testing for 

Solar Reflectors

Preprint

Wesley Jones, Ryan Elmore, Jinsuk Lee, 

and Cheryl Kennedy

Presented at SolarPACES 2011

Granada, Spain

September 20-23, 2011

Conference Paper

NREL/CP-2C00-52624

September 2011
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1

STEP-STRESS ACCELERATED DEGRADATION TESTING FOR 

SOLAR REFLECTORS

Wesley Jones1, Ryan Elmore2,

 

Jinsuk Lee3, and Cheryl Kennedy4 

1 Senior Scientist, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401 USA, wesley.jones@nrel.gov, 

1.303.275.4070

2 Senior Scientist, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401 USA

3 Post-Doctoral Researcher, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401 USA

4 Senior Scientist, National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, CO 80401 USA

Abstract

To meet the challenge of reducing the cost of electricity generated with concentrating solar power (CSP), new lowcost reflector materials are being developed, including metalized polymer reflectors, and must be tested and 

validated against appropriate failure mechanisms. We explore the application of testing methods and statistical 

inference techniques for quantifying estimates and improving service lifetimes of solar reflectors associated with 

failure mechanisms initiated by exposure to the ultraviolet (UV) part of the solar spectrum. In general, a suite of 

durability and reliability tests are available for testing a variety of failure mechanisms where the results of a set are 

required to understand the overall service lifetime of a CSP reflector. We will focus on the use of the Ultra

Accelerated Weathering System (UAWS) for assessing various degradation patterns attributable to accelerated UV 

exposure. Depending on number of samples, test conditions, degradation, and failure patterns, test results may be 

used to derive insight into failure mechanisms, associated physical parameters, service lifetimes, and uncertainties.

In the most complicated case warranting advanced planning and statistical inference, step-stress accelerated 

degradation testing (SSADT) methods are proposed.

Keywords: step-stress accelerated degradation testing, solar reflectors, ultra accelerated weathering system, service 

lifetime prediction

1. Introduction

1.1 Concentrating solar power

Commercialization of CSP technologies requires advanced optical materials that are low in cost and maintain high 

optical performance for lifetimes of 25 to 30 years under severe outdoor environments [1]. This includes 

maintaining greater than 95% specular reflectance into a small full-cone angle over the life of the reflector in trough, 

tower, dish, and linear Fresnel systems. The cone angle requirements are dependent on system technology.

1.2 Durability tests for CSP reflectors 

NREL uses several durability tests to aid the development and validation of advanced reflectors [2]. Outdoor testing 

of reflectors in a variety of settings provides the best long-term test; however, these tests are time-prohibitive due to 

the design goal of 25- to 30-year lifetimes for CSP reflectors. Accelerated testing of known and unknown failure 

mechanisms is required to decrease testing times such that advanced concepts can be developed and validated under 

a compressed schedule. Standard accelerated durability testing begins with exposing reflectors to light, heat, and 

humidity at stress levels that are greater than normally experienced in dry climates. The neutral salt spray (NSS) or 

copper accelerated acetic acid salt spray (CASS) tests introduce additional stresses [10]. Soiling and cleaning of 

advanced mirrors is a topic of increasing interest.
2

1.3 UV as a special case for polymeric reflectors

Polymer materials and silvered-polymer reflectors in particular are known to be especially susceptible to 

degradation and failure mechanisms associated with exposure to the UV part of the solar spectrum [3]. Specifically, 

Jorgensen et al. present experimental results of the effects of exposure to such UV light [7].

1.4 UAWS

To rapidly test and validate the performance and durability 

solar reflectors subject to this degradation path, a unique 

accelerated testing device, the Ultra Accelerated Weathering 

System (UAWS), is utilized. The UAWS is an outdoor 

weathering system that uses Fresnel mirrors to concentrate 

the UV portion of natural sunlight 50 to 100 times. The 

UAWS dramatically increases the UV radiant exposure per 

unit time over what is attainable with current accelerated 

exposure chambers. The system shows high fidelity to natural 

solar UV spectral power distributions while attenuating 

visible and IR wavelengths to maintain acceptable specimen 

exposure temperatures [3]. The temperature of the samples 

may be controlled so that two sets of samples are stressed at 

two different temperatures simultaneously while being 

exposed.

1.5 Accelerated degradation testing and lifetime testing

To validate the failure mechanisms of CSP reflectors, 

reflector samples are exposed in the UAWS at different temperatures and different intensities of light depending on 

initial tests. The specular and hemispherical reflectance of the samples is measured at regular intervals to track the 

degradation of the mirror. The expected outcomes range from no degradation to a complete failure of the mirror with 

respect to a given threshold of reflectance. Service lifetime prediction depends on the availability of data from the 

exposure to multiple stress levels. If sudden failure occurs, accelerated lifetime testing (ALT) techniques may be 

applied. If there is measurable degradation, accelerated degradation testing (ADT) techniques may be applied. ADT 

relies on degradation data instead of failure data. In general, a multiple constant-stress ADT (MCSADT) and ALT

(MCSALT) may be used for life prediction of products, while single constant-stress ADT (e.g., Damp-Heat Test) 

can be used for qualification testing with a specific durability criteria. When the samples are subject to a specific 

intensity of light, a constant stress, for the first part of a test, and it is warranted to measure the degradation rate at a 

second stress by subjecting the sample to a lower (or higher) intensity of light, step-stress accelerated degradation 

testing (SSADT) and inference may be applied.

1.6 Advanced physics-based statistical inference

Estimates of service lifetime focus on identifying physical mechanisms of degradation and defining a durability test 

that will have an associated acceleration factor for similar samples such that a product’s service lifetime may be 

estimated or ensured to last for some defined amount of time. For example, if a sample is exposed to twice as much 

light during a test as it would be exposed to in a natural use condition, its life is expected to be half as much. When 

degradation patterns are identified, they are fit by equations that are motivated by physical phenomena. 

Alternatively, the dependence of the rate at which degradation occurs on natural stressors may also be investigated. 

An example is the common assumption that Arrhenius’ equation applies for temperature dependence.

To build on the success of such techniques, advanced ALT and ADT methods explicitly include the patterns of 

degradation and the physically motivated dependence on natural stressors. In addition, they include a probability 

distribution on the lifetime data so that estimates of uncertainty may be included in the mathematical representation 

Fig. 1. UAWS at NREL.
3 

0 5 10 15 20 25 30

equivalent natural UV exposure (years)

% solar−weighted hemisperical specular reflectance

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80% 85% 90% 95% 100%

of a set of samples. In general, to make predictions about natural conditions that vary requires at least two 

experiments at two different stress levels so that predications can be interpolated or extrapolated to the natural use 

condition. Step-stress methods are special methods that include two or more stress levels in a single test. 

In this paper, we discuss the expected reflector failures associated with exposure in the UAWS. We define failure 

and then categorize several primary degradation patterns in Section 2. Test plans for physics-of-failure and failure 

distribution tests are described in Section 3. In Section 4, we describe potential test result outcomes in the context of 

the primary degradation patterns and tests in Section 4. Finally, we propose and describe the use of the step-stress 

statistical inference method in Section 5. 

2. Degradation/failure test components 

2.1 Reflector failure 

When the measured performance of a reflector passes a pre-defined threshold, typically 10% loss in reflectance from 

the initial value, the reflector under test has failed. The goal of the U.S. Department of Energy’s (DOE) CSP 

program associated with the DOE SunShot Initiative is for a reflector to maintain 95% specular reflectance over the 

30-year lifetime of the reflector. Thresholds associated with the hemispherical reflectance may also be used to define 

failure and will be used in our discussions below. 

2.2 Primary degradation/failure patterns 

For failure mechanisms associated with exposure to the UV part of the solar spectrum, four primary degradation 

patterns are expected: no failure, sudden failure, gradual degradation failure, and break-in patterns. These patterns 

are depicted in Figure 1 and explained in the subsequent paragraphs. 

No failure: A reflector may not experience “measurable” degradation during the accelerated test. This pattern is 

represented as the blue line in Figure 2. In particular, a mature or production-quality reflector is not likely to exhibit 

“measurable” degradation or failure during a test. If the accumulated solar radiation is greater than 30 years 

equivalent at elevated temperatures, this is an 

indication that the reflector has been designed 

to address failure mechanisms associated with 

exposure to UV solar radiation. 

Sudden failure: The reflector shows little to 

no degradation followed by rapid degradation 

in performance past the pre-determined 

threshold value (denoted by the green line in 

Figure 2). In this scenario, the materials that 

form the reflector’s structure may be slowly 

degrading over time without affecting 

hemispherical reflectance. At some point, the 

structural materials degrade beyond a critical 

point, and the degradation is manifest in the 

reflector’s hemispherical or specular 

reflectance. The period where the failure rate is 

increasing is known as the wearout failure 

period. In general, one of the main goals of 

reliability testing is to assure that the onset of 

the wearout period occurs far enough away in 

time as not to be a concern during the useful 

life of the product [5]. 

Fig. 2. The four primary degradation/failure patterns are shown: 

no failure (blue), sudden failure (green), gradual degradation 

(yellow), and break-in (red). 
4

Gradual Degradation: A reflector that degrades according to a pattern (possibly according to a physical model for 

extrapolation) until the performance falls below a threshold [6]. This pattern is shown as the yellow line in Figure 2.

Break-in patterns: Some reflectors may experience initial degradation, increase, or fluctuation, and then follow one 

of the three patterns discussed above; this is denoted by the red line in Figure 2. Early life behavior is not necessarily 

indicative of the long-term behavior of the reflector.

3. Physically based statistical models

In general, physics-based statistical models of each relevant failure mechanism may be formulated and integrated 

into a greater understanding of failure of a device. The UAWS is capable of running at multiple temperatures and 

intensities of light and thus may be used to understand the dependence of failure on those two stressors.

For metalized polymer reflector materials, the degradation is expected to be proportional to (IUV)

n where n has been 

found to be approximately one and proportional to exp(-Ea /kT), an Arrhenius physical relationship [7]. IUV is the 

intensity of the UV part of the solar spectrum, n is a material dependent constant, Ea is the material dependent 

activation energy, and k is the Boltzmann’s constant. There is evidence in glazed materials that n may be less than 1 

[2].

In the event that a degradation curve is measurable, insight into the fundamental mechanisms of degradation may be 

ascertained dependent on the shape of the observed curve [8]. Understanding of the physical mechanism or 

underlying physical processes may be used to justify greater extrapolation than can otherwise be achieved.

Reliability studies and cases [8] have discussed and various statistical models for the shape of the observed curve 

presented in Figure 2. For example, basic patterns such as linear, exponential, power, and logarithmic are commonly 

modified and applied to specific products that have these unique degradation patterns.

In the event that mirrors are susceptible to a failure mechanism initiated by a specific test, and the reliability of a 

product needs to be estimated, more than three samples should be subjected to the stress test such that the failure 

distribution may be ascertained. In this case, a likelihood function may be combined with a physical model of 

degradation. SSADT, MSCADT, or MCSALT may be used.

4. Approach

4.1 Test plans

Two primary types of tests can be run: a physics-of-failure test and a failure distribution test. The UAWS has space 

for a limited number of samples, so the test can depend to some extent on the question being investigated. The 

physics-of-failure test uses fewer samples per type of sample so that multiple types of samples can be tested 

simultaneously. The failure distribution test is run after a sample has been tested and characterized and is understood 

well enough to warrant the entire UAWS capacity for several months on a single sample type.

For the physics-of-failure test, two sets of three 2.25-cm square samples of each reflector sample type to be tested 

are prepared, including initial specular and hemispherical reflectance measurements. Samples are exposed to the UV 

portion of the solar spectrum at 100 times the normal solar intensity using natural sunlight. Specular and 

hemispherical reflectance of the reflectors is measured periodically, approximately equivalent to 1 to 2 years of solar 

light exposure. Thirty years of equivalent exposure requires approximately 4 months, depending on weather and 

time of year.

Many of the physical phenomena involved in the reliability of a device are highly dependent on temperature. Each 

of the UAWS’ two plates hosts a set of three samples for a given sample type and is cooled to a different 

temperature, usually 30°C and 60°C. This is an MCSADT and MCSALT testing plan.

If there is measurable degradation, the light concentration of the UAWS can be lowered during the test to 50 times, 

such that data can be collected concerning the dependence of degradation on the solar radiation intensity. This is an 
5 

0 5 10 15 20 25 30

equivalent natural UV exposure (years)

% solar−weighted hemisperical specular reflectance

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80% 85% 90% 95% 100%

100X; 30C

50X; 30C

100X; 60C

50X; 60C

SSADT testing plan, and testing time is still measured in months and equivalent exposure in years. For the failure 

distribution test, a single type of sample is run, occupying the entire capacity of the UAWS, and may be run with 

one or two different temperatures depending on the result of the physics-of-failure run.

4.2 Test analysis and statistical inference 

There are four distinct expected outcomes from the test that are related to the primary degradation/failure patterns. 

As the explanation of the failures associated with this exposure is integrated into a larger understanding of the 

failure of the reflector in general, a different set of methods is applied to the different outcomes. 

In the case of no failure, the failure mechanisms associated with exposure to UV light are likely to have been 

addressed in the reflector design, and the reflector is considered to have been tested and validated for this failure 

mechanism. The encompassing model of failure would take this into account. 

If the samples experience short-term performance variation at the beginning of the sample life (break-in behavior 

patterns), those patterns can be taken into consideration before classifying the failure according to the latter part of 

the degradation pattern. If those patterns are significant, they may be investigated in their own right. 

The test result associated with a sudden failure pattern may occur. In some cases, we will simply compare this test 

result with another test result to identify the reflector that should be further investigated. Inspection of the results of 

spectrum associated with the hemispherical reflectance may reveal specific parts of the spectrum that degrade. 

MCSALT methods may be applied because samples are tested at two different temperatures, including fitting a 

physical model, as described above, to estimate the activation energy. Consideration of optical measurement and 

activation energy estimates in conjunction with macro and microscopic inspection of the sample may be used to 

identify the root cause and possible mitigating processes. 

In the case where the reflector fails, but the failure time is long enough to be acceptable for production, MCSALTderived estimates of mean time to failure can be made. In this case, a failure distribution test on production samples 

would be recommended, so that the failure distribution of the production reflector can be estimated, in addition to 

the uncertainty and reliability of the mirror. 

The test result associated with a gradual degradation pattern may occur similarly to the simulated example given in 

Figure 3. Again, the spectrum may be inspected, MCSADT methods applied, and the activation energies 

determined. In addition, information associated 

with the degradation pattern may be utilized. 

The character of the degradation pattern may 

be used to derive hypotheses concerning 

physical mechanisms causing the degradation. 

The slope or parameter associated with how 

rapidly the degradation occurs is associated 

with activation energy. The service lifetime 

may be estimated by determining where the 

degradation crosses the threshold of failure via 

interpolation or extrapolation. 

If a step down to 50 times the normal intensity 

of light were warranted, SSADT methods may 

be applied, and a model that includes both 

activation energy and dependence on intensity 

of light can be fit. This is especially important 

if n, the exponent of the power law associated 

with the intensity of light in the physical 

model, is less than 1. A failure distribution test 

Fig. 3. Hypothetical degradation pattern of solar-weighted 

hemispherical reflectance for a two-temperature design and a 

step in UV intensity near 15 equivalent years. 
6 

and application of SSADT methods may also be useful in the case that the service lifetimes need to be quantified 

including uncertainty. 

5. Step-stress statistical inference 

In the most complicated—and possibly most important—scenario for production-quality manufactured products, a 

failure distribution test will be warranted, a degradation failure will have occurred in the previous test, and the 

resulting rate of degradation will have been affected by both temperature and intensity of light. The data might look 

something like the data in Figure 3, except that there might be 36 tracks instead of two. In this scenario, service 

lifetime is expected to be important, as is quantifying the response due to random non-normal variation in the 

samples of the same type. We will work within the context of assuming one primary failure mechanism. 

We propose two different models and discuss their characteristics. The first stage in constructing either model is to 

identify the physical relationship of stress for degradation rate. Because the experiment is only carried out at two 

different temperatures and at two different intensities of light, the physical relationship is assumed known from 

previous work and can only depend on temperature and intensity of light [9]. All other factors are assumed to be 

constant. Previous work on silvered polymer reflectors has found the following relationship: 

where other stressors like relative humidity are including in the constant, c. The exponent of the intensity of light 

may be close to 1, and the use of the step-stress method will either validate this or provide a better estimate. Since 

we are working at 50 to 100 times acceleration, it may be important to derive small variations from n = 1. 

The second stage is to identify the degradation pattern. As a comparison, corrosion processes might be exponential, 

and kinetic processes might follow a power law. Previous work for silvered polymer reflectors assumes a linear 

degradation pattern [8]. The data taken from the physics-of-failure and a failure distribution test will allow us to 

validate this assumption or identify a different functional form. The third stage is to combine the physical 

relationship for stress with the degradation pattern. We expect to assume the following degradation model: 

d(t) = A⋅IUV

n ⋅ exp − Ea

kT





 



⋅t

Least squares estimation: The most common approach to estimation of a product’s service lifetime, activation 

energy, Ea, the exponent of the intensity, n, and the other constants in the degradation model, is to use the method of 

least squares (LS) on appropriately transformed variables. Because we have two temperatures and a step down in 

intensity, the degradation path, d, is written as 

d(t) = d(t |s1) if 0 ≤ t < τ 1

d(t +w1 −τ 1 |s2 ) if τ 1 ≤ t < τ 2







where τ1 is the time when the stress is changed from 100 times to 50 times and τ2 is the end of the experiment. w is 

the time at which the observed degradation under the first stress level would have occurred for the second stress 

level, had the second stress level been applied from the beginning of the experiment. In the development of this 

approach, the cumulative damage is taken into account when stepping to the next intensity. Thus, the product’s 

entire exposure history is properly built in to the final degradation model. 

Maximum likelihood estimation: Alternatively, we use the method of maximum likelihood (ML) to estimate the 

parameters defined in the physical model (i.e., Ea, n, and c) and derive the associated quantities of interest, including 

the point estimate and confidence interval of service lifetime. The major advantage ML estimation exhibits over LS 

b = c ⋅IUV

n ⋅ exp − Ea

kT





 



 (1) 

(2) 

(3) 
7 

estimation is that you can quantify the uncertainty surrounding your point ML point estimates in the form of 

confidence intervals. See [11] for a theoretical overview of ML techniques.

In order to use maximum likelihood estimation (MLE) techniques, we need to assume a probability distribution on 

the lifetime of each sample. It is therefore necessary to transform the degradation data into failure data (e.g., via 

extrapolation) so that we can examine the failure-time distribution using standard goodness-of-fit statistics (e.g., chisquare test, Kolmogorov-Smirnov test, and Anderson-Darling test) [12]. For explanatory purposes, we assume that 

the sample lifetimes follow an exponential distribution; additional candidates include, but are not limited to, the 

Weibull and log-normal distributions. 

Coupling the failure distribution with the degradation model, we can construct a likelihood function as the basis for 

estimation/inference [13], e.g., 

where we have assumed an exponential model with failure rate, λ, defined by the log-linear life stress function [13], 

log(λi) = β0 + β1x1 + β2 x2

where βs are unknown parameters (to be estimated), x1 is a stress of temperature, and x2 is a stress of UV intensity. 

This likelihood includes both r failed and m-r survival samples at the end of testing (see [13-14] for a more detailed 

discussion). The likelihood function is built with two segments of UV intensity where the segments of each sample 

are based on the memoryless property of the exponential distribution. The method of maximum likelihood 

estimation is based on the optimization (maximization) of Equation (4) with respect to the defining parameters. The 

resulting estimates can be used to estimate the key quantities of interest: mean time to failure, warranty time, etc. 

Finally, we would like to stress that the failure distribution test and the inclusion of a non-normal failure distribution 

is not simply to try to minimize the error in the estimate by having a large number of samples. Indeed, the point is 

to capture the stochastic nature of the distribution of failure times and, hence, to estimate the uncertainty 

surrounding the estimates of the key parameters of interest. For example, we can estimate the mean time to failure of 

CSP reflectors in a low-humidity environment and provide a confidence interval for this quantity. Capturing the 

nature of the failure distribution is similar to capturing the nature of the dependence of the degradation rate on 

temperature, by discussing it in the context of the Arrhenius equation and activation energy. 

6. Summary 

Solar reflectors may be susceptible to a number of failure mechanisms. Metalized polymer reflectors are known to 

be particularly susceptible to failure mechanisms associated with exposure to the UV part of the solar spectrum. The 

UAWS is a system that enables the rapid application of this stress to samples in order to test and validate these 

samples. We have described expected failure signatures, test plans, and hypothetical results for physics-of-failure 

and failure distribution tests. Expected failures are primarily categorized as sudden failure or gradual degradation 

failures. When production samples are subject to these failure mechanisms and require better estimates of service 

lifetime, including warranty time and uncertainty, a failure distribution test will be required. In the most complicated 

case warranting advanced planning and statistical inference, step-stress accelerated degradation methods may be 

applied. We propose the use of maximum likelihood estimation methods with integrated physical models. UV solar 

radiation represents only one type of stress, so results and inferences from the tests will need to be integrated with 

results for other tests to obtain a greater understanding of service lifetime and potential failure mechanisms. Next 

steps include application of step-stress and multiple constant-stress accelerated testing statistical methods and 

models for newly developed and commercial silvered polymer reflectors, for which testing has begun. We also plan 

L(t | λ)∝ λi

C exp(−λiC

tjC )

jC= rp−1 p=1

i







 



+1

rp p=1

i

C



∏

















 i

C=100X&50X  ∏ exp(−λ50X,Ct50X.C ( ))

m−r

















 C=30C&60C  ∏ (4) 

(5) 
8

to expand the methods to other systems and other reflectors, including silvered glass, anodized aluminum, and front 

surface reflectors.

Acknowledgements

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308 with the 

National Renewable Energy Laboratory.

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NREl/CP-510-24058, 1999.

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[10] ISO 9227:2006 Corrosion tests in artificial atmospheres, Salt spray tests, 2006.

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