Service life prediction for aircraft coatings

Service life prediction for aircraft coatings

Olga Guseva*, Samuel Brunner, Peter Richner

Swiss Federal Laboratory for Materials Testing and Research, Uberlandstrasse 129, CH-8600 Dubendorf, Switzerland

Received 3 February 2003; received in revised form 14 March 2003; accepted 16 March 2003

Abstract

A model with three stress types, the temperature, UV and aerosol, for estimating the service life of organic coatings under serviceconditions has been proposed. The model has been applied to the estimation of the service life for aircraft coatings concerning lossof gloss. The results obtained from a unique natural exposure programme for a reference polyurethane coating have been compared

with the results from the specially designed accelerated ageing tests, which were performed with a new designed and constructedweathering device. As a special point of interest, the influence of sulphuric aerosol, which has simulated the stratosphere conditionsafter a big volcano eruption, on the service life of the reference coating has been investigated.

# 2003 Elsevier Ltd. All rights reserved.

Keywords: Coatings; Weathering; Accelerated tests; Service life prediction

1. Introduction

The organic coating industry has been performingresearch in order to find new chemistry formulationswith enhanced stability against environmental influ-ences, and at the same time with possibly smaller con-tents of hazardous substances. The service life of thesenew chemistry formulations is often unknown. Usually,the field experiments (natural exposure) for moderncoatings take prolonged time of several years, which isnot acceptable for manufactures. Therefore a needexists for a methodology which is capable of makingreliable service life predictions from accelerated experi-ments. Such Service Life Prediction (SLP) methodologywas proposed by Martin et al. [1]. In this paper weapplied this approach to the ageing of aircraft coatings.The degradation of aircraft coatings was considered as aloss of gloss provided that other requirements, such asthe absence of cracking and delamination, were fulfilled.The work was supported by a special research pro-

gramme, whereby in-service data from the exposure ofproducts on B-747 escape hatches were compared to thedata obtained using special designed accelerated tests,

focusing on the development of a service life predictionmodel.As the initial step, the environmental factors that are

relevant for the ageing of aircraft coatings had beenanalysed [2]. It is known that the weathering of thosecoatings is not only determined by UV radiation, tem-perature and humidity but also by pollutants. This wasclearly demonstrated during the eruption of volcanoPinatubo: in June 1991 the volcanic eruption broughtmore than 20 million tons of sulphur dioxide into thestratosphere raising the SO2-level from normal range of0.01–0.05 ppbv to more than 10 ppbv in September1991. Within the next four months the concentration ofgaseous SO2 in the stratosphere had gradually decreasedtoward its usual value [3]. The aircrafts, however,showed a fast decrease of gloss in their coating during thefollowing 4 years. It was found that SO2 actually formeda sulphuric acid aerosol, which remained dispersed in thestratosphere for a period of several years after eruptionthat acted destructively on aircraft coatings [2,3].

2. Natural exposure: Escape Hatch Programme

In order to investigate the degradation of the aircraftcoatings under service conditions, the so-called use levelconditions, a research programme (Escape Hatch Pro-gramme) was carried out by AKZO Nobel together with

0141-3910/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0141-3910(03)00124-1

Polymer Degradation and Stability 82 (2003) 1–13

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* Corresponding author Tel.: +41-1-823-4361; fax: +41-1-823-

4015.

E-mail address: [email protected] (O. Guseva).

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KLM starting September 1994. According to this Pro-gramme, four different coatings were applied to eachescape hatch of a B-747 aircraft for natural exposure(Fig. 1).Every 3 months gloss and colour of the hatches were

measured. Altogether, 15 aircrafts were involved in theProgramme. One of the pigmented polyurethane coat-ings with a light blue colour was applied to differentescape hatches providing the possibility for statisticalanalysis. This coating is being referred to as a ‘‘referencecoating’’ throughout the paper. The colour values forthe unexposed panels in the CIE 1976 L*a*b* coloursystem were L*=55, a*=�26, b*=�41. Definitionsand details of the measure procedure of colour can befound in Ref. [4]. The gloss degradation curves for gloss60� for the reference coating are shown in Fig. 2. One ofthe curves in Fig. 2 (with black filled squares) shows thefaster degradation than others. The reason for this fastdegradation is that the aircraft with this coating at the

escape hatch was in operation during the years 1994–1996, when the sulphuric aerosol content in the strato-sphere after the Pinatubo eruption was still noticeable(for details see Ref. [2]). This curve was omitted fromthe statistical analysis as an outlier. All other degrada-tion curves in Fig. 2 were measured when the aerosolconcentration at a flight height of about 10 km wasnormal. Definitions and details of the measure proce-dure of gloss can be found in Ref. [4].The failure criterion for the gloss loss, which was

defined by airline representatives, was 60 GU measuredfor gloss 60�. The interceptions of degradation curvesand the failure-criterion-line (see Fig. 2) gave times-to-failure. It should be noted that the experimental pointswere measured every 3 months. Therefore, in order toobtain the exact times-to failure, the degradation curveswere interpolated with polynomials. As shown in Fig. 2there were 11 degradation curves altogether, wherebytwo of them (dashed curves) did not reach the failurecriterion at the time of paper writing. These curves wereconsidered as censored data in the further calculations.From this data it was possible to form the sample

cumulative distribution function (cdf) and fit it to aparticular theoretical cdf (for basic definitions of thereliability theory see Appendix A). There are many dif-ferent lifetime distributions that can be used for the dataanalysis. The most commonly used are exponential,Weibull, normal and lognormal distributions. The cur-rently available sample size of 10 times-to-failure, how-ever, was too small for a reliable determination of theunderlying distribution. The simplest suitable para-metric distributions, which include the degradationmechanism (their hazard function can be increasing),are the Weibull, normal and lognormal. The compar-ison of the Likelihood Function values for the earlier-mentioned distributions showed that the Weibull dis-
Fig. 1. Escape hatch of the B-747 (shown with the arrow).
Fig. 2. Gloss 60�-curves for the reference coating applied on escape hatches. The bold horizontal line represents a failure criterion of 60 GU.

2 O. Guseva et al. / Polymer Degradation and Stability 82 (2003) 1–13

tribution suited slightly better to the experimental data.Therefore, the Weibull distribution was chosen as anunderlying distribution throughout the work. Theapplication of the basic definitions of the reliabilitytheory to the Weibull distribution are presented inAppendix A.Linearized Weibull cdf for the Escape Hatch data is

shown in Fig. 3, the reliability function and probabilitydensity function (pdf) in Fig. 4. The calculations weremade with Weibull++ program [5]. With the Weibulldistribution parameters, the shape parameter �=9.4and the scale parameter �=52.0 months, available, onecan calculate various reliability parameters—some of

them are presented in Table 1. From the Table 1 fol-lows, that the expected life (mean life) for the referencecoating was about 49 months, whereas the warrantytime 90%, which means that only 10% of the coatingsreached the failure criterion, was about 41 months.

3. SLP model for organic coatings with three stresses:

temperature, UV and aerosol

3.1. Accelerated testing

In typical life data analysis one determines a life dis-tribution that describes the times-to-failure of a productat the usual operating conditions. Statistically speaking,one wishes to obtain ‘‘the use level probability densityfunction’’ of the times-to-failure. Once this pdf isobtained, all other desired reliability parameters, suchas for example, percentage failing under warranty (per-centile), mean time to failure, mode life can be easilydetermined. However, coatings are supposed to have arather prolonged life of several years. At the stage ofdevelopment of a new formulation, researchers usuallydo not have enough time to carry out the natural ageingat the so-called use level conditions. To reduce the timeof experiment one performs experiments at theenhanced stress levels to obtain pdfs at these high stresslevels. The goal is to determine the use level pdf fromthese accelerated life test data rather than from dataobtained under use conditions. To accomplish this, arelationship should be found that allows extrapolatingfrom data collected at accelerated conditions to use levelconditions, the so-called life-stress relationship. Some ofthe most commonly used life-stress relationships inaccelerated life testing are Arrhenius (when the tem-perature is an accelerating factor), inverse power law(usually used for non-thermal accelerated stresses) andEyring (for thermal or humidity stresses) (see AppendixB). Schematically the procedure of service life predictiondescribed above is presented in Fig. 5. Here it is worth

Fig. 3. Linearized cdf (solid line) with 90% two-sided confidence

bounds (dashed lines) of Escape Hatch Data for the reference coating

for gloss 60� with a failure criterion of 60 GU.

Fig. 4. Reliability function (solid line) with 90% two-sided confidence

bounds (dashed lines) (left) and pdf (dotted line) (right) of Escape

Hatch Data for gloss 60� with a failure criterion of 60 GU.

Table 1

Reliability parameters together with 90% two-sided confidence

bounds for gloss loss of reference coating obtained in the Escape

Hatch Programme for gloss 60� with a failure criterion of 60 GU

90%Two-sided confidence bounds

Lower limit
Upper limit
b
9.4 6.5 13.7
Characteristic life (Z)[month]

52.0
49.5 54.5
Mean life [month]
49.3 46.7 52.0
Median life [month]
50.0 47.4 52.6
Mode life [month]
51.3 48.7 54.1
Warranty time 90%

[month]

40.9
36.8 45.5
O. Guseva et al. / Polymer Degradation and Stability 82 (2003) 1–13 3

to note that the accelerated test should be designed insuch a way that it does not change the failure modesthat would be encountered at use conditions. Forexample, a high temperature stress level for a coatingshould not exceed the glass transition temperature.Analysis of accelerated life test data, then, consists of

an underlying life distribution that describes the productat different stress levels and a life–stress relationshipthat quantifies the manner in which the life distributionchanges across different stress levels.

3.2. SLP model with three stresses

As discussed earlier, aircraft coatings are sensitive tothe following stress parameters: temperature, UVradiation, humidity and sulphuric aerosol [2]. Althoughthe actual stresses vary with time both in the naturalweathering and in the artificial ageing employed, in thispaper we made the assumption of constant stress levels,that the stress loads applied to panels were constantwith respect to time. The averaging procedures aredescribed later.Humidity as a stress parameter was excluded from

further considerations because the variation of thisparameter across different aircrafts is not so distin-guishable. Therefore the influence of this parameter wasnot investigated directly in this work. However, in theartificial weathering procedure employed the effect ofhumidity was not ignored: relative humidity changesfrom 10% to 100% during the weathering cycle wereapplied.The data obtained from the accelerated weathering

were analysed assuming an Arrhenius life–stress rela-tionship for temperature and the inverse power life–stress relationship for UV irradiance (Appendix B). TheArrhenius term is widely used for the dependence ofcoating photooxidation on temperature [6,7] and apower law expression for the influence of ultravioletirradiance [6,7]. The third stress factor, the aerosol

effect, was treated as an indicator variable, taking thediscrete values of zero (0), when no aerosol was applied,and one (1), when aerosol was put into a chamber. Tocombine all these stress types together, we used theGeneral Log–Linear relationship (see Appendix B). TheGeneral Log–Linear–Weibull model was derived bysetting the scale parameter � to the life–stress relation-ship for a model with three stress types; the shapeparameter � was assumed to remain constant acrossdifferent stress levels (Appendix C). The general modelfor three stress factors is, therefore,

� ¼ e�0þ�1

1V1

þ�2ln V2ð Þþ�3V3¼ e�0e

�11V1V�2

2 e�3V3 ; ð1Þ

where � is the scale parameter of Weibull distribution(characteristic life), �0, �1, �2, �3 are the model para-meters, V1 is the thermal stress, with the temperatureexpressed in absolute units (K), V2 is the UV irradianceat 340 nm in [W/(m2 nm)], V3 is the aerosol stress,assuming values of 0 and 1. Note, that the parameter Bof the Arrhenius relationship from Table 6 is equal tothe log-linear coefficient �1, and the parameter n of theinverse power relationship from Table 6 is equal to(��2).The General Log–Linear–Weibull pdf for these three

stresses is given by:

f t;V1;V2;V3ð Þ ¼ �t��1e��0þ�1

1V1

þ�2ln V2ð Þþ�3V3

�

e�t�e��

��0þ�1

1V1

þ�2ln V2ð Þþ�3V3

�:

ð2Þ

Parameters �, �0, �1, �2, �3 can be obtained by max-imising the log-likelihood function, � (see Appendix C),using ALTA PRO program [8].

4. Experimental apparatus

In order to test coatings for aircraft applications, adevice based on a modified commercial AcceleratedWeathering Tester QUV was designed and constructedat EMPA [9]. The commercial device was equippedwith eight separate thermally insulated chambers whereeight weathering experiments can be run simulta-neously. The damaging effects of sunlight were simu-lated by fluorescent UVA-340 lamps. The selection ofthe lamp type suitable for the weathering of aircraftcoatings was discussed in details in Ref. [2]. The fol-lowing weathering cycle was used: 8 h of UV withapproximately 15% humidity followed by 4 h of con-densation without irradiation with approximately 100%humidity. An additional water cooling system wasinstalled in the chambers 1 and 2 that allowed us toachieve a maximal temperature difference of 20 Kbetween the different chambers. For more details seeRef. [9].

Fig. 5. General scheme of SLP model for organic coatings.


In the following calculations we considered the tem-perature and UV stresses as constant stresses with thevalues obtained by averaging over the cycle. For thetemperature and UV the weighted averages over thecycle for each chamber were calculated using proceduredescribed later [see Eq. (4)] which are presented inTable 2.In order to investigate the influence of the sulphuric

aerosol on coatings, sulphuric acid with a concen-tration of 0.5 mol/l was injected using a nebulizerinto five chambers. The duration of aerosol applica-tion was 40 min once a week per chamber. For thefurther calculations, this third stress, aerosol, wastreated as an indicator variable, assuming discretevalues of zero (no aerosol application) and one(aerosol application).Two test panels with the reference coating were

placed in each chamber for exposure. It should benoted that those panels had been purposely manu-factured using different batches and by different per-sons. In order to obtain the uniform exposition of allpanels, a rotational procedure was employed: once aweek the position of all panels was changed accordingto the schema described in Ref. [9]. Measurements ofgloss were performed every 3 weeks. Five points fromthe top to the middle of the panel were measured.These points were treated independently in the follow-ing calculations, so that for each combination of stresseswe dealt with a collection of 10 points. The averagedexperimental curves for all chambers for gloss measuredat 60� are shown in Fig. 6, where the filled black sym-bols were used for the chambers with aerosol applica-tion. From Fig. 6 follows that the sulphuric aerosolapplication considerably accelerated the degradation ofthe reference coating. The panels in the chamber 2 hadnot reached the failure criterion at the time of paperwriting. In order to obtain times-to-failure the graphicalextrapolation was used.

5. Results and discussion

5.1. Shape parameter

First, separate calculations for each chamber assum-ing the Weibull distribution were performed by meansof the program Weibull++ [5]. For parameter estima-tion, the Least Squares method, or more precisely, theRank Regression on X (RRX), was used. This methodrequires that a straight line be fitted to a set of datapoints such that the sum of the squares of horizontaldeviations from the points to the line is minimised. Themeasure of how well the linear model fits the data is thecorrelation coefficient, denoted here by �. The summaryis presented in Fig. 7 and Table 3. Although the valuesof � seem to be different (see Table 3), they do not muchinfluence the shape of the Weibull distribution: in Fig. 7all lines are almost parallel. The coefficient of skewness(for definition see Appendix A), which is a measure forthe distribution asymmetry, ranges between �0.75 (for�=13) and �1.1 (for �=121).For the analysis of accelerated test data the assump-

tion of the common shape parameter � across thechambers (which supposes the parallelism of the lines inFig. 7) should be made. Assuming the underlying Wei-bull distribution with the common shape parameter �and the general log–linear life–stress relationship, thecalculation of the service life for reference coating at aparticular use level was performed using the programALTA PRO 6 [8]. For the parameter estimation, theMaximum Likelihood Parameter estimation (MLE)method was used. The calculated value for the commonshape parameter � was 18.9. The use level was assumedto be 32 �C (305 K) for the temperature parameter and0.24 W/(m2 nm) for the UV parameter; the aerosol para-meter was set to zero (see the later definition of the uselevel conditions). The results are shown in Fig. 8. In orderto justify the assumption of the common � for our data

Table 2

Averaged stress levels used in each chamber for the accelerated ageing

of reference coating

Chamber
Stress 1 Stress 2 Stress 3
Temperature

T [�C]

Temperature

T [K]

UV radiation

UV [W/m2 nm]

Aerosol

1
37.5 310.7 0.58 1a
2
38.1 311.2 0.41 0
3
57.5 330.7 0.42 1
4
58.2 331.4 0.57 0
5
53.8 326.9 0.60 1
6
54.3 327.4 0.43 1
7
56.2 329.4 0.63 0
8
56.5 329.6 0.62 1
a 1 Means sulphuric aerosol application 40 min once a week; 0—no

aerosol application.

Fig. 6. Experimental gloss-60� curves for the reference coating for

chambers 1–8. Filled black symbols denote the chambers with aerosol

application.


set, the likelihood ratio (LR) test was applied (AppendixD) using ALTA PRO 6 software [8], which gave the resultthat the shape parameter estimates of 18.9 did not differstatistically significantly at the 90% level.

5.2. Life–stress relationship

Using the procedure described in the section ‘‘SLPmodel with three stresses’’ the following parameterswere obtained for the life–stress relationship usingnotations of the Eq. (1): �0=�10.7114, �1=4215 K,�2=�0.4608, �3=-0.5249. While the parameter �0 is a

constant, the parameters �1, �2 and �3 correspond to theinfluence of the temperature, UV irradiance, and aero-sol, respectively, on the service life.The calculation of the apparent activation energy

(Ea=�1.R, where the gas constant R=8.314 JK�1

mol�1) gave a value of 8.4 kcal/mol, which was withinthe interval 7.4–10.3 kcal/mol (30.8–43.1 kJ/mol)obtained by Allen et al. for photooxidative degradationof low-density polyethylene film materials containingnine types of titanium dioxide pigments [10]. A value forthe apparent activation energy of approximately 7.2kcal/mol (30 kJ/mol) was also utilised in the work ofSampers [11] for the estimation of the lifetime for LDPEfilms with and without stabilisers. These values for theapparent activation energy are close to the values of 5–8kcal/mol used by Bauer [6] for photooxidation in auto-motive coatings. A similar approach to Bauer’s wasemployed by Jorgensen et al. [7] for the service life pre-diction for clear coat/coloured basecoat paint systems.The following generalised cumulative dosage model forthe loss in performance, �P, was used in Ref. [7]:

DP tð Þ ¼ A

ðt

0

IUV �ð Þ½ �ne�E=kT �ð Þd�; ð3Þ

Fig. 7. Cumulative distribution functions for gloss loss for the refer-

ence coating with a failure criterion of 60 GU for gloss 60�, shown on

Weibull paper for all chambers together. Filled black symbols denote

the chambers with aerosol application.

Table 3

Shape parameter (�) and scale parameter (characteristic life �) for the

gloss loss with a failure criterion of 60 GU measured at gloss 60� for

the reference coating calculated for each chamber separately

Chamber
� � �
1
29.9 11.4 0.96
2
13.3 20.7 0.96
3
55.7 5.9 0.97
4
19.4 8.2 0.90
5
121.2 5.3 0.95
6
64.8 5.7 0.91
7
27.2 8.2 0.95
8
39.8 4.9 0.98
Fig. 8. Cumulative distribution functions for gloss loss for the refer-

ence coating with a failure criterion of 60 GU for gloss 60�, shown on

Weibull paper assuming the common shape parameter across all

chambers. The dashed line represents the extrapolation to the use

level. Filled black symbols denote the chambers with aerosol applica-

tion.


where IUV is the cumulative UV light dosage integratedover a bandwidth of 290–385 nm; A, n, E are fittingparameters, where E denotes the activation energy; k isthe Boltzmann constant. Depending on the system, thevalues 3.8–8.4 kcal/mol for the apparent activationenergy and 0.64–0.71 for the power parameter n wereobtained.The parameter �2=�0.46, gained in our calculations,

which characterises the influence of the UV-A irra-diance at 340 nm on the reference coating, is close to themodel parameter n of Jorgensen et al. [7]. In othermodels this parameter was usually assumed to be 1[11,12].For the first time the influence of the aerosols on

the service life of coatings was considered quantita-tively. It is known that the service life of aircraftcoatings was reduced by approximately 50% in theyears from 1992 to 1995 following the eruption of thevolcano Pinatubo in Philippines in June 1991 [2]. Ourfirst simplified approximation using indicator variableshowed that the presence of the sulphuric aerosolshortened the service life of the reference coating by atleast of 40%: keeping other parameters V1 (tempera-ture) and V2 (UV) fixed at the use level, the ratio ofthe characteristic lives (�) with and without aerosol

application is� V3¼1

�� V3¼0

�� ¼ 0:59. More precise conclusions

can be made using the quantitative value for the con-centration of the sulphuric atoms absorbed by thecoating during the ageing process. A suitable methodfor obtaining such values is X-ray photoelectron spec-troscopy (XPS). Our first preliminary XPS measure-ments showed that the chosen concentration of thesulphuric aerosol combined with the application dura-tion in our weathering experiments roughly corres-ponded to the Pinatubo influence on the referencecoating. It follows, therefore, that our experimentalconditions simulated well the influence of the big vol-cano eruption on the aircraft coatings.

5.3. Determination of the use level conditions

Definition of the use level conditions for aircrafts isquite a complicated problem. Our goal here was to obtaintwo numbers for the temperature and the UV-irradianceat 340 nm averaged over time (including different seasons)and space (across different destinations throughout theworld). The averaging proposed later was not perfectbecause too many factors had to be taken into account.Nevertheless, for the first estimation of the use level con-ditions we used the following procedure, where theArrhenius term was used for the averaging of tempera-ture and a power law for the averaging of UV radiation.For the first simplified estimation, the whole time inter-val was represented by a sum of subintervals �ti for thetemperature and the UV intensity, respectively,

T� ¼X

i

Ti pið Þ=X

i

pi I� ¼X

i

Ii pið Þ=X

i

pi ; ð4Þ

where the weighting function has the form

pi ¼ I nUVðat340nmÞi e

� Ea=RTiÞ½ � Dti ð5Þ

with Ea=8.4 kcal/mol and n=0.46 as it was obtained inthe previous section as fitting coefficients for the life–stressrelationship in the accelerated weathering test for thereference coating. Calculations were made using the aboveapproach with the averaging over one year. We assumedthat the temperature ageing of aircraft coatings occursmainly on ground and during take-offs and landings.Mathematically, for the calculations of use level condi-tions, the Arrhenius term in the Eq. (5) is very small forthe temperature of approximately �50 �C at the flightheight. In order to determine how much time an aircraftspend on the ground, the flying time data available fromthe Escape Hatch Programme were analysed, fromwhich an assumption of flying time of approximately62% was made. From the climatic databases [13,14], airtemperatures and UV data for some destination sites inthe USA, Europe, Far East and Africa were taken. Inour weathering experiments, however, we were dealingwith the panel temperatures, measured at the backside ofpanels. It is known, that the panel temperature is con-siderably higher than the air temperature: 5–7 �C forlight and 15–30 �C for dark colours [6]. To find out theactual temperature difference between the panel and airtemperatures for our particular reference coating with alight blue colour (L*=55, a*=�26, b*=�41) an addi-tional natural exposure experiment was carried out. Thepanels were exposed during one summer month in thesuburban National Air Pollution Monitoring Network(NABEL) site in Dubendorf, Switzerland [15]. In orderto model the airport conditions, the panels were placedabove the asphalt ground. The sensors were mounted tothe backside of the panels. The experiment was con-ducted for the panels with isolated and non-isolatedback sides. All measured temperatures were comparedwith the air temperature measured at the test site. Thefollowing results were obtained for the noon time: thepanel temperature was about 3 K higher than themeteorologically measured air temperature for the non-isolated panel and about 16 K higher for the isolatedone. As in the case of aircraft coatings we are dealingwith the thermally isolated aircraft body, the differenceof 16 K for panel temperature was added to the airtemperatures for all destination sites as the input tem-perature in Eq. (4) before the averaging. The calculateduse level conditions obtained with this procedure were32 �C (305 K) for the temperature and 0.24 W/(m2 nm)for the UV-parameter.The aerosol parameter for the use level for the current

conditions (after 1996) was assumed to be zero: there


were no big volcano eruptions in the past since thePinatubo eruption in 1991, which could have a sig-nificant influence on aircraft coatings.

5.4. Reliability parameters at the use level

The inclined dashed line on the right in Fig. 8 showsthe extrapolation to the use level. It should be notedthat the calculated reliability parameters at the use levelwere dependent much on the choice of the use levelconditions, especially temperature. Calculations showedthat a difference of two degrees led to a difference ofabout 3 months in the prediction times.

The calculated cdf and pdf at the use level are shownin Fig. 9.The calculated reliability parameters at a use level of

temperature of 32 �C, UV of 0.24 W/(m2 nm) andaerosol parameter of zero are presented in Table 4.The linearised life–stress relationships and the accel-

eration factors were obtained by keeping two of thethree stresses at the use level and varying the other one.The plots are presented in Fig. 10, for temperature asthe acceleration factor, and in Fig. 11 for UV as theacceleration factor. The aerosol parameter was set tozero in these calculations. For example, at 60 �C (333K), UV=0.24 W/(m2 nm) and aerosol parameter=0,the acceleration factor is 3.2; and at UV=0.8 W/(m2

nm), if the temperature and aerosol parameter are keptat a use level of 32 �C and 0, respectively, the accelera-tion factor is 1.7. The influence of the aerosol applica-tion on the service life is presented in Fig. 12. As

Fig. 9. Reliability function with 90% two-sided confidence bounds

(left) and pdf (right) at the use level for the reference coating for gloss

60� with a failure criterion of 60 GU.

Table 4

Reliability parameters together with 90% two-sided confidence

bounds for gloss loss of reference coating at the use level for gloss 60�

with a failure criterion of 60 GU

90% Two-sided confidence bounds

Lower limit
Upper limit
�
18.9 16.4 21.8
Characteristic life �

[month]

43.2
40.1 46.6
Mean life [month]
42.0 39.0 45.3
Median life [month]
42.4 39.3 45.7
Mode life [month]
43.1 40.0 46.4
Warranty time 90%

[month]

38.4
35.5 41.5
Fig. 10. Linearized life–stress plot (left) and the acceleration factor (right) for the temperature when UV and aerosol parameter are kept at a use

level of 0.24 W/(m2 nm) and zero, respectively. The dashed lines denote the 90% two-sided confidence bounds.


discussed earlier, the aerosol application procedureemployed led to the reduction in the service life of thereference coating by approximately 40%.

5.5. Comparison of service lives obtained from artificialageing and natural exposure (Escape Hatch Pro-gramme) for reference coating

For comparison of the service lives for the referencecoating obtained from the natural exposure and the

predicted service life from the artificial ageing using theEMPA weathering device the two pdfs are shown toge-ther in Fig. 13. One pdf (Fig. 13, dashed line) was takenfrom the Escape Hatch Programme, Fig. 4, and theother (Fig. 13, solid line) presents the calculated pdf fora use level of 32 �C, 0.24 W/(m2 nm) and zero for thetemperature, UV and aerosol parameter, respectively(see Fig. 9). The parameters to compare for both Wei-bull distributions are presented in Tables 1 and 4. Theshape of both curves in Fig. 13 is similar, slightly nega-

Fig. 11. Linearized life–stress plot (left) and the acceleration factor (right) for the UV when the temperature is kept at a use level of 32 �C (305 K)

and the aerosol parameter is set to zero. The dashed lines denote the 90% two-sided confidence bounds.

Fig. 12. Linearized life–stress plot for the aerosol parameter when the

temperature and UV are kept at a use level of 32 �C (305 K) and 0.24

W/(m2 nm), respectively.

Fig. 13. Probability density functions for gloss loss with a failure cri-

terion of 60 GU measured at gloss 60� for the reference coating

obtained from the natural exposure experiment (dashed line) and the

artificial ageing (solid line) calculated for a use level of 32 �C (305 K),

0.24 W/(m2 nm) and zero for the temperature, UV and aerosol para-

meter, respectively.


tively skewed, both shape parameters � are close: �obtained from the natural exposure experiment was 9.4and � calculated from the artificial ageing was 18.9 withthe coefficients of skeweness �0.6 and �0.9, respec-tively. From the Fig. 13 follows, that the distributionobtained from the natural exposure is much broaderthan that from the artificial weathering, their standarddeviations are 6.3 and 2.7 months, respectively. This canbe explained both by variations in the actual conditionsbetween different planes and by other factors that werenot included in the weathering procedure employed,such, for example, as variations in coating applicationconditions and aircraft washing.Both curves in Fig. 13 are closely located with a dif-

ference of about 8 months: the mode life, which corre-sponds to the maximum of pdf-curve, for naturalexposure was 51.3 months, whereas that from the arti-ficial ageing experiment was 43.1 months. However, forthe warranty time 90% (the 10th percentile �0.1), whichperhaps is a more useful parameter for the prediction ofthe service life for coatings, the difference is muchsmaller: only 2.5 months.

6. Conclusions

A model with three stress types, the temperature, UVand aerosol, was proposed for calculating the service lifefor organic coatings under service conditions. Themodel was applied to the estimation of the service lifefor aircraft coatings concerning the gloss loss. The fail-ure criterion, which was defined by airline representa-tives, was set to 60 GU for gloss 60�. The validation ofthe model was performed for reference polyurethanecoating with a light blue colour. Firstly, gloss degrada-tion curves for the reference coating were obtained in aunique natural exposure programme (Escape HatchProgramme) and the service life was calculated using theWeibull distribution. Secondly, the specially designedaccelerated ageing tests were performed with the samecoating using the new designed and constructed weath-ering device. In order to compare both results the life–stress relationship was found and the use level condi-tions were determined. For the temperature, the Arrhe-nius life–stress relationship with a value for theapparent activation energy of 8.4 kcal/mol was used andfor the UV-A irradiance at 340 nm the inverse powerlife–stress relationship with a power coefficient of 0.46was taken. The third stress, the aerosol, was treated asan indicator variable taking discrete values of zero (noaerosol application) and one (aerosol application).The estimation of the service conditions for aircraft

coatings were performed by using an Arrhenius weight-ing term for temperature and a power weighting termfor UV. Here we based on the climatic data for airtemperature and UV irradiance at 340 nm at some ran-

domly chosen destination sites together with the spe-cially performed experiment for determination of thedifference between air and panel temperatures. Thecalculated service conditions (the use level) were 32 �Cfor the panel temperature, 0.24 W/(m2 nm) for the UVand zero for the aerosol parameter. The calculatedmean life for the gloss loss of reference coating at theassumed use level with a failure criterion of 60 GUmeasured at gloss 60� was 42.0 months and the 90%warranty time (time at which only 10% of the panelshad reached the failure criterion—this reliability para-meter is perhaps more useful for the prediction of theservice life for coatings) was 38.4 months. The meanlife and the 90% warranty time obtained from the nat-ural weathering (Escape Hatch Programme) of the samecoating were 49.3 and 40.9 months, respectively. Bothexperimental results were in good agreement, whichvalidated the model.Humidity as a stress parameter was excluded from

analysis because the variation of this parameter acrossdifferent aircrafts is not so distinguishable. Thereforethe influence of this parameter was not investigateddirectly in this work. However, in the artificial weath-ering procedure employed the effect of humidity was notignored: relative humidity changes from 10 to 100%during the weathering cycle were applied. For analysisof degradation of coatings for another applications, forexample, for automotive coatings, the influence ofhumidity has to be studied more carefully.Our method gives a unique opportunity to investigate

the aerosol influence on coatings. Starting from the fact,that the service life of aircraft coatings was reduced byapproximately 50% in the years from 1992 to 1995 fol-lowing the eruption of the volcano Pinatubo in June1991, the specially designed weathering experiment wasconducted which simulated the post-eruption strato-sphere conditions. The most simple mathematical modelfor the aerosol parameter using indicator variableshowed that the sulphuric aerosol shortened the servicelife of the reference coating by at least of 40%, whichsuits perfectly with the earlier mentioned 50% reduc-tion. Therefore, the experimental conditions were cho-sen correctly. The further development of the model canbe made using X-ray photoelectron spectroscopy mea-surements, which could introduce a quantitativeamount of sulphuric atoms cumulated in the coatingduring the ageing. Regarding the degradation of thereference coating, the conclusion can be made thatthe reference polyurethane coating under investigationwas sensitive to the sulphuric aerosol. For the timebeing, the use level parameter for sulphuric aerosolwas set to zero based on the fact that no big volcanoeruptions have taken place which could have broughta considerable amount of aerosol into the strato-sphere for the duration of the Escape Hatch Pro-gramme.


For new coatings now under development, it can be aquestion of interest whether a new product is resistant tosulphuric aerosol. Moreover, other pollutants, for exam-ple, acid rain simulation can be included into the investi-gation, which is important for automotive coatings.

Acknowledgements

This research was supported by the Swiss Commis-sion for Technology and Innovation, Akzo Nobel, SRTechnics and KLM. We are grateful to Dr. Dick vanBeelen, Dr. Hans Polak, Dr. Ruud van Overbeek andPierre J.M. Moors of Akzo Nobel Aerospace Coatings;Leo G.J. van der Ven, S.M. Koeckhoven, Ritse E.Boomgaard, Dr. Klaus Zabel, J.J. Udema and RobLagendijk of Akzo Nobel; Hanspeter Roth, Peter Mul-ler, Wilbert Meijer, Herbert Ackermann and Hans Gutof SR Technics; Jan van der Woning, Adrian Gerritsenand Carlo N.J. Bakker of KLM and Oliver von Trze-biatowski of EMPA for helpful discussions.

Appendix A. Basic concepts of Reliability theory

applied to the Weibull distribution

Basic definitions and their application to the Weibulldistribution can be found, for example, in [5,16–21] andsummarily are shown in Table 5.

Appendix B. Life–Stress relationships

Some of most common used life–stress relationships[8,17,21] are presented in Table 6When a test involves multiple accelerating stresses, a

general log–linear relationship (GLL), which describes alife characteristic as a function of a vector of n stresses,or X ¼ X1;X2; . . .Xnð Þ. Software ALTA 6 PRO [8]includes this model and allows up to eight stresses.Mathematically the model is given by,

L Xð Þ ¼ e�0þPn

j¼1

�jXj

;

where �j are model parameters, X is a vector of n stres-ses.This relationship can be further modified through the

use of transformations and can be reduced to the mod-els discussed previously (Table 6). If one applies aninverse transformation, such that V=1/X, the relation-ship would reduce to the Arrhenius relationship (with�j=B from the Table 6), a logarithmic transformation,V=ln(X) leads to the inverse power relationship (with�j=�n from the Table 6). If no transformation isapplied, the stress–life relationship has an exponentialform. Furthermore, if more than one stress is present,one could choose to apply a different transformation toeach stress to create combination models.

Table 5

Basic concepts of Reliability theory applied to the Weibull distribution

Concept
Description Weibull distribution
�

Cumulative

distribution

function F(t)

(cdf)

Gives the probability that a panel will fail

before time t:

FðtÞ ¼ PrðT4 tÞ

F tð Þ ¼ 1� exp �t

� ��" #

" #
Reliability function R(t)
�

Gives the probability of surviving beyond

time t

R tð Þ ¼ Pr T > tð Þ ¼ 1� F tð Þ

R tð Þ ¼ exp �t

� ��

" #
Probability density function (pdf)
� � �

Represents relative frequency of failure

times as a function of time

f tð Þ ¼ dF tð Þdt

f tð Þ ¼� t� ��1

exp �t

� ��

Hazard function (h.f.), or instantaneous

failure rate function

Expresses the propensity to fail in the next

small interval of time, given survival to time t:

h tð Þ ¼ limDt !0

Pr t<T4 tþDt T>tjð Þ

Dt ¼f tð ÞR tð Þ

h tð Þ ¼�

�

t

�

� ��1

b<1—decreasing h.f., describes

products that improves with age

(infant mortality)

�=1—constant h.f., describes

products with random failures

(exponential distribution)

�>1—increasing h.f., describes

products ageing


Var Tð Þ ¼ �2 G2

�þ 1 � G

1

�þ 1

� �

Var Tð Þ½ �

Appendix C. General Log-Linear-Weibull model

The General Log–Linear–Weibull (GLL–Weibull)model can be derived by setting the scale parameter � tothe life–stress relationship L Xð Þ (see Appendix B). Herewe will follow the notations assumed in ReliaSoft [8].

� ¼ L Xð Þ;

while the shape parameter � is assumed to remain con-stant across different stress levels. This yield the follow-ing GLL-Weibull pdf,

Table 5 (continued)

Concept
Description Weibull distribution
Mean life T or expectation E(T)
T ¼ E Tð Þ �Ð1�1
tf tð Þdt
T� ¼ �G1
�þ 1

� �,Ð1 �t x�1
where G xð Þ ¼ 0 e t dt x > 0ð Þ
Variance
Measure of the spread of the distribution.
Var(T) has the units of time squared.

Var Tð Þ �Ð1�1

t � E Tð Þ½ �2f tð Þdt ¼ jÐ1

�1t2f tð Þdt � E Tð Þ½ �

2

� � � �2 !

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis
Standard deviation Has the units of life, for example, months
or hours

� Tð Þ ¼ Var Tð Þ½ �1=2

�T ¼ � G2þ 1

� �� G

1þ 1

� �2

Coefficient of skewness
Measure for the asymmetry of the
distribution

s �

Ð1

�1t�E Tð Þ½ �

3f tð Þdt

3=2

s ¼

G 1þ3

�

� �� 3G 1þ

2

�

� �G 1þ

1

�

� �þ 2 G 1þ

1

�

� �� 3

G 1þ2

�

� �� G 1þ

1

�

� �� 2" #3=2

for 1<�<3.6, s> 0 the pdf is skewed

to the right (has a right tail)

for �> 3.6, s<0 the pdf is skewed to

the left (has a left tail)

for 3.0<�<4.6, jsj<0.2 the distribution

is almost symmetric (similar in shape

to a normal distribution)

1

Median life T�
Value of the random variable that has
exactly one-half of the area under the pdf

to its left and one-half to its rightÐ T��1

f tð Þdt ¼ 0:5

T� ¼ � ln 2ð Þ½ ��

1� �1

�

Mode T~
The maximum value of T that satisfiesd f tð Þ½ �
dt ¼ 0

T~ ¼ � 1��

100Pth Percentile of a distribution �P
Age by which a proportion P the
population fails. It is the solution of

P ¼ F �Pð Þ:

�P ¼ � �ln 1� Pð Þ½ �1=�

Warranty time 90%
is the 10th percentile, which means that
90% of all panels survived (have not

reached the failure criterion)

�0.1

Important examples:

�0.632��—scale parameter

�0:5 ¼ � ln 2ð Þ½ �1=�— median

Table 6

Life–Stress relationships

Model parameters

Arrhenius
L Vð Þ ¼ CeBV C>0, B
1
Inverse Power Law (IPL) L Vð Þ ¼
KVn
K>0, n
A B

Eyring
L Vð Þ ¼VeV A, B
L, is a quantifiable life measure, such as mean life, median life, char-

acteristic life, percentile, etc.; V, represents the stress levels, [tempera-

ture values should be expressed in absolute units (K)].


f t;Xð Þ ¼ �t��1e�� 0þ

Pn

j¼1

�jXj

� �e�t�e

�� 0þPn

j¼1

�jXj

� �:

The total number of unknowns to solve for in thismodel is n+2, i.e. �, �0, �1, . . ., �n.The maximum likelihood estimation method [16,17]

can be used to determine the parameters for the GLLrelationship and the selected life distribution. The log-likelihood function for the Weibull distribution for rightcensored data is given by Ref. [8],

ln Lð Þ ¼ L

¼XF

i¼1

ln �T��1i e�T �

ie

�� 0þPn

j¼1

�jXi;j

� �e�� 0þ

Pn

j¼1

�jXi;j

� �2664

3775

�XS

i¼1

T0

i

� ��e�� 0þ

Pn

j¼1

�jXi;j

� �;

where F is the number of exact times-to-failure datapoints; � is the Weibull shape parameter (unknown, to beestimated); �0, �1, . . ., �n, are the (n+1) GLL parameters(unknown, to be estimated); X ¼ X1;X2; . . .Xnð Þ is thevector of n stresses; Ti is the exact failure time; S is thenumber of suspension data points; and Ti

0; is the runningtime of the suspension data points.The solution (parameter estimates) can be found by

maximising L, i.e. by simultaneous solving of (n+2)equations such that

@L@�

¼ 0;

@L@�i

¼ 0; i ¼ 0; :::; n

Appendix D. Likelihood ratio test

In order to justify the assumption of a common shapeparameter among the data obtained at different stresslevels, the likelihood ratio (LR) test can be performed[17]. The LR test statistic T, can be calculated from

experimental data: T ¼ 2 L1 þ L2 þ . . .þ Ln � L0ð Þ,where L1, L2, . . ., Ln are the log–likelihood valuesobtained by fitting a separate distribution to the datafrom each of the n stress levels. The log–likelihood valueL0 is obtained by fitting a model with a common shapeparameter and a separate scale parameter for each ofthe n stress levels. If the shape parameters are equal,than the distribution of T is approximately w2 with(n�1) degrees of freedom.

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http://www.empa.ch/nabel.3d

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Service life prediction for aircraft coatings