RAMS 2013 Accelerated Testing for 2 year Storage


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Paper given at RAMS 2013 on a case study for Accelerated Testing for devices expected to withstand a two year storage period.

Two accelerated life tests (ALT’s) explored two failure mechanisms of concern for a product expected to experience a 2-year storage period. Each ALT focused on a specific failure mechanism and required different applied stress.
Making periodic measurements permitted the experiments to illustrate the stability of the performance of the units over the aging process. The life data analysis for each set of data also permitted the calculation of the expected reliability performance of the population after two years of storage.

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RAMS 2013 Accelerated Testing for 2 year Storage

  1. 1. Accelerated Testing for 2-year StorageFred Schenkelberg, Ops A La Carte, LLCKey Words: accelerated testing, storage, failure mechanisms, test design SUMMARY & CONCLUSIONS of the failure mechanism we expect increasing the temperature will increase the rate of chemical degradation of the joint. Two accelerated life tests (ALT’s) explored two failure When the joint fails the functional based tests of the entiremechanisms of concern for a product expected to experience a assembly permit detection of the failure. The testing includes2-year storage period. Each ALT focused on a specific failure current draw, flow rate, and use simulation. It is unclear whichmechanism and required different applied stress. will provide the best response related to the joint failure and Making periodic measurements permitted the experiments post testing failure analysis will need to confirm the failure isto illustrate the stability of the performance of the units over due to joint failure.the aging process. The life data analysis for each set of data We do not have a reasonable estimate for the reaction’salso permitted the calculation of the expected reliability activation energy and we will have to determine that value asperformance of the population after two years of storage. part of the experiment. Therefore, the test approach will 1 INTRODUCTION include three stress levels in order to determine if there exists a relationship between temperature stress and time to joint A small mechanical medical device must function after up failure. Since the use test is destructive (i.e. the unit is a one-to a 2-year storage period. Like many accelerated life testing time use device) we need sufficient samples to make theplans, this plan must consider the expected failure mechanisms periodic measurements. The acceleration factor for planning isand available models. based on a few assumptions and the actual acceleration factor The previous product testing and experience narrow the comes from the test results. For brevity we will focus onexpected failure mechanisms to either mechanical fatigue due current draw only.to Coefficient of Thermal Expansion (CTE) mismatches or Given the testing is on complete units, the stress will alsooxidation of a critical joint within the product. Therefore, the accelerate any other failure mechanism accelerated throughteam created two ALT’s, one for thermal cycling, and one for thermal cycling. All failures will receive a complete andthermal exposure. The thermal cycling experienced during thorough failure analysis to verify root cause.storage is a the diurnal change in ambient temperature. Theoxidation of the joint adhesive does not have an adequate 1.3 Delivery plate crackingacceleration model for use in this case; therefore the testing The early prototypes have micro cracks within thehas to estimate the activation energy and fitting. delivery plate. There is some evidence through environmental This paper is a case study of the test design and test testing that the structure propagates the crack during thermalresults. The paper discusses the use of engineering judgment cycling. The storage conditions will experience diurnaland appropriate statistical analysis to estimate the suitability of temperature change as expected in a sheltered, inhabitablethe design to withstand at least two years of storage. enclosure. It is not expected to always have environmental1.1 Failure Mechanisms and Test Approach controls to mitigate the outdoor daily temperature swings. In addition to the current draw and other functional Previous work within the design team identified two testing, it is possible to visually detect the plate cracking.failure mechanisms of primary concern for the storage period Excessive cracking does lead to failure and is detectable withof the product: epoxy joint failure and delivery plate cracking. a change in the current draw.Both failure mechanisms led to product failure during use. The ALT approach is to accelerate the expected dailyOther failure mechanisms are expected to occur at a lower rate temperature change within a chamber at a faster rate than onceor probability. Past experience does not provide any basis for per day, and slow enough to achieve the entire range oflifetime estimates for these two failure mechanisms. motion caused by the coefficient of thermal expansion effects.Therefore, the team decided to conduct two ALT’s to estimate One test cycle equals one day of storage. The accelerationthe storage life related to these specific failure mechanisms. factor depends only how fast the test cycling occurs.1.2 Epoxy joint failure 2 ENVIRONMENT Based on experimentation and vendor information, a The expected storage environment is indoor shelteredprimary means for the epoxy to fail over time is when poorly conditions that may or may not have temperature control. Incured or bonded material oxidizes. Given the chemical nature
  2. 2. some situations the storage temperatures may match the 3.1 Sample size life demonstrationoutdoor ambient temperatures. The unit’s storage is expected The basic test is a pass/fail (unit performance withinto be in populated areas of the world. specifications) after a simulated 2 years of storage under Rather than use rated limits or absolute maximum storage cyclic stress. Equation 1 is based on the binomial distributiontemperature expectations which would only apply to a very and assuming no failures permits the determination of thefew situations and units, we will use the 90th percentile values sample size for a given confidence and reliability. [2]for daily average temperature and daily average temperaturerange. The National Climatic Data Center [1] has available (1)worldwide weather station daily data readings. where C is the type I statistical confidence 0.95, The weather data is from 20 randomly selected weather and, R is the reliability, 0.95.stations with data from July 1st, 2005 to July 1st, 2010 from theworldwide list of stations within the database. The resulting The calculation results in 58.4 which is rounded up to 59162,000 lines of daily data readings include minimum, samples that must pass functional tests within specificationsmaximum, and average temperatures. after experiencing two years of simulated cyclic stress. Using 60 samples for the test gives the test a small additional margin.2.1 Thermal cycling conditions 3.2 Sample size stability Calculating the difference between daily minimum andmaximum temperatures provides the daily temperature range. For the second objective of stability, we are using anThen using the Excel percentile function to determine the 90 th additional 60 samples with ten being destructively tested at 3,percentile temperature range to be 19°C. The average 6, 9, 12, 18, and 24 months of simulated storage. The timetemperature range is 10.9°C with a standard deviation of periods and sample sizes are per internal organization5.8°C for the dataset. guidelines for testing stability. The intent is to evaluate the The 90th percentile maximum temperature is 31°C and the readings at each time point and test that the slope of a fitted th10 percentile minimum temperature is 19.4°C. The test line to the data is not different from zero meaning it is stable.temperature range is anchored at the maximum value and the 4 THERMAL CYCLING ALT RESULTSchamber should operate from 31°C to 12°C Due to thermal cycling stress representing a 2-year2.2 Thermal exposure conditions storage period, with 95% confidence, there is a 1.7% chance The dataset suggests the daily 90th percentile maximum of current draw being above 68mA. Or stated another way,temperature is 31°C. The maximum temperature is generally there is a 95% confidence of at least 98.3% reliability over aonly obtained for an hour or so per day. The temperature 2-year storage period. The units appear to be stable over theeffect on the epoxy is temperature dependent and the time at entire two-year period.temperature is important also. Assuming an accumulated The current draw limit is 68mA during functional testingdamage model for the effects of temperature and the expected of the unit. In this paper we are not discussing the other testingdaily temperature changes, we decided to use the daily parameters used to fully evaluate the units.average temperature rather than the maximum values. The post testing determined all units operated within The 90th percentile daily average temperature is 24.4°C. specifications. The visual inspection of the units found onlyFor the expected thermal exposure we rounded this value to modest increases in crack length. The thermal cycling25°C. The test temperature will be higher than these values to expected during storage appears to have a minor effect ofaccelerate the testing. 25°C is the expected environmental product performance.temperature we will use for the life prediction based on the 4.1 Hypothesistest results. We expect a drift up in current draw corresponding to the 3 THERMAL CYCLING ALT PLAN amount of thermal cycling experienced. The test plan has two objectives: first to demonstrate at Considering the readings are destructive each unit wasleast 95% reliability with 95% confidence; and, to demonstrate measured once. Samples were drawn at random from thestability over the two-year period. Given an unknown chamber for readings for each scheduled test point.relationship between the temperature range and crack growth, 4.2 Analysis for stabilitywe decided to not increase the thermal range to achieveadditional acceleration. One test cycle equals one day in real The analysis uses test points (TP1, TP2, etc.) and hours oftime. Through experimentation we found the units come to testing interchangeablyusing the following conversion, 96thermal equilibrium in less than 5 minutes. Therefore for hours of testing equals one month of storage time. One testtesting we set the dwell time at both extremes to 5 minutes cycle took approximate 3.2 hours due to increasing the dwellonce the chamber temperature is within 2°C of the set point. time to 30 minutes and the slow ramp rates actually achieved.The available chamber has a ramp rate of about 3°C per The longer than planned dwell time was to insure completeminute which will avoid thermal shock damage. thermal saturation of the units.
  3. 3. The first step is to view the data. Figure 1 provides a box include the 95% confidence bound error bars about the means.plot view of the data over the six test points. The vertical axis If one is able to pass a horizontal line through all the erroris current (mA) and has an upper specification of 68mA. The bars, it is likely that all the TPs are reading from the samehighest value of any unit is 59.5mA within the TP4 samples. population, meaning there is no change over time due to thermal cycling. Next plot with linear regression fit of the measurements at Current Draw, TP1,2,3,4,5,6 each test point. Using hours rather than TP number for the plot to provide a continuous variable for the axis and regression, 60 see Figure 3. Test points correspond to hours and days roughly as follows: TP1 at 288, TP2 at 551, TP3 at 837, TP4 at 1103, TP5 at 1672, and TP6 at 2192 (all in hours). 55 50 Current Draw over 2 years thermal cyclingCurrent Draw (mA) 60 45 55 40 50 Current Draw (mA) 35 45 30 1 2 3 4 5 6 40 Test Points Figure 1 Box plot of current draw results 35 30 TP Means with 95% Confidence Level error bars 500 1000 1500 2000 Hours 55 Figure 3Linear regression fit of current draw The coefficients of the fitted line are in Table 1. Estimate Std. t Pr(>|t|)Current Draw (mA) 50 Error value Intercept 48.8 1.7 28.7 <2e-16 Significant Slope -0.0006 0.001 -0.46 0.647 Not Significant 45 Table1Linear regression coefficients The slope is not different than zero and therefore the units exhibit stability over the duration of the storage period n=10 n=10 n=10 n=10 n=10 n=15 simulation. A check of the regression residuals (plots not TP1 TP2 TP3 TP4 TP5 TP6 shown) did not reveal any anomalies or concerns. Test Points 4.3 Analysis for reliability Figure 2Test point means and confidence Fitting the data using a generalized log-linear – Weibull Given the relative small sample size of TP1 through TP5 model with ALTA Pro software, the software uses thethere is insufficient evidence to conclude the spread (variance) likelihood function in equation 2.[3]is different or related to time. (2) Another way to view the data (Figure 2) is by plotting the where, t is time, directly related to number of test cyclesmean of the current draw readings within each test point and 0 and 1 are fitted parameters, where exp( 0) is the y-
  4. 4. intercept and 1 is the relationship between thermal cycles 5 THERMAL EXPOSURE ALT PLANand current draw. The failure mechanism of concern related to the epoxy Each set of data from each test point are fit to a joint is chemical breakdown of the epoxy over time. It may beWeibull distribution, where = 0 + 1t, and beta is the related to a poorly formed or cured joint, yet is notcommon beta value to for all test points. immediately obvious. Prior testing has found that temperature Using ALT Pro to perform the maximum likelihood does seem to accelerate the failure mechanism which has beenestimator fit on the data points results shown in Table 2. confirmed by the adhesive vendor.Note this is a fit of the expected performance not a failure Without a reasonable estimate of the activation energy wedistribution. decided to run an ALT that would provide an estimate of the activation energy. Three stresses and measuring time to failure Lower Estimated Upper information may provide a means to relate stress to time to bound bound failure.Beta, 7.0 8.2 9.6 As with the thermal cycling, there are multiple functionAlpha(0), 0 3.88 3.94 3.99 tests that may indicate product failure. For the purpose of thisAlpha(1), 1 -4.4E-05 -6E-06 3.2E-05 paper we are only considering the current draw test. The full set of testing is destructive to the unit. Table2GLL-Weibull fitted parameters 5.1 Thermal Aging ALT Plan The exp( 0) is approximately 54mA which is very near Select 200 units at random from latest 3 builds and verifythe grand average of the data. The 1 is the slope of the the units meet all ‘ready to ship’ requirements. Units are not infitted line, and is not different than zero or slope is about protective boxes, wraps or enclosures.zero. This indicates, as the fitted line in figure 3, there is no Set the thermal chambers to temperature set points ofchange over the storage time due to thermal cycling stress. 45°C, 52.5°C and 60°C. Place 114, 57, and 29 randomly The GLL-Weibull model permits one to plot (figure 6) selected units in the 40°C, 50°C, and 60°C chambers,and calculate the reliability values for the 2-year storage respectively. Table 3 shows the days and number to measureperiod based on all the available test data. schedule. 60°C Chamber 52.5°C 45°C Chamber Chamber Test Number Day Number Day Number Day Point Initial 29 0 57 0 114 0 1 9 2 13 4 27 8 2 3 3 10 6 20 12 3 4 6 10 12 20 24 4 4 9 10 18 20 36 5 9 10 14 20 27 40 Table3Thermal aging sample and time of reading The samples are distributed in a 4:2:1 ratio from the lowest to highest stress chamber deliberately to increase the likelihood of detecting current draw changes at the lowest Figure 42-year storage life CDF plot for thermal cycling stress. The timing of the measurements are based on the Using the fitted model parameters with time set to 2 assumed (some prior evidence from environmental testing)years, we can calculate with 95% confidence that the units time to failure distribution. Previous experimentation tohave at least 98.3% reliability, based only on the current determine the rate of current draw change at 60°C provided adraw test parameter. rough estimate of the timing to current draw degradation to Finally, since none of the 60 samples that operated near the failure threshold as approximately a week.over the two year simulated storage period failed any 5.2 Determination of thermal set pointsperformance test, the test demonstrated at least 95%reliability with 95% confidence. The difference in the The chamber set points are set using the guidelines forresults between the models is the GLL-Weibull model is ALT design in the Meeker and Hahn monograph [4] using theusing the current draw readings to fit the data, whereas, following information:the binomial model is using only the count of units tested. TH = 60°C, the glass transition temperature of the epoxy is 70°C which limits the high temperature exposure. TD = 25°C, the 90th percentile of storage temperature.
  5. 5. p = 0.05, the assumed probability of failure at the design Figure 8 shows formula 3 with the planning values. Ittemperature over the 2 year storage life period. highlights the tradeoff between sample size, precision, and pH = 0.90, the assumed probability of failure when confidence.exposed at high test temperature over planned duration of test. 6 THERMAL EXPOSURE ALT RESULTS pD = 0.001, the assumed probability of failure whenexposed to the nominal temperature over duration of test. The results of thermal aging of the units in the ALT τ = 3 months, expected test duration indicate at least a 95% confidence of 99.41% reliability over n = 200, expected total sample size available. the two year storage period. The units appear to be stable over The Meeker and Hahn guideline assumes the units are the entire two-year period.only measured before and after the testing period. The The current draw limit is 68mA during functional testingguideline expects the testing to permit at least five failed units of the unit. In this paper we are not discussing the other testingper test temperature. Given this test benefits from the parameters used to fully evaluate the units.monotonic degradation of current draw we expect to be able to The post testing determined all units operated withinproject each sample to estimate the time to failure. The specifications. The thermal aging expected during storageguideline provides a convenient means to balance the appears to have a minor effect of product performance.acceleration temperature range and the sample size 6.1 Hypothesisdistribution across the chambers to permit a statisticallyefficient design. We expect a change in current draw corresponding to the amount of thermal aging experienced.5.3 Determination of sample size Considering the readings are destructive each unit was Formula 3 is based on the Weibull distribution and measured once. Samples were drawn at random from theassuming at least 25% of units show failures permits the chamber for readings for each scheduled test point.determination of the sample size for a given confidence and 6.2 Analysis for stabilityprecision.[5] (3) where, Current Draw 45°C Samples R′ is the ratio of the compromise variance over theoptimum variance - calculated. V is the variance factor for the optimum plan - calculated. Kγ is the standard normal 100(1+γ)/2 percentile. 60 w is the bound about the true value (precision about truevalue is +/- w) 50 40 30 20 TP0 TP1 TP2 TP3 TP4 TP5 Figure 6 Box plot of 45°C current draw results For each of the three test temperatures, 45°C, 52.5°C and Figure 5Sample sizegiven precision and confidence level 60°C we first plot the data in a boxplot. Figure 9has an example boxplot showing the results for the 45°C group. The The second element of the sample size estimate is the vertical axis is Current (mA) and the upper specification forestimate of the Weibull distribution. Assuming the unit will current draw is 68 mA. The highest value of any unit is 67have a probability of failure of 0.001 at 24 months. And, the mA. Given the relative small sample size per TP1 though TP5failure rate increases over time with a slope of 1.5 (beta value there is insufficient evidence the spread (variance) is differentfor Weibull distribution). This is a rough estimate based on or related to time. The boxplots for the 52.5°C and 60°C werevery limited prior experimental data. similar and no samples were outside specifications.
  6. 6. Next a plot (figure 6) with the linear regression fit of the 60 0.12 measurements at each test point. Again using testing days Table5Slopes of fitted line for each temperature rather than TPs in order to plot and fit with a continuous variable. Therefore, we are concluding the units exhibit stability based on the assumed model relating test temperature Aged at 45°C Current Draw acceleration will cover at least two years of storage at 25°C. 6.3 Analysis for reliability The data used in ALTA Pro included three columns, Current in mA, Age in days, and Temperature in Kelvin. Age 60 is the period of time in days the unit was within the aging chamber. Temperature was converted from °C to K by adding 217.15. 50 The data is fit to a Temperature-NonthermalWeibullCurrent model. It uses an Arrhenius model for the effects of temperature, and an inverse power law model for the effects of 40 time, that enables us to model the destructive measurement, degradation accelerated life test data. The likelihood function for the model is in equation 4. 30 (4) Where, t is the age or time in days; T is temperature in 20 Kelvin: and, B, C, and n are the model parameters to estimate. 0 10 20 30 40 Using ALTA Pro to perform the maximum likelihood Days estimator fit on the 219 data points (a total of 220 units tested with one unit removed after being dropped and damaged) Figure 7Linear regression plot of 45°C current draw provided the results shown in figure 13. The coefficients of the fitted line are in Table 4. Lower Estimated Upper bound bound Estimate Std. t Pr(>|t|) Beta, 7.0 7.6 8.3 Error value B -382 -35.7 311 Intercept 48.5 0.61 78.5 <2e-16 Significant C 21.4 60.8 172 Slope 0.015 0.03 0.50 0.614 Not Significant n -0.01 0.01 0.03 Table 4Linear regression coefficients of 45°C current draw Table 6Fitted Parameters for Temperature- NonthermalWeibull model The slope is not different than zero and therefore the units exhibit stability over the duration of the exposure to 45°C. A The C parameter is the y-intercept and is approximately check of the regression residuals (plots not shown) did not the mean value of the data, which is true. With B and n not reveal any anomalies or concerns. different than zero (90% confidence), it indicates there is not a Each test temperature group revealed similar results with conclusive effect of time or temperature on the performance of not showing a significant slope. Table 5 shows the results of the units. the three regressions. While there appears to be a relationship Using the fitted data as the best available estimate, one between the stress and the slope, none of the fitted slopes were can use the use the natural log of the likelihood function to statistically significantly different than zero. plot that expected life distribution at 25°C at 2-years (730 days) of use. Equation 5 has the natural log of the likelihood function in equation 4. Aging Temperature (°C) Slope 45 0.02 (5) 52.5 0.09 And Figure 8 has the resulting plot.
  7. 7. http://www.weibull.com/acceltestwebcontents.htm, accessed April 3-8, 2012. 4. William Q. Meeker and Gerald J. Hahn, How to Plan an Accelerated Life Test, ASQC, Milwaukee, WI, 1985. 5. Wayne Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, New York, John Wiley & Sons, 1990, p. 348. 6. Accelerated Life Testing Reference, ReliaSoft Alta Pro software manual, etextbook, http://www.weibull.com/acceltestwebcontents.htm, accessed April 3-8, 2012. BIOGRAPHY Fred Schenkelberg Figure 8 2-year storage life CDF plot for thermal aging 15466 Los Gatos Blvd #109-371 Los Gatos, CA, 95032, USA Based on the fitted model and calculating the probabilityof having a value above 68 mA at 25°C and 2 years results in e-mail: fms@opsalacarte.coma value of 0.0058% or very low. The lower 95% confidence Fred Schenkelberg is a reliability engineering andbound on this value is 0.59%, still only about a half percent management consultant with Ops A La Carte, LLC, with areaschance of being out of spec. The test results demonstrate of focus including reliability engineering management trainingTCAG (current draw) will survive 2 years of storage and accelerated life testing. Previously, he co-founded andtemperature stress with at least 99.41% reliability with 95% built the HP corporate reliability program, includingconfidence. consulting on a broad range of HP products. He is a lecturer with the University of Maryland teaching a graduate level REFERENCES course on reliability engineering management. He earned a Master of Science degree in statistics at Stanford University in1. National Climatic Data Center, U.S. Department of 1996. He earned hisbachelor’s degrees in Physics at the Commerce, as of July 6, 2012, United State Military Academy in 1983. Fredis the immediate http://www7.ncdc.noaa.gov/CDO/cdoselect.cmd?dataseta Past-Chair of the American Society of Quality Reliability bby=GSOD&countryabby=&georegionabby= Division, active with IEEE and IEC reliability standards2. Gary S. Wasserman,Reliability Verification, Testing, and development teams. Fred is also the founder of the No MTBF Analysis in Engineering Design, New York, Marcel movement and website nomtbf.com. He is a Senior Member of Dekker, 2003, p. 209. ASQ and IEEE. He is an ASQ Certified Quality and3. Accelerated Life Testing Reference, ReliaSoft Alta Pro Reliability Engineer. software manual, etextbook,