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Software Used: Software Used: ALTA PRO
Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)
Consider a test in which multiple stresses are applied simultaneously to a particular automotive part in order to precipitate failures more quickly than they would occur under normal use conditions. The engineers responsible for the test are able to quantify the combination of applied stresses in terms of a “percentage stress” as compared to typical stress levels (or assumed field conditions). In this scenario, the typical stress (field or use stress) is defined as 100% and any combination of the test stresses is quantified as a percentage over the typical stress. For example, if the combination of stresses on test is determined to be two times higher than typical conditions, then the stress on test is said to be at 200%.
Engineering analysis has indicated that at higher temperatures the QM has a higher rate of decrease. Assuming that the product’s normal use temperature is 20ºC (or 293 K), determine the shelf life of the product via an accelerated degradation test.
The test is set up and run as a step-stress test (i.e., the stresses are increased in a stepwise fashion) and the time on test is measured in hours. The step-stress profile used is as follows: until 200 hours, the equivalent applied stress is 125%; from 200 to 300 hours, it is 175%; from 300 to 350 hours, it is 200% and from 350 to 375 hours, it is 250%. The test is terminated after 375 hours and any units that are still running after that point are right-censored (suspended). Additionally, and based on prior analysis/knowledge, the engineers also state that each hour on test under normal use conditions (i.e., at 100% stress measure) is equivalent to approximately 100 miles of normal driving.
The test is conducted and the following failure and suspension times under the stated step-stress profile are observed (note that XXX+indicates a non-failed unit—that is, a suspension): 252, 280, 320, 328, 335, 354, 361, 362, 368, 375+, 375+, 375+ hours.
After performing failure analysis on the failed parts, it is determined that the failure that occurred at 328 hours is due to mechanisms other than the ones considered. That data point is therefore identified as a suspension in the current analysis. The modified data set for this analysis is: 252, 280, 320, 328+, 335, 354, 361, 362, 368, 375+, 375+, 375+ hours.
The test objective is to estimate the B1 life for the part (i.e., time at which reliability is equal to 99%) at the typical operating conditions (where stress = 100%), in miles.
Step 1: Utilizing ALTA PRO, the analyst first creates a new standard folio for non-grouped failure and suspension times, using “Percent Stress” as the stress type and entering 100 as the use stress level. Then the “Automotive” stress profile is created and defined as shown next.
Figure 1: Completed “Automotive” stress profile.
Step 2: Once the profile is defined, the analyst selects the cumulative damage life-stress model (in order to use a time-dependent stress) and the Weibull distribution, then clicks Stress Transformation and selects the logarithmic (power LSR) transformation (since the effect of the stress was deemed to be mechanical and more appropriately modeled by a power function). The analyst then enters the observed times, their state (i.e., Failed F or suspended S) and assigns the stress profile to each data point by clicking in the stress column. After calculating the data, the folio appears as shown next.
Step 3: There are several methods available to ascertain adequacy of fit, including residual plots and use level probability plots, as shown below.
Figure 3: The Cox-Snell residuals plot.
Figure 4: The use level Weibull probability plot.
Step 4: The last part remaining is to determine the B1 life at the part’s use stress level. Using the QCP, the B1 life is found to be 658 hours, as shown next. Based on the given multiplier, the B1 life in miles would then be 658 test hours * 100 (miles per test hour) = 65,800 miles.
Figure 5: QCP showing the extrapolated B1 life (in hours) at 100% stress.
