Background
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%.

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 hrs, it is 175%; from 300 to 350 hrs, it is 200% and from 350 to 375 hrs, it is 250%. The test is terminated after 375 hours and any units that are still running after that point are right-censored (suspended). Figure 1 shows this Stress Profile, as defined in ALTA 7 PRO, and Figure 1A shows an automatically generated report for this profile. 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.

After performing failure analysis on the failed parts, it is determined that the failure that occurred at 328 hrs 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+ hr.

The test objective is to estimate the B(1) life for the part (i.e. time at which reliability is equal to 99%) at the typical operating conditions (i.e. Stress=100%), in miles.

Analysis
Step 1: Utilizing ALTA 7 PRO, the analyst first creates a new Standard Folio for non-grouped time-to-failure and time-to-suspension data, using "Other" as the stress type and entering 100 as the use stress, and then defines the Stress Profile, as shown in Figure 1.

Step 2: Once the profile is defined, the analyst selects the cumulative damage life-stress model (to use a time-varying stress) and the Weibull distribution, then 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) in the Stress Transformation window. The analyst then enters the observed times, their state (i.e. Failed F or non-failed S) and a reference to the profile used in the ALTA Data Folio. Figure 2 illustrates this.

Step 4: The last part remaining is to determine the B(1) life at the part's use stress level. Using the QCP, the B(1) life is found to be 657 hours, as shown in Figure 4. Based on the given multiplier, the B(1) life in miles would then be 657 test-hr*100 (miles/test-hr)= 65,700 miles.