Analyzing Step-Stress Data

[Editor's Note: This article has been updated since its original publication to reflect a more recent version of the software interface.]

Step-stress testing is a popular method of conducting accelerated tests. In a step-stress test, the units are tested at a given stress level for a fixed amount of time. At the end of that time, if there are units surviving, the stress level is increased and held for another amount of time. This process is repeated until all of the test units are failed or the predetermined test time has expired. This method of accelerated testing is a good way to obtain failures in a relatively short amount of time. However, analyzing step-stress data has been rather difficult and practitioners have generally had to rely on shortcuts or estimations to obtain reliability information from step-stress data. ReliaSoft offers a tool that allows the user to conduct a complete analysis of step-stress data. This article gives a case study of a step-stress test and the use of ReliaSoft's ALTA PRO to analyze the data from the test. The cumulative damage model is used to obtain an analytical solution for data with time-varying stress.

Consider a test in which multiple stresses were applied simultaneously to a particular automobile part in order to precipitate failures more quickly than they would occur under normal use conditions. The engineers responsible for the test were 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) was defined as 100% and any combination of the test stresses was quantified as a percentage over the typical stress. For example, if the combination of stresses on test was determined to be two times higher than baseline conditions, then the stress on test was said to be at 200%.

The test was set up and run as a step-stress test (i.e., the stresses were increased in a stepwise fashion) and the time on test was measured in hours. The step-stress profile used was as follows: until 200 hours, the equivalent applied stress was 125%; from 200 to 300 hours it was 175%; from 300 to 350 hours it was 200%; and from 350 to 375 hours it was 250%. The test was terminated after 375 hours and any units that were still running after that point were suspended (right-censored). The following chart shows this stress profile.

Step-Stress Stress Profile for Automotive Part

Objective and Test Data
Based on prior experience, the engineers could state that each hour on test under baseline use conditions (i.e., at 100% stress measure) was equivalent to approximately 100 miles of normal driving. The test objective was to estimate the B1 life for the part at the baseline operating conditions, in miles.

The test was conducted and failures occurred at the following times: 252, 280, 320, 328, 335, 354, 361, 362 and 368 hours. Additionally, there were three units that were still running when the test was concluded. These represent suspensions at 375 hours. After performing failure analysis on the failed parts, it was determined that the failure that occurred at 328 hours was due to a failure mechanism of no interest to the engineers, and that too would be considered to be a suspension. The following table shows the final time and disposition values for the test units.

Test Unit	Time	Disposition
1	252	Failure
2	280	Failure
3	320	Failure
4	328	Suspension
5	335	Failure
6	354	Failure
7	361	Failure
8	362	Failure
9	368	Failure
10	375	Suspension
11	375	Suspension
12	375	Suspension

Analysis
Using ReliaSoft's ALTA PRO, the analyst first created a spreadsheet for non-grouped failure times and suspensions, and used the stress profile folio to define the profile, as shown in the following figure.

Stress Profile Explorer with the Automotive Step-Stress Profile

Once the profile was defined, the analyst entered the observed times and their disposition (i.e., failed = F or suspended = S) into the standard folio and selected the cumulative damage life-stress relationship (to use a time-varying stress) with the Weibull life distribution. A power transformation was applied to the stress since the effect of the stress was deemed to be mechanical and more appropriately modeled by a power function. Finally references to the new stress profile were entered in the data sheet's stress column. The following figure illustrates this.

ALTA's Data Folio with data, calculated results and the analysis options highlighted

The software then solves the cumulative damage model to obtain parameters that can then be used to generate a variety of reliability-oriented information, including reliability vs. time, failure rates, MTTF, etc. In this case, we are interested in the B1 life at the use stress of 100%. This can easily be calculated using the Quick Calculation Pad, as illustrated in the following figure.

The B1 life results in ALTA's QCP

As can be seen, the B1 life at the use stress of 100% is 657.8 hours. Since each hour on test represents 100 miles of normal driving, the engineers can now predict that the B1 life for the part in question is 65,780 miles.