Using Quantitative Accelerated Life Testing Models for Other Applications
Although the phrase “accelerated life testing” often brings to mind images of temperature chambers filled with electronic components, the methodology for analyzing data from accelerated life tests can also be used in many other applications. Some of the potential applications include analyses to quantify reliability under different operating conditions, degradation analyses and stability/shelf-life studies. This article provides a brief overview of accelerated life testing analysis modeling and demonstrates the use of the analysis methodology in two non-accelerated applications.
Overview of Accelerated Life Testing Analysis Models
As an example, consider a component where the times-to-failure follow a Weibull distribution and the characteristic life (scale parameter) is affected by temperature following an Arrhenius relationship. As shown in Figure 1, the resulting accelerated life model can be viewed as a three-dimensional Weibull plot with each axis representing probability of failure, time and temperature respectively. The model can also be viewed as a three-dimensional survival plot of reliability versus time versus stress, as shown in Figure 2. The analysis allows the engineer to obtain the survival curve for the component under different operating stress levels. The methodology can also be expanded to incorporate multiple stress types.
Figure 1: Accelerated life model as 3D probability plot
Figure 2: Accelerated life model as 3D survival plot
Even from this simple example, it is easy to identify cross-applications to other reliability modeling situations where one or more stress types affect life. The following examples demonstrate situations where quantitative accelerated life testing analysis methods can be used for other non-accelerated applications.
Under Different Operating Conditions
Table 1: Pump motor data set, obtained under four different operating environments.
QALT analysis can be used to derive a probabilistic failure model for different speeds and densities. Assuming a Weibull life distribution and a two-stress proportional hazard model for the life-stress relationship, a reliability plot like the one shown in Figure 3 can then be obtained at different RPM and density levels. This plot shows the reliability curve for the motor at 300 RPM and a density of 1.1 g/ml.
Figure 3: Reliability plot at 300 RPM, Density = 1.1 g/ml
Analysis of Degradation Information
QALT modeling can be used to analyze this data set and, in this case, the Weibull life distribution along with a proportional hazard relationship were utilized. The random variable is the remaining tread and the covariates (stresses) are the mileage and the tire location (i.e., front or rear).
This analysis can be used to answer the question of whether there is a difference between the tread wear and location of the tires. It can also help to establish warranty guidelines, such as the mileage for which the tires should be operated such that 99% of the tires maintain a tread thickness of at least 1 mm. Figure 4 and Figure 5 graphically illustrate the answers to these questions based on the analysis. Based on Figure 4, one expects that 99% of the front tires will maintain a tread thickness in excess of 1 mm after approximately 43,500 miles. From Figure 5 (for the rear tires), this value is approximately 46,200 miles. Both figures illustrate these values utilizing a 95% lower one-sided confidence interval.
Figure 4: Tread versus mileage for front tires
Figure 5: Tread versus mileage for rear tires