Volume 3, Issue 1

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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 
Accelerated testing can be divided into two areas: qualitative accelerated testing and quantitative accelerated life testing. In qualitative accelerated testing, the engineer is mostly interested in identifying failures and failure modes without attempting to make predictions as to the product’s life under normal use conditions. In quantitative accelerated life testing (QALT), the engineer is interested in predicting or quantifying the life characteristics of the product at normal use conditions from data obtained during a test where the test conditions are not identical to the use (life) conditions. Typically, the stresses that contribute to product failure are increased to shorten test times. When analyzing results from such quantitative accelerated life tests, the QALT model expresses the life characteristics of the product as a function of the applied stress. 

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. 

Probability plot

Figure 1: Accelerated life model as 3D probability plot

3D 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. 

Quantify Reliability Under Different Operating Conditions 
One non-accelerated application for QALT methods is to quantify the reliability for a product under different operating conditions. To demonstrate this, consider a motor for a pump that can be used to pump different liquids at different speeds. For this example, we will assume that two main factors can affect the reliability characteristics of the pump: liquid density and the speed at which the motor is operating. Table 1 displays the data set for this motor, which was obtained from four different life tests under four different environments, varying motor speed and liquid density. 

Table for pump motor data set

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. 

Reliability plot

Figure 3: Reliability plot at 300 RPM, Density = 1.1 g/ml

Analysis of Degradation Information 
Quantitative accelerated life testing analysis methods can also be used for degradation analyses involving destructive testing, as the following example demonstrates. Suppose that in an effort to study tread wear on a set of tires, four identical vehicles were used on a test track. The vehicles were removed from the track for detailed analysis at 20, 25, 30 and 40 thousand miles. The tires from the vehicles were removed from each vehicle and sent back to the manufacturer for analysis. Table 2 shows the data collected for the tread wear of these tires. 

Table of tire tread wear data

Table 2: Tire tread wear data for four vehicles

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. 

Plot of tread vs. mileage

Figure 4: Tread versus mileage for front tires

Plot of tread vs. mileage

Figure 5: Tread versus mileage for rear tires

Conclusion 
As illustrated by the pump motor and tire tread degradation examples, quantitative accelerated life test (QALT) analysis methods can be applied to solve a variety of non-accelerated testing problems. These methodologies may be appropriate any time additional covariates or explanatory variables are present in the data. ReliaSoft’s ALTA 6 and ALTA 6 PRO software provides the QALT tools necessary to perform this type of analysis. Information about the ALTA 6 software is available on the Web at http://www.ReliaSoft.com/alta/.

 

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