Reliability HotWire

Issue 50, April 2005

Reliability Basics
Introduction to the Temperature-Humidity Relationship

When performing accelerated life testing analysis, a life distribution and a life-stress relationship are required. The temperature-humidity (T-H) relationship, a variation of the Eyring relationship, has been proposed for predicting the life at use conditions when temperature and humidity are the accelerated stresses in a test. This combination model is given by:

 (1)

where:

• is one of the three parameters to be determined,
• b is the second of the three parameters to be determined (also known as the activation energy for humidity),
• A is a constant and the third of the three parameters to be determined,
• U is the relative humidity (decimal or percentage),

• V is temperature (in absolute units).

The T-H relationship can be linearized and plotted on a life vs. stress plot. The relationship is linearized by taking the natural logarithm of both sides in Eqn. (1):

 (2)

Since life is now a function of two stresses, a life vs. stress plot can only be obtained by keeping one of the two stresses constant and varying the other one. Doing so will yield a straight line as described by Eqn. (2), where the term for the stress, which is kept at a fixed value, becomes another constant (in addition to the ln (A) constant). In Figures 1 and 2 below, data obtained from a temperature and humidity test were analyzed and plotted on Arrhenius paper. In Figure 1, life is plotted versus temperature with relative humidity held at a fixed value. In Figure 2, life is plotted versus relative humidity with temperature held at a fixed value.

Fig. 1: Life vs. temperature plot, for a fixed relative humidity

Fig. 2: Life vs. relative humidity plot, for a fixed temperature

Note that the life vs. stress plots in both Figures 1 and 2 are plotted on a log-reciprocal scale. Also note that the points shown in these plots represent the life characteristics at the test stress levels (the data points were fitted to a Weibull distribution, thus the points represent the scale parameter, ). For example, the points shown in Figure 1 represent at each of the test temperature levels (two temperature levels were considered in this test).

A Look at the Parameters and b

Depending on which stress type is kept constant, it can be seen from Eqn. (2) that either the parameter or the parameter b is the slope of the resulting line. If, for example, the humidity is kept constant (Figure 1) then is the slope of the life line in a life vs. temperature plot. The steeper the slope, the greater the dependency of product life on the temperature. In other words,   is a measure of the effect that temperature has on the life and b is a measure of the effect that relative humidity has on the life. The larger the value of , the higher the dependency of the life on the temperature. Similarly, the larger the value of b, the higher the dependency of the life on the humidity. For example, it can be seen by comparing Figures 1 and 2 that, for this data, temperature has a greater effect on the life than humidity.

Additional information on quantitative accelerated life testing analysis, the temperature-humidity relationship and ReliaSoft's ALTA can be found at http://ALTA.ReliaSoft.com.