Tensile Components Example

A tensile component of a landing gear was put through an accelerated reliability test to determine whether the life goal would be achieved under the designed-in load. Fifteen units, N =15, were tested at three different shock loads. The component was designed for a peak shock load of 50 kips with an estimated return of 10% of the population by 10,000 landings. Using the inverse power law lognormal model, determine whether the design life was met.

Solution to Example 4: Tensile Components Exampls

The data were entered into ALTA, and the following estimates were obtained for the parameters of the IPL-lognormal model:

Std = 0.179080,
K = 8.953055E – 13,
N = 4.638882.

The probability plot at each test stress level (73 kips, 95 kips and 123 kips) was then obtained, as shown next.

In this plot, it can be seen that there is a good agreement between the data and the fitted model. The probability plot at a use stress level of 50 kips is shown next.

Using the use level probability plot, the cycles-to failure for a 10% probability of failure can be estimated. From the plot, this time is estimated to be T(Q = 0.10 = 10%) 12,000 landings.

Another way to obtain life information is by using a life vs. stress plot. Once a life vs. stress plot is selected, the 10% unreliability (probability of failure) line must be plotted. To do this, click Life Lines... in the plot control panel and select the 10% Unreliability box (or enter 10 in one of the boxes and select the box) in the Specify Life Lines window, as shown next.

In the following plot, the 10% unreliability line is plotted (the first line from the left). For a stress of 50 psi (X-axis) and for the 10% unreliability line, the cycles-to-failure can be obtained by reading the value on the Y-axis. Again, T(0.1) 12,000 landings.

However, a more accurate way to obtain such information is by using the Quick Calculation Pad (QCP) in ALTA. Using the QCP, the life for a 10% probability of failure at 50 kips is estimated to be 11,668.73 cycles (or landings), as shown next

The design criterion of 10,000 landings is met.

Example 5: Tensile Components Example Continued

In the tensile components example, it was found that the 10,000 landings life criterion for a 90% reliability was met. However, the estimate of 11,668.73 cycles (or landings) is very close to the requirement. Additionally, this estimate was obtained at the 50% confidence level. In other words, 50% of the time life will be greater than 10,544.899 landings and 50% of the time life will be less. A lower confidence level is thus crucial before any decisions are made. Repeat the calculation of the previous example, this time including a 90% lower 1-sided confidence bound on the estimation.

Solution to Example 5: Tensile Components Example Continued

Using ALTA's QCP, the 90% lower 1-sided confidence bound on the 11,668.73 cycles-to-failure can be obtained.

The 90% lower 1-sided confidence bound is estimated to be 9,680.51 landings. Thus the 10,000 landings criterion is not quite met.