Template:Example: Stress-Strength Analysis with Parameter Uncertainty

Stress-Strength Analysis with Parameter Uncertainty

Assume we are going to use stress-strength analysis to estimate the reliability of a component used in a vehicle. The stress is the usage milage distribution and the strength is the failure mile distribution of the component. The warranty is 1 year and 15,000 miles, which is earlier. The milage distribution per year is given the table below.

The strength distribution or the failure mile distribution is given in the next table:

Please estimate the reliability of the component within the warranty period (1 year/15,000 miles).

Solution

First, we need to estimate the stress and strength distribution using the above data. The estimated stress distribution is given in the figure below.



The estimated strength distribution is given as:



Add one Stress-Strength Folio and choose the stress and strength distribution:



The stress-strength tool shows the pdf of the selected data folio. The pdf cuvers are given in the below figure:



Since the warranty is 1 year/15,000 miles, all the vehicles with mileage larger than 15,000 should not be considered in the calculation. Therefore, the conditional stress distribution conditioning on the mileage less than 15,000 should be used. This is done by using the following settings in the stress-strength calculation:



The calculated results are given in below:



The estimated reliability for vehicles less than 15,000 miles per year is 98.84%. The associated confidence bounds are estimated from the variance of the distribution parameters. With larger samples for the stress and strength data, the width of the bounds will be narrower.