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 mileage distribution and the strength is the miles-to-failure distribution of the component. The warranty is 1 year or 15,000 miles, whichever is earlier. This table gives the data for the mileage distribution per year (stress):

This table gives the data for the miles-to-failure distribution (strength):

The goal is to 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 distributions using the above data. The estimated stress distribution is:



The estimated strength distribution is:



Then we open the Stress-Strength tool and choose to compare the two data sheets. The following picture shows the pdf curves of the two data sets:



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. This is done by using the following settings in the tool:



The calculated results are:



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.