# Stress-Strength Parameter Uncertainty Example

This example appears in the Life Data Analysis Reference book.

Assume that 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. The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).

The following table gives the data for the mileage distribution per year (stress):

 Stress: Usage Mileage Distribution 10096 12405 10469 12527 10955 12536 11183 12595 11391 12657 11486 13777 11534 13862 11919 13971 12105 14032 12141 14138

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

 Strength: Failure Mileage Distribution 13507 16125 13793 16320 13943 16327 14017 16349 14147 16406 14351 16501 14376 16611 14595 16625 14746 16670 14810 16749 14940 16793 14951 16862 15104 16930 15218 16948 15303 17024 15311 17041 15480 17263 15496 17347 15522 17430 15547 17805 15570 17884 15975 18549 16003 18575 16018 18813 16052 18944

Solution

First, estimate the stress and strength distributions using the given data. Enter the stress and strength data into two separate data sheets and analyze each data sheet using the lognormal distribution and MLE analysis method. The parameters of the stress distribution are estimated to be log-mean = 9.411844 and log-std = 0.098741.

The parameters of the strength distribution are estimated to be log-mean = 9.681503 and log-std = 0.083494.

Next, 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. To do this, go to the Setup page of the control panel and select the Override auto-calculated limits check box. Set the value of the upper limit to 15,000 as shown next.

Recalculate the results. 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.