Template:Example: Stress-Strength Analysis with Parameter Uncertainty

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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.

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


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

Strength: Failure 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

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.

Stress-Strength Example 1 Stress-Distribution.png

The estimated strength distribution is given as:

Stress-Strength Example 1 Strength-Distribution.png

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

Stress-Strength Example 1 Choose Folios.png

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

Stress-Strength Example 1 pdf curve.png

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:

Stress-Strength Example 1 Calculation Settings.png

The calculated results are given in below:

Stress-Strength Example 1 Calculation Results.png