Template:Example: Stress-Strength Analysis with Parameter Uncertainty: Difference between revisions
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Add one '''Stress-Strength | Add one '''Stress-Strength''' Folio and choose the stress and strength distribution: | ||
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Revision as of 21:38, 27 February 2012
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.
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:
