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| '''Stress-Strength Analysis with Parameter Uncertainty'''
| | [[Category: For Deletion]] |
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| 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):
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| {| cellspacing="0" border="1" style="margin: 1em auto;" class="wikitable"
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| | align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" | '''Stress: Usage Mileage Distribution'''<br>
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| |-
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| | align="center" | 10096
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| | align="center" | 12405
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| |-
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| | align="center" | 10469
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| | align="center" | 12527
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| |-
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| | align="center" | 10955
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| | align="center" | 12536
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| |-
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| | align="center" | 11183
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| | align="center" | 12595
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| |-
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| | align="center" | 11391
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| | align="center" | 12657
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| |-
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| | align="center" | 11486
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| | align="center" | 13777
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| |-
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| | align="center" | 11534
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| | align="center" | 13862
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| |-
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| | align="center" | 11919
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| | align="center" | 13971
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| |-
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| | align="center" | 12105
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| | align="center" | 14032
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| |-
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| | align="center" | 12141
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| | align="center" | 14138
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| |}
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| <br> This table gives the data for the miles-to-failure distribution (strength):
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| {| cellspacing="0" border="1" style="margin: 1em auto;" class="wikitable"
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| | align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" | '''Strength: Failure Mileage Distribution'''<br>
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| | align="center" | 13507
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| | align="center" | 16125
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| | align="center" | 13793
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| | align="center" | 16320
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| |-
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| | align="center" | 13943
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| | align="center" | 16327
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| |-
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| | align="center" | 14017
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| | align="center" | 16349
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| |-
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| | align="center" | 14147
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| | align="center" | 16406
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| |-
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| | align="center" | 14351
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| | align="center" | 16501
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| |-
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| | align="center" | 14376
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| | align="center" | 16611
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| |-
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| | align="center" | 14595
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| | align="center" | 16625
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| |-
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| | align="center" | 14746
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| | align="center" | 16670
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| |-
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| | align="center" | 14810
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| | align="center" | 16749
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| |-
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| | align="center" | 14940
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| | align="center" | 16793
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| |-
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| | align="center" | 14951
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| | align="center" | 16862
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| |-
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| | align="center" | 15104
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| | align="center" | 16930
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| |-
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| | align="center" | 15218
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| | align="center" | 16948
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| |-
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| | align="center" | 15303
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| | align="center" | 17024
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| |-
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| | align="center" | 15311
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| | align="center" | 17041
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| |-
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| | align="center" | 15480
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| | align="center" | 17263
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| |-
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| | align="center" | 15496
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| | align="center" | 17347
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| |-
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| | align="center" | 15522
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| | align="center" | 17430
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| |-
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| | align="center" | 15547
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| | align="center" | 17805
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| |-
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| | align="center" | 15570
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| | align="center" | 17884
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| |-
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| | align="center" | 15975
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| | align="center" | 18549
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| |-
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| | align="center" | 16003
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| | align="center" | 18575
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| |-
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| | align="center" | 16018
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| | align="center" | 18813
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| |-
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| | align="center" | 16052
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| | align="center" | 18944
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| |}
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| The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).
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| <br> '''Solution'''
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| First, we need to estimate the stress and strength distributions using the above data. The estimated stress distribution is:
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| [[Image:Stress-Strength Example 1 Stress-Distribution.png|thumb|center|250px]]
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| The estimated strength distribution is:
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| [[Image:Stress-Strength Example 1 Strength-Distribution.png|thumb|center|250px]]
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| 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:
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| [[Image:Stress-Strength Example 1 pdf curve.png|thumb|center|250px]]
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| 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:
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| [[Image:Stress-Strength Example 1 Calculation Settings.png|thumb|center|250px]]
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| The calculated results are:
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| [[Image:Stress-Strength Example 1 Calculation Results.png|thumb|center|250px]] | |
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| 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.
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