|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| '''Stress-Strength Analysis with Parameter Uncertainty'''
| | #REDIRECT [[Stress-Strength_Analysis_in_Design_for_Reliability]] |
| | |
| 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):
| |
| | |
| {| cellspacing="0" border="1" style="margin: 1em auto;" class="wikitable"
| |
| |-
| |
| | align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" | '''Stress: Usage Mileage Distribution'''<br>
| |
| |-
| |
| | align="center" | 10096
| |
| | align="center" | 12405
| |
| |-
| |
| | align="center" | 10469
| |
| | align="center" | 12527
| |
| |-
| |
| | align="center" | 10955
| |
| | align="center" | 12536
| |
| |-
| |
| | align="center" | 11183
| |
| | align="center" | 12595
| |
| |-
| |
| | align="center" | 11391
| |
| | align="center" | 12657
| |
| |-
| |
| | align="center" | 11486
| |
| | align="center" | 13777
| |
| |-
| |
| | align="center" | 11534
| |
| | align="center" | 13862
| |
| |-
| |
| | align="center" | 11919
| |
| | align="center" | 13971
| |
| |-
| |
| | align="center" | 12105
| |
| | align="center" | 14032
| |
| |-
| |
| | align="center" | 12141
| |
| | align="center" | 14138
| |
| |}
| |
| | |
| <br> This table gives the data for the miles-to-failure distribution (strength):
| |
| | |
| {| cellspacing="0" border="1" style="margin: 1em auto;" class="wikitable"
| |
| |-
| |
| | align="center" style="background: none repeat scroll 0% 0% rgb(240, 240, 240);" colspan="2" | '''Strength: Failure Mileage Distribution'''<br>
| |
| |-
| |
| | align="center" | 13507
| |
| | align="center" | 16125
| |
| |-
| |
| | align="center" | 13793
| |
| | align="center" | 16320
| |
| |-
| |
| | align="center" | 13943
| |
| | align="center" | 16327
| |
| |-
| |
| | align="center" | 14017
| |
| | align="center" | 16349
| |
| |-
| |
| | align="center" | 14147
| |
| | align="center" | 16406
| |
| |-
| |
| | align="center" | 14351
| |
| | align="center" | 16501
| |
| |-
| |
| | align="center" | 14376
| |
| | align="center" | 16611
| |
| |-
| |
| | align="center" | 14595
| |
| | align="center" | 16625
| |
| |-
| |
| | align="center" | 14746
| |
| | align="center" | 16670
| |
| |-
| |
| | align="center" | 14810
| |
| | align="center" | 16749
| |
| |-
| |
| | align="center" | 14940
| |
| | align="center" | 16793
| |
| |-
| |
| | align="center" | 14951
| |
| | align="center" | 16862
| |
| |-
| |
| | align="center" | 15104
| |
| | align="center" | 16930
| |
| |-
| |
| | align="center" | 15218
| |
| | align="center" | 16948
| |
| |-
| |
| | align="center" | 15303
| |
| | align="center" | 17024
| |
| |-
| |
| | align="center" | 15311
| |
| | align="center" | 17041
| |
| |-
| |
| | align="center" | 15480
| |
| | align="center" | 17263
| |
| |-
| |
| | align="center" | 15496
| |
| | align="center" | 17347
| |
| |-
| |
| | align="center" | 15522
| |
| | align="center" | 17430
| |
| |-
| |
| | align="center" | 15547
| |
| | align="center" | 17805
| |
| |-
| |
| | align="center" | 15570
| |
| | align="center" | 17884
| |
| |-
| |
| | align="center" | 15975
| |
| | align="center" | 18549
| |
| |-
| |
| | align="center" | 16003
| |
| | align="center" | 18575
| |
| |-
| |
| | align="center" | 16018
| |
| | align="center" | 18813
| |
| |-
| |
| | align="center" | 16052
| |
| | align="center" | 18944
| |
| |}
| |
| | |
| The goal is to estimate the reliability of the component within the warranty period (1 year/15,000 miles).
| |
| | |
| <br> '''Solution'''
| |
| | |
| First, we need to estimate the stress and strength distributions using the above data. The estimated stress distribution is:
| |
| | |
| [[Image:Stress-Strength Example 1 Stress-Distribution.png|thumb|center|250px]]
| |
| | |
| The estimated strength distribution is:
| |
| | |
| [[Image:Stress-Strength Example 1 Strength-Distribution.png|thumb|center|250px]]
| |
| | |
| 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:
| |
| | |
| [[Image:Stress-Strength Example 1 pdf curve.png|thumb|center|250px]]
| |
| | |
| 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:
| |
| | |
| [[Image:Stress-Strength Example 1 Calculation Settings.png|thumb|center|250px]]
| |
| | |
| The calculated results are:
| |
| | |
| [[Image:Stress-Strength Example 1 Calculation Results.png|thumb|center|250px]] | |
| | |
| 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.
| |