Template:Example: Stress-Strength Analysis with Parameter Uncertainty: Difference between revisions

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'''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 failure mileage distribution of the component. The warranty is 1 year or 15,000 miles, whichever is earlier. The table below gives the mileage distribution per year.
 
{| border="1" class="wikitable" style="margin: 1em auto 1em auto"
| align="center" style="background:#f0f0f0;"|'''Stress: Milage Distribution'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| 10096||12405
|-
| 10469||12527
|-
| 10955||12536
|-
| 11183||12595
|-
| 11391||12657
|-
| 11486||13777
|-
| 11534||13862
|-
| 11919||13971
|-
| 12105||14032
|-
| 12141||14138
|-
|
|}
 
 
The next table gives the strength distribution or the failure mileage distribution.
 
{|border="1" class="wikitable" style="margin: 1em auto 1em auto"
| align="center" style="background:#f0f0f0;"|'''Strength: Failure Distribution'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| 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
|-
|
|}
 
The goal is to 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 distributions using the above data. The estimated stress distribution is:
 
[[Image: Stress-Strength Example 1 Stress-Distribution.png|thumb|center|400px]]
 
The estimated strength distribution is:
 
[[Image: Stress-Strength Example 1 Strength-Distribution.png|thumb|center|400px]]
 
Add one '''Stress-Strength''' folio and choose the stress and strength distributions:
 
[[Image: Stress-Strength Example 1 Choose Folios.png|thumb|center|400px]]
 
The stress-strength tool shows the ''pdf'' of the selected data folio. The ''pdf'' curves are shown next:
 
[[Image: Stress-Strength Example 1 pdf curve.png|thumb|center|400px]]
 
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:
 
[[Image: Stress-Strength Example 1 Calculation Settings.png|thumb|center|400px]]
 
The calculated results are given in below:
 
[[Image: Stress-Strength Example 1 Calculation Results.png|thumb|center|400px]]
 
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.

Latest revision as of 06:44, 15 August 2012

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