Stress-Strength Analysis in Design for Reliability: Difference between revisions

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'''Using Stress-Strength Analysis to Determine the Required Strength Distribution'''
<noinclude>{{Banner Weibull Examples}}
 
''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.
Assume the stress distribution for a component is known and it is a Weibull distribution with beta=3 and eta=2000. For the current design, the strength distribution is also a Weibull distribution with beta =1.5 and eta=4000.
 
:*Evaluate the current reliability.
:*If the reliability does not meet the target reliability of 90%, use the Target Reliability Parameter Estimator to determine what parameters would be required for the strength distribution in order to meet the specified target.


</noinclude>
<!-- THIS PAGE IS LINKED TO THE WEIBULL++/ALTA8 HELP FILE -->
Assume that the stress distribution for a component is known to be a Weibull distribution with beta = 3 and eta = 2000. For the current design, the strength distribution is also a Weibull distribution with beta =1.5 and eta=4000. Evaluate the current reliability of the component. If the reliability does not meet the target reliability of 90%, determine what parameters would be required for the strength distribution in order to meet the specified target.


'''Solution'''
'''Solution'''


First, we need to create two empty Weibull++ standard folios and enter the distribution parameters for the stress and strength distributions. For example, for the stress distribution, it is:
The following picture shows the stress-strength tool and the calculated reliability of the current design.
 
[[Image: Stress Distribution Example 2.png|thumb|center|400px]]
 
 
Then, following the steps given in [[Stress-Strength Parameter Uncertainty Example| Example 1]], the reliability of the current design is given in the following figure:
 
[[Image: Stress-strength example 2 current reliability.png|thumb|center|400px]]
 
The above result shows that the current reliability is about 74.05%, which is below the target value of 90%. We need to use the '''Target Reliability Parameter Estimator''' to determine the parameter for the strength distribution that would be required to meet the target. Click on the following icon:
 
[[Image:Stress-strength example 2 target R icon.png|thumb|center|400px]]
 
 
Choose to calculate for eta under '''Strength Parameters''', set the Target Reliability to 90%, and click '''Calculate''':
 
[[Image:Stress-strength example 2 Result.png|thumb|center|400px]]


[[Image: Stress-strength example 2 current reliability.png|center|700px]]


The calculated eta is 8192.2385 hours. Click '''Update''' to perform the stress-strength analysis again using the altered parameters for the strength distribution.
The result shows that the current reliability is about 74.0543%, which is below the target value of 90%. We need to use the '''Target Reliability Parameter Estimator''' to determine the parameters for the strength distribution that, when compared against the stress distribution, would result in the target reliability.  


The plot shows the calculated reliability indeed is 90%.  
The following picture shows the Target Reliability Parameter Estimator window. In the '''Strength Parameters''' area, select '''eta'''. Set the Target Reliability to '''90%''' and click '''Calculate'''. The calculated eta is 8192.2385 hours.


[[Image:Stress-strength example 2 Confirmed Result.png|thumb|center|400px]]
[[Image:Stress-strength example 2 Result.png|center|650px]]


Click '''Update''' to perform the stress-strength analysis again using the altered parameters for the strength distribution. The following plot shows that the calculated reliability is 90%. Therefore, in order to meet the reliability requirement, the component must be redesigned such that the eta parameter of the strength distribution is at least 8192.2385 hours.


Therefore, in order to meet the reliability requirement, the component must be redesigned with the eta to be at least 8192.2385 hours.
[[Image:Stress-strength example 2 Confirmed Result.png|center|700px]]

Latest revision as of 18:54, 18 September 2023

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This example appears in the Life data analysis reference.


Assume that the stress distribution for a component is known to be a Weibull distribution with beta = 3 and eta = 2000. For the current design, the strength distribution is also a Weibull distribution with beta =1.5 and eta=4000. Evaluate the current reliability of the component. If the reliability does not meet the target reliability of 90%, determine what parameters would be required for the strength distribution in order to meet the specified target.

Solution

The following picture shows the stress-strength tool and the calculated reliability of the current design.

Stress-strength example 2 current reliability.png

The result shows that the current reliability is about 74.0543%, which is below the target value of 90%. We need to use the Target Reliability Parameter Estimator to determine the parameters for the strength distribution that, when compared against the stress distribution, would result in the target reliability.

The following picture shows the Target Reliability Parameter Estimator window. In the Strength Parameters area, select eta. Set the Target Reliability to 90% and click Calculate. The calculated eta is 8192.2385 hours.

Stress-strength example 2 Result.png

Click Update to perform the stress-strength analysis again using the altered parameters for the strength distribution. The following plot shows that the calculated reliability is 90%. Therefore, in order to meet the reliability requirement, the component must be redesigned such that the eta parameter of the strength distribution is at least 8192.2385 hours.

Stress-strength example 2 Confirmed Result.png
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