Logistic Distribution Example: Difference between revisions

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''This example appears in the [[The_Logistic_Distribution#General_Example|Life Data Analysis Reference book]]''.</noinclude>
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<br>The lifetime of a mechanical valve is known to follow a logistic distribution. Ten units were tested for 28 months and the following months-to-failure data was collected.


<center><math>\overset{{}}{\mathop{\text{Table 10}\text{.1 - Times-to-Failure Data with Suspensions}}}\,</math></center>
The lifetime of a mechanical valve is known to follow a logistic distribution. Ten units were tested for 28 months and the following months-to-failure data was collected.
 
 
<center><math>\overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\,</math></center>
<center><math>\begin{matrix}
<center><math>\begin{matrix}
   \text{Data Point Index} & \text{State F or S} & \text{State End Time}  \\
   \text{Data Point Index} & \text{State F or S} & \text{State End Time}  \\
Line 20: Line 20:
\end{matrix}</math></center>
\end{matrix}</math></center>
    
    
:* Determine the valve's design life if specifications call for a reliability goal of 0.90.
:* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?


This data set can be entered into Weibull++ as follows:
* Determine the valve's design life if specifications call for a reliability goal of 0.90.
* The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?
 
 
Enter the data set in a Weibull++ standard folio, as follows:


[[Image:Logistic Distribution Exmaple 1 Data.png|thumb|center|400px| ]]  
[[Image:Logistic Distribution Exmaple 1 Data.png|thumb|center|400px| ]]  
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\end{align}</math>
\end{align}</math>


:* The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:  
 
The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:  


[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png|thumb|center|400px| ]]  
[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png|thumb|center|400px| ]]  


:* The probability, along with 90% two sided confidence bounds, that the pump fails due to a valve failure during the first month is obtained as follows:
 
The probability, along with 90% two sided confidence bounds, that the pump fails due to a valve failure during the first month is obtained as follows:




[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png|thumb|center|400px| ]]
[[Image:Logistic Distribution Exmaple 1 QCP Reliability.png|thumb|center|400px| ]]

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This example appears in the Life Data Analysis Reference book.

The lifetime of a mechanical valve is known to follow a logistic distribution. Ten units were tested for 28 months and the following months-to-failure data was collected.


[math]\displaystyle{ \overset{{}}{\mathop{\text{Times-to-Failure Data with Suspensions}}}\, }[/math]
[math]\displaystyle{ \begin{matrix} \text{Data Point Index} & \text{State F or S} & \text{State End Time} \\ \text{1} & \text{F} & \text{8} \\ \text{2} & \text{F} & \text{10} \\ \text{3} & \text{F} & \text{15} \\ \text{4} & \text{F} & \text{17} \\ \text{5} & \text{F} & \text{19} \\ \text{6} & \text{F} & \text{26} \\ \text{7} & \text{F} & \text{27} \\ \text{8} & \text{S} & \text{28} \\ \text{9} & \text{S} & \text{28} \\ \text{10} & \text{S} & \text{28} \\ \end{matrix} }[/math]


  • Determine the valve's design life if specifications call for a reliability goal of 0.90.
  • The valve is to be used in a pumping device that requires 1 month of continuous operation. What is the probability of the pump failing due to the valve?


Enter the data set in a Weibull++ standard folio, as follows:

Logistic Distribution Exmaple 1 Data.png

The computed parameters for maximum likelihood are:

[math]\displaystyle{ \begin{align} & \widehat{\mu }= & 22.34 \\ & \hat{\sigma }= & 6.15 \end{align} }[/math]


The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:

Logistic Distribution Exmaple 1 QCP Reliable Life.png


The probability, along with 90% two sided confidence bounds, that the pump fails due to a valve failure during the first month is obtained as follows:


Logistic Distribution Exmaple 1 QCP Reliability.png