Logistic Distribution Example: Difference between revisions

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''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude>
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The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.
<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.
 
{| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"  
|- align="center"
!Data Point Index
!State F or S
!State End Time
|- align="center"
|1 ||F || 8
|- align="center"
|2 ||F || 10
|- align="center"
|3 ||F || 15
|- align="center"
|4 ||F || 17
|- align="center"
|5 ||F || 19
|- align="center"
|6 ||F || 26
|- align="center"
|7 ||F || 27
|- align="center"
|8 ||S || 28
|- align="center"
|9 ||S || 28
|- align="center"
|10 ||S || 28
|}


<center><math>\overset{{}}{\mathop{\text{Table 10}\text{.1 - Times-to-Failure Data with Suspensions}}}\,</math></center>
<center><math>\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></center>
    
    
:* Determine the valve's design life if specifications call for a reliability goal of 0.90.
* 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?
* 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:
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|center|650px| ]]  


The computed parameters for maximum likelihood are:  
The computed parameters for maximum likelihood are:  
Line 32: Line 44:
   & \widehat{\mu }= & 22.34 \\  
   & \widehat{\mu }= & 22.34 \\  
  & \hat{\sigma }= & 6.15   
  & \hat{\sigma }= & 6.15   
\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:


[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png|thumb|center|400px| ]]
The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP 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 Reliable Life.png|center|500px| ]]


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|center|500px| ]]

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This example appears in the Life data analysis reference.

The lifetime of a mechanical valve is known to follow a logistic distribution. 10 units were tested for 28 months and the following months-to-failure data were collected.

Data Point Index State F or S State End Time
1 F 8
2 F 10
3 F 15
4 F 17
5 F 19
6 F 26
7 F 27
8 S 28
9 S 28
10 S 28


  • 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
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