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'''A Logistic Distribution Example'''
#REDIRECT [[Example:_Logistic_Distribution]]
 
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>
<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.
:* 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:
 
[[Image:Logistic Distribution Exmaple 1 Data.png|thumb|center|250px| ]]
 
The computed parameters for maximum likelihood are:
 
::<math>\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:
 
[[Image:Logistic Distribution Exmaple 1 QCP Reliable Life.png|thumb|center|300px| ]]
 
:* 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|300px| ]]

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