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| '''A Logistic Distribution Example'''
| | #REDIRECT [[Example:_Logistic_Distribution]] |
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| 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.
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| <center><math>\overset{{}}{\mathop{\text{Table 10}\text{.1 - Times-to-Failure Data with Suspensions}}}\,</math></center>
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| <center><math>\begin{matrix}
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| \text{Data Point Index} & \text{State F or S} & \text{State End Time} \\
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| \text{1} & \text{F} & \text{8} \\
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| \text{2} & \text{F} & \text{10} \\
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| \text{3} & \text{F} & \text{15} \\
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| \text{4} & \text{F} & \text{17} \\
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| \text{5} & \text{F} & \text{19} \\
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| \text{6} & \text{F} & \text{26} \\
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| \text{7} & \text{F} & \text{27} \\
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| \text{8} & \text{S} & \text{28} \\
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| \text{9} & \text{S} & \text{28} \\
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| \text{10} & \text{S} & \text{28} \\
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| \end{matrix}</math></center>
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| :• Determine the valve's design life if specifications call for a reliability goal of 0.90.
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| :• 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?
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| This data set can be entered into Weibull++ as follows:
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| [[Image:sof-folio.png|thumb|center|400px| ]] | |
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| The computed parameters for maximum likelihood are:
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| ::<math>\begin{align}
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| & \widehat{\mu }= & 22.34 \\
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| & \hat{\sigma }= & 6.15
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| \end{align}</math>
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| :• The valve's design life, along with 90% two sided confidence bounds, can be obtained using the QCP as follows:
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| [[Image:ldaLD10.6.gif|thumb|center|300px| ]]
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| :• 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:
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| [[Image:ldaLD10.7.gif|thumb|center|300px| ]]
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