# Logistic Distribution Example

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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. 10 units were tested for 28 months and the following months-to-failure data were collected.

- 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:

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:

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: