Logistic Distribution Example
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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:
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:
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:
