Logistic Distribution Example: Difference between revisions
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<noinclude>{{Banner Weibull Examples}} | <noinclude>{{Banner Weibull Examples}} | ||
''This example appears in the [ | ''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.</noinclude> | ||
The lifetime of a mechanical valve is known to follow a logistic distribution. | 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. | ||
{| 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 | |||
|} | |||
* 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? | ||
| Line 26: | Line 37: | ||
Enter the data set in a Weibull++ standard folio, as follows: | Enter the data set in a Weibull++ standard folio, as follows: | ||
[[Image:Logistic Distribution Exmaple 1 Data.png|center| | [[Image:Logistic Distribution Exmaple 1 Data.png|center|650px| ]] | ||
The computed parameters for maximum likelihood are: | The computed parameters for maximum likelihood are: | ||
| Line 33: | 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: | 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|center|500px| ]] | [[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: | 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|center|500px| ]] | [[Image:Logistic Distribution Exmaple 1 QCP Reliability.png|center|500px| ]] | ||
Latest revision as of 21:39, 18 September 2023
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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:
