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{{Banner Weibull Examples}}
<noinclude>{{Banner Weibull Examples}}{{Navigation box}}
===Example 1===
''These examples appear in the [[The_Normal_Distribution|Life Data Analysis Reference book]] book.''


<br>
{{Example: Normal General Example (RRX Plot)}}


</noinclude>
The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


===Example 2===


<br>
==Complete Data==
{{Example: Normal General Example (RRX QCP)}}
Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:


:1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
:2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
:3. Obtain the  <math>pdf</math>  plot for the data.
:4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
:5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


===Example 3===
 
'''Solution'''
 
The following figure shows the data as entered in Weibull++, as well as the calculated parameters.
 
 
[[Image:Normal Distribution Example 8 Data.png|center|550px| ]]
 
 
The following figures show the probability plot with the 90% two-sided confidence bounds and the '''pdf''' plot.
 
 
[[Image:Normal Distribution Example 8 Probability Plot.png|center|500px|Probability Plot ]]
 
 
[[Image:Normal Distribution Example 8 pdf Plot.png|center|500px|PDF Plot ]]
 
 
Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.
 
 
[[Image:Normal Distribution Example 9 QCP 1.png|center|550px| ]]
 
 
[[Image:Normal Distribution Example 9 QCP 2.png|center|550px| ]]
 
 
==Example 3==


<br>
<br>

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These examples appear in the Life Data Analysis Reference book book.


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


Template loop detected: Template:Example: Normal General Example (RRX Report)


Example 4


Template loop detected: Template:Example: Normal General Example Interval Data


Example 5


Template loop detected: Template:Example: Normal General Example Complete Data


Example 6


Template loop detected: Template:Example: Normal General Example Suspension Data


Example 7


Template loop detected: Template:Example: Normal General Example All Data Type


Example 4


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


Template loop detected: Template:Example: Normal General Example (RRX Report)


Example 4


Template loop detected: Template:Example: Normal General Example Interval Data


Example 5


Template loop detected: Template:Example: Normal General Example Complete Data


Example 6


Template loop detected: Template:Example: Normal General Example Suspension Data


Example 7


Template loop detected: Template:Example: Normal General Example All Data Type


Example 5


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


Template loop detected: Template:Example: Normal General Example (RRX Report)


Example 4


Template loop detected: Template:Example: Normal General Example Interval Data


Example 5


Template loop detected: Template:Example: Normal General Example Complete Data


Example 6


Template loop detected: Template:Example: Normal General Example Suspension Data


Example 7


Template loop detected: Template:Example: Normal General Example All Data Type


Example 6


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


Template loop detected: Template:Example: Normal General Example (RRX Report)


Example 4


Template loop detected: Template:Example: Normal General Example Interval Data


Example 5


Template loop detected: Template:Example: Normal General Example Complete Data


Example 6


Template loop detected: Template:Example: Normal General Example Suspension Data


Example 7


Template loop detected: Template:Example: Normal General Example All Data Type


Example 7


The following examples illustrate the different types of life data that can be analyzed in Weibull++ using the Normal distribution.


Complete Data

Six units are tested to failure. The following hours-to-failure data are obtained: 12125, 11260, 12080, 12825, 13550 and 14670 hours. Assuming that the data are normally distributed, do the following:

1. Find the parameters for the data set, using the Rank Regression on X (RRX) parameter estimation method
2. Obtain the probability plot for the data with 90%, two-sided Type 1 confidence bounds.
3. Obtain the [math]\displaystyle{ pdf }[/math] plot for the data.
4. Using the Quick Calculation Pad, determine the reliability for a mission of 11,000 hours, as well as the upper and lower two-sided 90% confidence limit on this reliability.
5. 2. Using the Quick Calculation Pad, determine the MTTF, as well as the upper and lower two-sided 90% confidence limit on this MTTF.


Solution

The following figure shows the data as entered in Weibull++, as well as the calculated parameters.


Normal Distribution Example 8 Data.png


The following figures show the probability plot with the 90% two-sided confidence bounds and the pdf plot.


Probability Plot


PDF Plot


Both the reliability and MTTF can be easily obtained from the QCP. The QCP, with results, for both cases is shown in the next two figures.


Normal Distribution Example 9 QCP 1.png


Normal Distribution Example 9 QCP 2.png


Example 3


Template loop detected: Template:Example: Normal General Example (RRX Report)


Example 4


Template loop detected: Template:Example: Normal General Example Interval Data


Example 5


Template loop detected: Template:Example: Normal General Example Complete Data


Example 6


Template loop detected: Template:Example: Normal General Example Suspension Data


Example 7


Template loop detected: Template:Example: Normal General Example All Data Type

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