Warranty Data Analysis Times-to-Failure Format with Plot Example: Difference between revisions

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<noinclude>{{Banner Weibull Examples}}
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The warranty analysis folio includes different formats to accommodate several types of claims data. The Times-to-Failure format is the simplest format because it is similar to a Weibull++ standard folio, but with added functionality to generate forecasts.
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<br>
There are several different folio formats in Warranty Analysis. The Times-to-Failure format is the simplest one. It is like the Weibull++ standard folio, but you can use it to generate forecast.


Assume we have the following information of a product.
</noinclude>'''Times-to-Failure Format Warranty Analysis'''


'''Times-to-Failure Data:'''
Assume that we have the following information for a given product.


{|  border="1" class="wikitable" style="margin: 1em auto 1em auto"
{|  border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+ '''Times-to-Failure Data '''
|-
| align="center" style="background:#f0f0f0;"|'''Number in State'''
| align="center" style="background:#f0f0f0;"|'''Number in State'''
| align="center" style="background:#f0f0f0;"|'''State F or S'''
| align="center" style="background:#f0f0f0;"|'''State F or S'''
| align="center" style="background:#f0f0f0;"|'''State End Time'''
| align="center" style="background:#f0f0f0;"|'''State End Time (Hr)'''
|-
|-
| 2||F||100
| 2||F||100
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|}
|}


'''Future Sales:'''
 
{| | border="1" class="wikitable" style="margin: 1em auto 1em auto"
{| | border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+ '''Future Sales'''
|-
| align="center" style="background:#f0f0f0;"|'''Quantity In-Service'''
| align="center" style="background:#f0f0f0;"|'''Quantity In-Service'''
| align="center" style="background:#f0f0f0;"|'''Time (Hr)'''
| align="center" style="background:#f0f0f0;"|'''Time (Hr)'''
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|}
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Use the time-to-failure warranty analysis folio to analyze the data and generate a forecast for future returns.


We can use Warranty Analysis to analyze the above data and generate forecast for future returns.
'''Solution'''
 
 
'''Solution.'''
 
'''Step 1:''' Create a Warranty folio by selecting the '''I want to enter data in the times-to-failure format'''.
 
[[image: Warranty Select Data Type.png|thumbe|center|400px]]
 
'''Step 2:''' Enter the above data into the Data and Future Sales sheet.
 
'''Step 3:''' Use the following setting to calculate the data. The results are:


[[image: Warranty Select Data Result.png|thumbe|center]]
Create a warranty analysis folio and select the times-to-failure format. Enter the data from the tables in the '''Data''' and '''Future Sales''' sheets, and then analyze the data using the 2P-Weibull distribution and RRX analysis method. The parameters are estimated to be beta = 3.199832 and eta=814.293442.  


'''Step 4:''' Click on the Forecast button to get the following window.
Click the '''Forecast''' icon on the control panel. In the Forecast Setup window, set the forecast to start on the '''100'''th hour and set the number of forecast periods to '''5'''. Set the increment (length of each period) to '''100''', as shown next.  


[[image: Warranty Select Data Forecast setup.png|thumbe|center]]
[[image: Warranty Select Data Forecast setup.png|center]]


Click on OK. The predicted future returns are:
Click '''OK'''. A Forecast sheet will be created, with the following predicted future returns.


[[image: Warranty Select Data Forecast Result.png|thumbe|center|600px]]
[[image: Warranty Select Data Forecast Result.png|center|800px]]


We will use the first row to explain how the forecast for each cell is calculated. For example, there are 1500 units with current age of 200. The probability of failure in next 100 hours can be calculated in QCP as:
We will use the first row to explain how the forecast for each cell is calculated. For example, there are 1,500 units with a current age of 200 hours. The probability of failure in the next 100 hours can be calculated in the QCP, as follows.


[[image: Warranty Select QCP Result.png|thumbe|center|400px]]
[[image: Warranty Select QCP Result.png|center|400px]]


Therefore, the predicted number of failures for the first 100 hours is:
Therefore, the predicted number of failures for the first 100 hours is:


::<math>1500\times 0.02932968=43.99452</math>
::<math>1500\times 0.02932968=43.99452\,\!</math>


This is the same as the result given in the forecast folio (the 3rd cell in the first row) in Warranty analysis. The bounds and the values in other cells can be calculated similarly.  
This is identical to the result given in the Forecast sheet (shown in the 3rd cell in the first row) of the analysis. The bounds and the values in other cells can be calculated similarly.  


All the plots in the standard folio are available in Warranty Analysis, such as the probability plot, Reliability plot, etc. One additional plot in Warranty Analysis is the “Expected Failures” plot. It is given in below.
All the plots that are available for the standard folio are also available in the warranty analysis, such as the Probability plot, Reliability plot, etc. One additional plot in warranty analysis is the Expected Failures plot, which shows the expected number of failures over time. The following figure shows the Expected Failures plot of the example, with confidence bounds.


[[image: Warranty Select Expected Failure Plot.png|thumbe|center|400px]]
[[image: Warranty Select Expected Failure Plot.png|center|550px]]

Latest revision as of 21:48, 26 September 2012

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The warranty analysis folio includes different formats to accommodate several types of claims data. The Times-to-Failure format is the simplest format because it is similar to a Weibull++ standard folio, but with added functionality to generate forecasts.


Times-to-Failure Format Warranty Analysis

Assume that we have the following information for a given product.

Times-to-Failure Data
Number in State State F or S State End Time (Hr)
2 F 100
3 F 125
5 F 175
1500 S 200


Future Sales
Quantity In-Service Time (Hr)
500 200
400 300
100 500

Use the time-to-failure warranty analysis folio to analyze the data and generate a forecast for future returns.

Solution

Create a warranty analysis folio and select the times-to-failure format. Enter the data from the tables in the Data and Future Sales sheets, and then analyze the data using the 2P-Weibull distribution and RRX analysis method. The parameters are estimated to be beta = 3.199832 and eta=814.293442.

Click the Forecast icon on the control panel. In the Forecast Setup window, set the forecast to start on the 100th hour and set the number of forecast periods to 5. Set the increment (length of each period) to 100, as shown next.

Warranty Select Data Forecast setup.png

Click OK. A Forecast sheet will be created, with the following predicted future returns.

Warranty Select Data Forecast Result.png

We will use the first row to explain how the forecast for each cell is calculated. For example, there are 1,500 units with a current age of 200 hours. The probability of failure in the next 100 hours can be calculated in the QCP, as follows.

Warranty Select QCP Result.png

Therefore, the predicted number of failures for the first 100 hours is:

[math]\displaystyle{ 1500\times 0.02932968=43.99452\,\! }[/math]

This is identical to the result given in the Forecast sheet (shown in the 3rd cell in the first row) of the analysis. The bounds and the values in other cells can be calculated similarly.

All the plots that are available for the standard folio are also available in the warranty analysis, such as the Probability plot, Reliability plot, etc. One additional plot in warranty analysis is the Expected Failures plot, which shows the expected number of failures over time. The following figure shows the Expected Failures plot of the example, with confidence bounds.

Warranty Select Expected Failure Plot.png