Warranty Analysis Non-Homogeneous Data Example: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(12 intermediate revisions by 4 users not shown)
Line 1: Line 1:
'''Warranty Analysis Non-Homogeneous Data Example'''
<noinclude>{{Banner Weibull Examples}}
''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.


A company keeps track of its production and returns. The company uses the '''Dates of Failure''' format to record the data. For the product in question, three versions (A, B and C) have been produced and put in service.


The in-service data is as follows (using the US date format of Month/Day/Year):
</noinclude>'''Warranty Analysis Non-Homogeneous Data Example'''


A company keeps track of its production and returns. The company uses the dates of failure format to record the data. For the product in question, three versions (A, B and C) have been produced and put in service. The in-service data is as follows (using the Month/Day/Year date format):


<center><math>\begin{matrix}
<center><math>\begin{matrix}
Line 26: Line 27:
   \text{1300} & \text{6/1/2005} & \text{Model C}  \\
   \text{1300} & \text{6/1/2005} & \text{Model C}  \\
   \text{1400} & \text{8/26/2005} & \text{Model C}  \\
   \text{1400} & \text{8/26/2005} & \text{Model C}  \\
\end{matrix}</math></center>
\end{matrix}\,\!</math></center>


Furthermore, the following sales are forecast:  
Furthermore, the following sales are forecast:  


<center><math>\begin{matrix}
<center><math>\begin{matrix}
Line 39: Line 39:
   \text{1300} & \text{9/27/2006} & \text{Model C}  \\
   \text{1300} & \text{9/27/2006} & \text{Model C}  \\
   \text{1250} & \text{11/26/2006} & \text{Model C}  \\
   \text{1250} & \text{11/26/2006} & \text{Model C}  \\
\end{matrix}</math></center>
\end{matrix}\,\!</math></center>
 
The return data are as follows. Note that in order to identify which lot each unit comes from and be able to compute its time-in-service, each return (failure) includes a return date, the date of when it was put in service and the Model (ID).


The return data are as follows. Note that in order to identify which lot each unit comes from, and to be able to compute its time-in-service, each return (failure) includes a return date, the date of when it was put in service and the model ID.


<center><math>\begin{matrix}
<center><math>\begin{matrix}
Line 69: Line 68:
   \text{44} & \text{1/26/2006} & \text{6/1/2005}  & \text{Model C} \\
   \text{44} & \text{1/26/2006} & \text{6/1/2005}  & \text{Model C} \\
   \text{26} & \text{1/26/2006} & \text{8/26/2005} & \text{Model C}  \\
   \text{26} & \text{1/26/2006} & \text{8/26/2005} & \text{Model C}  \\
   \end{matrix}</math></center>
   \end{matrix}\,\!</math></center>
 


Assuming that the above information is as of 5/1/2006,  analyze the data using the lognormal as the assumed distribution and MLE as the analysis method, for all models (Model A, Model B, Model C), and provide a return forecast for the next ten months.
Assuming that the given information is current as of 5/1/2006,  analyze the data using the lognormal distribution and MLE analysis method for all models (Model A, Model B, Model C), and provide a return forecast for the next ten months.
   
   
'''Solution'''
'''Solution'''


Create a warranty folio by clicking on Project and choosing Add Specialized Folio and then selecting Add Warranty. In the New Warranty Folio Setup window, choose ''I want to enter data in dates of failure format''.
Create a warranty analysis folio and select the dates of failure format. Enter the data from the tables in the '''Sales''', '''Returns''' and '''Future Sales''' sheets. On the control panel, select the '''Use Subsets''' check box, as shown next. This allows the software to separately analyze each subset of data. Use the drop-down list to switch between subset IDs and alter the analysis settings (use the lognormal distribution and MLE analysis method for all models).  
 
[[Image:dates-of-failurewarranty.png|thumb|center|400px| ]]
 
The return data are entered as follows:
 
[[Image:Non-Homogeneous Return Data.PNG|thumb|center|400px| ]]


The future sales data are entered as follows (note that the Use Subsets check box should be checked):
[[Image:Non-Homogeneous End Date.PNG|center|250px| ]]  
 
[[Image:Non-Homogeneous Future Sales Data.PNG|thumb|center|400px| ]]
 
Under the Analysis tab, set the Calculations End Date to (5/1/2006) as shown next:
 
[[Image:Non-Homogeneous End Date.PNG|thumb|center|400px| ]]  
 
The calculated parameters, assuming a lognormal distribution and using MLE as the analysis method, are:


In the '''End of Observation Period''' field, enter '''5/1/2006''', and then calculate the parameters. The results are:


<center><math>\begin{matrix}
<center><math>\begin{matrix}
Line 108: Line 92:
   {{{\hat{\sigma }}}_{T}}= & \text{1}\text{.92}  \\
   {{{\hat{\sigma }}}_{T}}= & \text{1}\text{.92}  \\
\end{matrix}  \\
\end{matrix}  \\
\end{matrix}</math></center>
\end{matrix}\,\!</math></center>
 
Note that in this example, the same distribution type and analysis method were assumed for each of the product models. If desired, different distribution types, analysis methods, confidence bounds methods, etc., can be assumed for each IDs.
 
To obtain the expected failures for the next 10 months, click the Generate Forecast button.
 
[[Image:forcast.png|thumb|center|400px ]]
 
OR:


[[Image:generateforcast.png|thumb|center|400px ]]
Note that in this example, the same distribution and analysis method were assumed for each of the product models. If desired, different distribution types, analysis methods, confidence bounds methods, etc., can be assumed for each IDs.


and enter the Start date of 5/2/2006, the Number of Periods as 10, and the Increment number (1) in Months (selected from the drop-down box), as shown next:
To obtain the expected failures for the next 10 months, click the '''Generate Forecast''' icon. In the Forecast Setup window, set the forecast to start on '''May 2, 2006''' and set the number of forecast periods to '''10'''. Set the increment (length of each period) to '''1 Month''', as shown next.


[[Image:Non-Homogeneous Forecast Setup.PNG|thumb|center|400px| ]]  
[[Image:Non-Homogeneous Forecast Setup.PNG|center|450px| ]]  


The forecast results are then displayed in a new sheet called Forecast. Part of the forecast table is shown next.
Click '''OK'''. A Forecast sheet will be created, with the predicted future returns. The following figure shows part of the Forecast sheet.


[[Image:Non-Homogeneous Forecast Data.PNG|thumb|center|400px| ]]  
[[Image:Non-Homogeneous Forecast Data.PNG|center|550px| ]]  


A summary of the analysis can also be obtained by clicking on the Show Analysis Summary (...). The summary of the forecasted returns is as follows:
To view a summary of the analysis, click the '''Show Analysis Summary (...)''' button. The following figure shows the summary of the forecasted returns.


[[Image:Non-Homogeneous Analysis Summary.PNG|thumb|center|400px| ]]  
[[Image:Non-Homogeneous Analysis Summary.PNG|center|450px| ]]  


The results can also be seen graphically in the following plot. This is a plot of the expected failures (in percent).
Click the '''Plot''' icon and choose the '''Expected Failures''' plot. The plot displays the predicted number of returns for each month, as shown next.  


[[Image:Non-Homogeneous Expected Failure.PNG|thumb|center|400px| ]]
[[Image:Non-Homogeneous Expected Failure.PNG|center|550px| ]]

Latest revision as of 18:54, 18 September 2023

Weibull Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at Weibull examples and Weibull reference examples.




This example appears in the Life data analysis reference.


Warranty Analysis Non-Homogeneous Data Example

A company keeps track of its production and returns. The company uses the dates of failure format to record the data. For the product in question, three versions (A, B and C) have been produced and put in service. The in-service data is as follows (using the Month/Day/Year date format):

[math]\displaystyle{ \begin{matrix} Quantity In-Service & Date of In-Service & ID \\ \text{400} & \text{1/1/2005} & \text{Model A} \\ \text{500} & \text{1/31/2005} & \text{Model A} \\ \text{500} & \text{5/1/2005} & \text{Model A} \\ \text{600} & \text{5/31/2005} & \text{Model A} \\ \text{550} & \text{6/30/2005} & \text{Model A} \\ \text{600} & \text{7/30/2005} & \text{Model A} \\ \text{800} & \text{9/28/2005} & \text{Model A} \\ \text{200} & \text{1/1/2005} & \text{Model B} \\ \text{350} & \text{3/2/2005} & \text{Model B} \\ \text{450} & \text{4/1/2005} & \text{Model B} \\ \text{300} & \text{6/30/2005} & \text{Model B} \\ \text{200} & \text{8/29/2005} & \text{Model B} \\ \text{350} & \text{10/28/2005} & \text{Model B} \\ \text{1100} & \text{2/1/2005} & \text{Model C} \\ \text{1200} & \text{3/27/2005} & \text{Model C} \\ \text{1200} & \text{4/25/2005} & \text{Model C} \\ \text{1300} & \text{6/1/2005} & \text{Model C} \\ \text{1400} & \text{8/26/2005} & \text{Model C} \\ \end{matrix}\,\! }[/math]

Furthermore, the following sales are forecast:

[math]\displaystyle{ \begin{matrix} Number & Date & ID \\ \text{400} & \text{6/27/2006} & \text{Model A} \\ \text{500} & \text{8/26/2006} & \text{Model A} \\ \text{550} & \text{10/26/2006} & \text{Model A} \\ \text{1200} & \text{7/25/2006} & \text{Model C} \\ \text{1300} & \text{9/27/2006} & \text{Model C} \\ \text{1250} & \text{11/26/2006} & \text{Model C} \\ \end{matrix}\,\! }[/math]

The return data are as follows. Note that in order to identify which lot each unit comes from, and to be able to compute its time-in-service, each return (failure) includes a return date, the date of when it was put in service and the model ID.

[math]\displaystyle{ \begin{matrix} Quantity Returned & Date of Return & Date In-Service & ID \\ \text{12} & \text{1/31/2005} & \text{1/1/2005} & \text{Model A} \\ \text{11} & \text{4/1/2005} & \text{1/31/2005} & \text{Model A} \\ \text{7} & \text{7/22/2005} & \text{5/1/2005} & \text{Model A} \\ \text{8} & \text{8/27/2005} & \text{5/31/2005} & \text{Model A} \\ \text{12} & \text{12/27/2005} & \text{5/31/2005} & \text{Model A} \\ \text{13} & \text{1/26/2006} & \text{6/30/2005} & \text{Model A} \\ \text{12} & \text{1/26/2006} & \text{7/30/2005} & \text{Model A} \\ \text{14} & \text{1/11/2006} & \text{9/28/2005} & \text{Model A} \\ \text{15} & \text{1/18/2006} & \text{9/28/2005} & \text{Model A} \\ \text{23} & \text{1/26/2005} & \text{1/1/2005} & \text{Model B} \\ \text{16} & \text{1/26/2005} & \text{1/1/2005} & \text{Model B} \\ \text{18} & \text{3/17/2005} & \text{1/1/2005} & \text{Model B} \\ \text{19} & \text{5/31/2005} & \text{3/2/2005} & \text{Model B} \\ \text{20} & \text{5/31/2005} & \text{3/2/2005} & \text{Model B} \\ \text{21} & \text{6/30/2005} & \text{3/2/2005} & \text{Model B} \\ \text{18} & \text{7/30/2005} & \text{4/1/2005} & \text{Model B} \\ \text{19} & \text{12/27/2005} & \text{6/30/2005} & \text{Model B} \\ \text{18} & \text{1/11/2006} & \text{8/29/2005} & \text{Model B} \\ \text{11} & \text{2/7/2006} & \text{10/28/2005} & \text{Model B} \\ \text{34} & \text{8/14/2005} & \text{3/27/2005} & \text{Model C} \\ \text{24} & \text{8/27/2005} & \text{4/25/2005} & \text{Model C} \\ \text{44} & \text{1/26/2006} & \text{6/1/2005} & \text{Model C} \\ \text{26} & \text{1/26/2006} & \text{8/26/2005} & \text{Model C} \\ \end{matrix}\,\! }[/math]

Assuming that the given information is current as of 5/1/2006, analyze the data using the lognormal distribution and MLE analysis method for all models (Model A, Model B, Model C), and provide a return forecast for the next ten months.

Solution

Create a warranty analysis folio and select the dates of failure format. Enter the data from the tables in the Sales, Returns and Future Sales sheets. On the control panel, select the Use Subsets check box, as shown next. This allows the software to separately analyze each subset of data. Use the drop-down list to switch between subset IDs and alter the analysis settings (use the lognormal distribution and MLE analysis method for all models).

Non-Homogeneous End Date.PNG

In the End of Observation Period field, enter 5/1/2006, and then calculate the parameters. The results are:

[math]\displaystyle{ \begin{matrix} Model A & Model B & Model C \\ \begin{matrix} {{{\hat{\mu }}}^{\prime }}= & \text{11}\text{.28} \\ {{{\hat{\sigma }}}_{T}}= & \text{2}\text{.83} \\ \end{matrix} & \begin{matrix} {{{\hat{\mu }}}^{\prime }}= & \text{8}\text{.11} \\ {{{\hat{\sigma }}}_{T}}= & \text{2}\text{.30} \\ \end{matrix} & \begin{matrix} {{{\hat{\mu }}}^{\prime }}= & \text{9}\text{.79} \\ {{{\hat{\sigma }}}_{T}}= & \text{1}\text{.92} \\ \end{matrix} \\ \end{matrix}\,\! }[/math]

Note that in this example, the same distribution and analysis method were assumed for each of the product models. If desired, different distribution types, analysis methods, confidence bounds methods, etc., can be assumed for each IDs.

To obtain the expected failures for the next 10 months, click the Generate Forecast icon. In the Forecast Setup window, set the forecast to start on May 2, 2006 and set the number of forecast periods to 10. Set the increment (length of each period) to 1 Month, as shown next.

Non-Homogeneous Forecast Setup.PNG

Click OK. A Forecast sheet will be created, with the predicted future returns. The following figure shows part of the Forecast sheet.

Non-Homogeneous Forecast Data.PNG

To view a summary of the analysis, click the Show Analysis Summary (...) button. The following figure shows the summary of the forecasted returns.

Non-Homogeneous Analysis Summary.PNG

Click the Plot icon and choose the Expected Failures plot. The plot displays the predicted number of returns for each month, as shown next.

Non-Homogeneous Expected Failure.PNG