View source for Warranty Analysis Usage Format Example

<noinclude>{{Banner Weibull Examples}}
''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.


</noinclude>'''Warranty Analysis Usage Format Example'''

Suppose that an automotive manufacturer collects the warranty returns and sales data given in the following tables. Convert this information to life data and analyze it using the lognormal distribution.

{| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+ '''Quality In-Service Data'''
|-
| align="center" style="background:#f0f0f0;"|'''Quantity In-Service'''
| align="center" style="background:#f0f0f0;"|'''Date In-Service'''
|-
| 9||Dec-09
|-
| 13||Jan-10
|-
| 15||Feb-10
|-
| 20||Mar-10
|-
| 15||Apr-10
|-
| 25||May-10
|-
| 19||Jun-10
|-
| 16||Jul-10
|-
| 20||Aug-10
|-
| 19||Sep-10
|-
| 25||Oct-10
|-
| 30||Nov-10
|-
|}


{| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+ '''Quality Return Data'''
|-
| align="center" style="background:#f0f0f0;"|'''Quantity Returned'''
| align="center" style="background:#f0f0f0;"|'''Usage at Return Date'''
| align="center" style="background:#f0f0f0;"|'''Date In-Service'''
|-
| 1||9072||Dec-09
|-
| 1||9743||Jan-10
|-
| 1||6857||Feb-10
|-
| 1||7651||Mar-10
|-
| 1||5083||May-10
|-
| 1||5990||May-10
|-
| 1||7432||May-10
|-
| 1||8739||May-10
|-
| 1||3158||Jun-10
|-
| 1||1136||Jul-10
|-
| 1||4646||Aug-10
|-
| 1||3965||Sep-10
|-
| 1||3117||Oct-10
|-
| 1||3250||Nov-10
|-
|}


'''Solution'''

Create a warranty analysis folio and select the usage format. Enter the data from the tables in the '''Sales''', '''Returns''' and '''Future Sales''' sheets. The warranty data were collected until 12/1/2010; therefore, on the control panel, set the '''End of Observation Period''' to that date. Set the failure distribution to '''Lognormal''', as shown next.

[[Image:Usage In-Service Weibull Data.png|center|500px| ]] 

In this example, the manufacturer has been documenting the mileage accumulation per year for this type of product across the customer base in comparable regions for many years. The yearly usage has been determined to follow a lognormal distribution with <math>{{\mu }_{T\prime }}=9.38\,\!</math>, <math>{{\sigma }_{T\prime }}=0.085\,\!</math>. The Interval Width is defined to be 1,000 miles. Enter the information about the usage distribution on the Suspensions page of the control panel, as shown next.

[[Image:Specify Usage Distribution.png|center|250px| ]] 

Click '''Calculate''' to analyze the data set. The parameters are estimated to be:

::<math>\begin{align}
  & {{\mu }_{T\prime }}= & 10.528098 \\ 
 & {{\sigma }_{T\prime }}= & 1.135150  
\end{align}\,\!</math>

The reliability plot (with mileage being the random variable driving reliability), along with the 90% confidence bounds on reliability, is shown next.

[[Image:Usage Example Reliability Plot.png|center|600px| ]]

In this example, the life data set contains 14 failures and 212 suspensions spread according to the defined usage distribution. You can display this data in a standard folio by choosing '''Warranty > Transfer Life Data > Transfer Life Data to New Folio'''. The failures and suspensions data set, as presented in the standard folio, is shown next (showing only the first 30 rows of data).

[[Image:Usage Example Weibull Std Folio Data.png|center|550px| ]]