Warranty Analysis Usage Format Example

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 book.

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.

Quality In-Service Data

Quantity In-Service	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

Quality Return Data

Quantity Returned	Usage at Return Date	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.

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]\displaystyle{ {{\mu }_{T\prime }}=9.38\,\! }[/math], [math]\displaystyle{ {{\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.

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

[math]\displaystyle{ \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.

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).