Analysis of Non-Homogeneous Warranty Data
In this article, we will explore how non-homogeneous warranty data can be analyzed and how predictions can be made from such data. To analyze such cases, one needs to extract each homogeneous group, fit a life model to each group and then project the expected returns for each group based on the number of units at risk for each specific group.
For the product in question, two versions (A and B) have been produced and put in service. In addition, a new version (C) is planed for future release. Therefore, the data set being analyzed is a non-homogeneous data set and in total 3 different categories make up the entire data set.
The in-service data set is as follows (using the U.S. date format of Month/Day/Year):
The following returns were experienced:
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 version type.
Assuming that the above information was collected on 1/31/2006, the manufacturer wants to analyze the data for all versions and provide a return forecast for the next 20 months.
Using IDs in the Warranty Sheet
Normally, a mixed-Weibull model is suitable for analyzing non-homogeneous data in which direct categorization is not possible. If multiple categories/sub-populations are believed to exist in the entire population, then the use of a mixed-Weibull model would uncover the existence of different sub-populations and would also describe them with representative models. However, it would not explain which category each data point would be put into. This is because a mixed-Weibull analysis simply fits a mixed model with multiple parameters to the entire data set. In the case of the non-homogeneous warranty data discussed in this article, the different categories are already identified. As can be seen in the above tables, the sales data and return data are identified by version name. Therefore, the more appropriate approach is to extract each category's data set and analyze it separately and make projections based on separate models that describe each unique category of the data set.
One of the new enhancements to the Warranty Analysis capabilities of Weibull++ 7 is the introduction of the optional Subset ID column that allows you to differentiate between different sales data (e.g. different product versions, different designs, different manufacturing facility lots) that express some sort of non-homogeneity within the entire population of sales or shipments. Based on an entry that includes different subset IDs, the data can be automatically separated into different groups and different distributions, analysis methods and confidence bounds methods can be used for each group. This also allows comparison of different categories' parameters, reliability, expected future failures, etc.
Create a warranty folio by selecting Add Specialized Folio then Add Warranty from the Project menu. In the New Warranty Folio Setup window, select I want to enter data in dates of failure format.
The sales data are entered as follows:
The return data are entered as follows:
On the Analysis tab of the Control Panel, set the Calculations End Date to (1/31/2006) as shown next:
The calculated parameters for versions A and B, assuming a lognormal distribution using MLE as the analysis method, are:
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 subset ID.
Based on the above analysis, Version A was determined to be a less reliable version, therefore a decision is made to discontinue producing that version and instead continue Version B in addition to a new version (C) that was tested in-house and found to be a more reliable version. The future shipments are expected to be as follows (entered in the Future Sales sheet):
When you click the Calculate icon, Weibull++ will display a message that requests the parameters of Version C. Distributions can be automatically fitted to lots that have return (failure) data, whereas if no returns have been experienced yet (either because the units are going to be introduced in the future or because no failures have happened yet), the user will be asked to specify the parameters, since they can not be computed. Consequently, subsequent estimations/predictions related to these lots would be based on the user-specified parameters. In this case, Version C is a product type that will be introduced in the future; therefore, no warranty return data have been experienced yet.
The manufacturer tested a number of prototypes of Version C and a lognormal distribution with μ' = 11.00 and σT = 2.2 was derived. These values are entered into the following window.
To obtain the expected failures for the next 10 months, click the Generate Forecast icon
and enter the Start date of 2/1/2006, the Number of Periods (20) and the Increment number (1 Month), as shown next:
The forecast results are then displayed in a new sheet called Forecast. A portion of the forecast table is shown next:
A summary of the analysis can also be obtained by clicking the Show Analysis Summary icon (...). The summary of the forecasted returns is as follows:
The Expected Failures vs Period plot and the Failure Rate plot are shown next.
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