Accurate predictions about the quantity of products that will be returned under warranty can provide huge benefits to manufacturing organizations. Among other advantages, better warranty data analysis allows an organization to make the most efficient allocation of resources to warranty services provision. Likewise, they allow the manufacturer to anticipate customer support needs and take the necessary steps to insure customer satisfaction with the warranty process. Warranty data analysis can also provide a valuable early-warning signal to the manufacturer when there is a serious product quality problem in the field, which gives the organization time to mobilize its resources to meet the challenge before serious financial, legal or other problems occur. This article presents the process on how warranty analysis can be accomplished in Weibull++ 6.
The Warranty Analysis utility that is available in Weibull++ 6 allows you to quickly and easily convert shipping and warranty return data into the standard reliability data form of failures and suspensions so that it can be easily analyzed with traditional life data analysis methods. The utility uses the life data to generate predictions about the quantity of warranty returns that can be expected in the future. The following examples illustrate the principles upon which this utility is based.
Shipping and warranty return quantities are the minimum data requirements for performing effective warranty data analysis. If an organization keeps track of the quantity of units that are shipped in each given time period (e.g. month) and the quantity of units from that shipment period that are returned in subsequent time periods, life data analyses (including failure predictions) can be performed. For each time period that elapses after the units are shipped, count the number of returns (failures) and calculate the number of units from the shipment that remain in the field (suspensions). The data can be organized in a diagonal chart like the one shown in Figure 1.
Figure 1: Shipment and returns data in Weibull++ 6.
Example 1: Generating Life Data
Suppose that your company keeps track of its shipments and warranty returns on a month-by-month basis. The table in Figure 1 shows shipments in June, July and August and warranty returns from July through September.
To convert this information to life data, you must examine the companys shipments and returns on a month-by-month basis. Out of 100 units shipped in June, 3 were returned in July. This is 3 failures at 1 month from the June shipment (FJUN,1 = 3). Likewise, 3 failures from the June shipment occurred in August (FJUN,2 = 3) and 5 in September (FJUN,3 = 5). At the end of the three-month analysis period, 11 units were returned and 89 units were still in the field. Those 89 units are considered to be suspensions at three months (SJUN,3 = 89). For the 140 units shipped in July, the following failures and suspensions are observed: FJUL,1 = 2, FJUL,2 = 4 and SJUL,2 = 134. For the final shipment of 150 in August, 4 failed in September (FAUG,1 = 4) with the remaining 146 units considered to be suspensions at 1 month of operation (SAUG,1 = 146).
To obtain a reliability data set, you must add the quantity of failures and suspensions for each month, as shown next:
To generate this data set with the Weibull++ Warranty Analysis utility, click the Create Weibull Data button to generate the results shown in Figure 2. This data set can be transferred to the Weibull++ Data Folio and analyzed. Using MLE analysis for a two-parameter Weibull distribution, the parameter estimates are: Beta = 2.49 and Eta = 6.70.
Figure 2: Reliability data generated in Weibull++ 6.
Example 2: Making Warranty Predictions
Once you have performed a life data analysis on warranty data, you can use the results to predict the quantity of warranty returns you can expect in subsequent time periods. Using the concept of conditional reliability, you can calculate the probability of failure for the remaining units after each shipment time period. Next, you can multiply this probability of failure by the number of units from that shipment period that remain in the field in order to predict the number of failures or warranty returns in the next time period.
Using the analysis performed in Example 1, you can determine the conditional probability of failure for each shipment time period and apply that probability to the number of units that were still operating at the end of September. The equation of the conditional probability of failure is:
For the June shipment, 89 units had not been returned by the end of September. The probability of one of these units failing in the next month is:
This value is multiplied by SJUN,3 = 89 to determine the number of failures or:
or 12 units.
Therefore, the forecasted number of returns for October from the June shipment is 12 units. Predictions for the quantity of returns that can be expected in October from the July and August shipments can be performed using a similar methodology. The forecasts generated in Weibull++ are presented in Figure 3.
Figure 3: Forecasted warranty returns
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