Quantifying Optimum Burn-in Period
Early life failures are usually attributed to problems in the manufacturing, packaging and assembling phases. After making improvements to the greatest possible extent in these phases, the only way to improve the products reliability is to eliminate defective units before they reach customers . A common approach used to weed out defective and weak parts before shipping them to customers is burn-in. Burn-in has become a frequently-used procedure in many industries, especially the electronics industry. One common problem that industries face when dealing with burn-in is quantifying and optimizing the burn-in testing period. This article introduces a simple method to optimize the burn-in period and illustrates how this analysis can be performed in Weibull++.
Definition of Burn-in
Many types of equipments and systems exhibit an inherent decreasing failure rate characteristic during their early operating life. A relatively high early failure rate is usually attributed to the inherent variability of the production process. Burn-in has been long recognized as a useful method for detecting and eliminating components or systems with early failures before customer delivery. Without burn-in, defective components could be delivered to customers, resulting in costly field repairs and reputation damage.
Note that burn-in is not a product improvement technique. Submitting a population of a product to burn-in does not improve each units individual reliability. However, burn-in improves the reliability of the whole population by weeding out the bad portion of the population, resulting in a more reliable and homogeneous population of units. Also, burn-in usually provides insightful information about the various failure mechanisms that cause early failures and also provides valuable feedback to the quality engineers who oversee the manufacturing process and the design engineers to help them analyze the variations that led to the emergence of these early failure mechanisms.
Optimizing Burn-in Period Based on Cost
Burn-in also requires testing of all units for the designated burn-in period. Accelerated life testing techniques may be applied to shorten the burn-in period. The primary concern for burn-in is the length of testing. In the following models, we assume that that failed units are disposed of and that only the surviving units are released to customers.
Costs are an important consideration when determining the appropriate duration for a burn-in test. Cost of carrying out the testing, cost of failures during burn-in, cost of failures during warranty (repair, replacements, shipping, personnel travel, parts, etc.) are all important factors. A trade-off between the costs of conducting the burn-in and the cost of failures can be achieved by optimizing the cost model presented next. 
Assume the following:
Assuming that n units are produced and that each has a reliability function R(t) and undergoes burn-in, the expected number of failures during burn-in is:
The expected number of failures during warranty (or operation) is:
The expected total cost is the sum of the burn-in phase cost (cost of running test and cost of failures) and the failures during warranty (or operational) cost. The expected cost per unit is:
For the Weibull distribution:
To calculate the optimum burn-in period (Tb), equations 3 and 4 can be minimized to find the the value of Tb that minimizes the cost ECV(Tb). Weibull++ provides a report template that facilitates this type of analysis. The report template, Optimum Burn-in.wrt, is available as part of the report templates that is shipped with the software.
The data set is analyzed using a Free-Form (Probit) data sheet.
Using the Weibull distribution as the assumed model, the parameters are found to be β = 0.5290 and ε = 168.0970 days.
The replacement cost of the product if it fails during its warranty period of 1 year (365 days) is CPF_F = $4,000. It costs the manufacturer CUT_B = $70 a day per unit tested to perform a burn-in test. Failures that occur during burn-in cost CPF_B = $500. Notice that β < 1 and that CPF_F > CPF_B; therefore a burn-in test is justified.
The optimum burn-in period considering the cost factors can be obtained by numerically minimizing Eqn. 4. The analysis can be performed using the Optimum Burn-in.wrt report in Weibull++.
Select Add Report... from the Project menu. In the Report Wizard, specify the calculated data sheet as the default data source and select to create the report based on the Optimum Burn-in.wrt report template that is shipped with the software, as shown next.
Enter the costs for this example in the Cost Inputs area at the top of the template (shown in bold blue text) and accept the other default inputs. The window will look like the figure shown next.
The optimum burn-in period, which minimizes
cost, is Tb
= 2.3 days and the expected cost is E[C] = $2,935.52.
Another type of burn-in (for repairable system) was discussed in Example 2 of last month's issue of HotWire. For other discussions related to burn-in, please refer to http://www.weibull.com/hotwire/issue21/hottopics21.htm.
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