Issue 58, December 2005

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 product’s reliability is to eliminate defective units before they reach customers [1]. 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
In MIL-STD-833C, Method 1015.3, “Burn-in Test”, burn-in is defined as follows:

Burn-in is a test performed for the purpose of screening or eliminating marginal devices, those with inherent defects or defects  resulting from manufacturing aberrations which cause time and stress dependent failures. [2]

Why Burn-in?
Reliability specialists often describe the lifetime of a population of products using a graphical model called the bathtub curve. The bathtub curve is composed of three periods: an infant mortality period with a decreasing failure rate followed by a normal life period (also known as "useful life") with a low, relatively constant failure rate and concluding with a wear-out period that exhibits an increasing failure rate.

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 unit’s 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
The components must have a decreasing failure rate if burn-in is to have any merit. For the case of the Weibull distribution, this means that the β parameter should be less than 1. The normal distribution always has an increasing failure rate and therefore components following the normal distribution do not qualify for burn-in. Similarly, components that follow the exponential distribution, which assumes a constant failure rate, do not qualify for burn-in testing.

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. [3]

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:
 

(4)

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. 

Example
An electronic component is undergoing burn-in testing. During initial testing, the following cumulative percent failed is observed:

• 6% failed by 1 day

• 10.1 failed by 2 days

• 12% failed by 3 days

• 13.8% failed by 4 days

• 14.5% failed by 5 days

• 15% failed by 6 days

• 15.1% failed by 7 days

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.

[Click to Enlarge]

The optimum burn-in period, which minimizes cost, is T_b = 2.3 days and the expected cost is E[C] = $2,935.52.
 

Closing Remarks

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.

References

1. Kececioglu, Dimitri B. and Sun, Feng-Bin, Burn-In Testing Its Quantification and Optimization, Prentice Hall, Inc., Englewood Cliffs, N.J., pp. 1, 1997

2. MIL-STD-833C, Test Methods and Procedures for Microelectronics, August 1983

3. Ebeling, Charles E., An Introduction to Reliability and Maintainability Engineering, McGraw-Hill Companies, Inc., Boston, M.S., pp. 312- 315, 1997

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