Optimize Reliability Predictions Based on Valid Test and Field Data

Bayesian analysis allows you to use any test and field data you have at the assembly level to predict component failure rates more accurately. The primary benefits of using Bayesian analysis are:

• Integration of current reliability data at the time the failure rate is predicted.
• Optimization of the reliability prediction based on valid historical data.

Bayesian analysis accounts for real-life experiences by combining the predicted component failure rate with empirical data. The following table describes the relevant test or field data needed to perform Bayesian analysis:

Data	Description
Experience Name	The name assigned to the field or test data.
Experience Type	The type of data, which generally includes Dormant, Field, Highly Accelerated Test, Operating Life, and more.
Field Failures	The number of failures in the test or field data.
Cumulative Hours	The cumulative number of hours.
Hours on Test	The number of test hours.
Test Temperature	The temperature of the assembly during testing.

To account for the quantity of relevant data, Bayesian analysis weights large data sets more heavily than small data sets. The failure rate estimate it obtains from the component failure rate prediction forms the "prior" distribution, comprised of a₀ and b₀.

When empirical data is available for an assembly, Bayesian analysis combines it with the best "pre-build" item failure rate estimate using the following equation:

Where:

Where:

If test data (in total test hours) taken at accelerated conditions is to be used in the Bayesian analysis, it must be converted to an equivalent number of field hours under actual field stresses. After you perform a traditional reliability prediction for the assembly at both the test and field conditions, you can determine the equivalent number of hours (b_i) by using the failure rate ratio between the test and use temperatures as follows:

Where:

Note: To avoid double counting of empirical data, you must not apply the empirical data at the child assembly level (subassembly) if that data has been collected at the parent assembly level. For example, if an assembly is tested for 1000 hours and experiences failures, only the empirical data for the assembly should reflect this data. You should not try to break this empirical data out further or reference it again at the child assembly level. The effect of doing this would be to double count the empirical data, thereby incorrectly biasing the calculated assembly failure rate.

By accounting for any test and field data you have at the assembly level, Bayesian analysis allows you to predict component failure rates more accurately. If you would like additional information about Bayesian analysis and how it is implemented in Relex, please e-mail info@relex.com.