Chi-Squared Accelerated Reliability Growth (CARG) Testing: Method & Applications

Alec Feinberg
Dr. Alec Feinberg is the founder of DfRSoft. He has a Ph.D. in Physics and is the principal author of the book, Design for Reliability. Alec has provided reliability engineering services in all areas of reliability including solar, thin film power electronics, defense, microelectronics, aerospace, wireless electronics, and automotive electrical systems. He has provided training classes in Design more


This webinar is co-hosted with the Statistics Division. The chi-squared distribution has been used as a traditional method of identifying reliability confidence bounds for the exponential failure lifetime behavior of components, assemblies, and systems and is often extended to accelerated life test data analysis. The distribution is key for assessment when observance of few or even zero failures occur in accelerated testing for estimates on reliability at a statistical significance level. It is therefore natural to consider using the chi-squared method in the application of accelerated reliability growth data analysis. Companies today can have repetitive testing on products. Often identical tests are performed on each new product such as high temperature, vibration test, temperature cycle, humidity, etc. Each test may only have one stress level, with multiple groups tested. Fixes can be incorporated without time to re-test, and the reliability engineer has few options for quantifying the reliability growth that has likely occurred in their testing work. The CARG method offers a way to estimate accelerated reliability growth and it incorporates a fix-effectiveness factor. Results have been shown to correlate reasonably well with field data. CARG also uses growth alphas and can be related to traditional growth methods like the Duane model. Finally, in addition to the CARG analysis, CARG planning can also be done.

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