Error-Correcting-Code Memory Reliability Calculations

The subject of this paper is the Mean Time to Failure (MTTF) calculation for a computer memory array with error correcting code (ECC) that detects and corrects 1-bit errors in memory words. The MTTF calculation is examined within the framework of the Whole Chip Failure Mode model. This paper has two main contributions: 1) The MTTF equation is derived in a way that is mathematically simpler and easier to understand. 2) An approximation to the exact equation is derived along with bounds on the accuracy of the approximation. This approximation has a simple, intuitive interpretation that relates the ECC case back to the simpler nonECC case. The first result provides insights to readers interested in the theory of memory reliability calculations while the second provides quick estimates to those in need of actual calculations.