Analysis of LSI failure distribution functions using statistical simulation

Abstract

With a view to predicting the reliability of large-scale LSI from the test results of smaller samples, the failure distribution functions followed by the LSI failure time are analyzed by simulation. The failure distribution function characteristic to the element technology of LSI is assumed. Random numbers following this function are generated and are considered as the failure time of the element in the LSI, while the minimum failure time among the elements is defined as the failure time of the LSI. As a result, the failure time distribution of the LSI containing more than 500 elements can always be approximated accurately by a Weibull distribution regardless of the function form of the failure distribution of the elements. It is shown that the failure time distribution of the LSI decreases as N−1/B for the number of elements N in the LSI and the Weibull shape parameter β. If the failure distribution of the element follows the lognormal distribution with the shape parameter σ0, the relationship β = 3.4/σ0 holds in the LSI failure distribution. It is found that the shape parameter does not change in the LSI if the failure distribution of the element follows the Weibull distribution. These relationships agreed well with the results of analysis using the approximate equation. On the other hand, it is shown that if the functional form of the failure distribution of the element is not known, reliability design becomes safe if the Weibull distribution is assumed. Based on these results, a computation method is proposed for predicting the reliability of the LSI from the reliability test results of the sample. © 2000 Scripta Technica, Electron Comm Jpn Pt 2, 83(5): 40–49, 2000