A study of statistical method on estimating rare event in IC Current

• Main Authors: Peng, Ya Ling, 彭亞凌
• Other Authors: Yue, Jack C.
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/58070911651492279886

碩士 === 國立政治大學 === 統計研究所 === 100 === To obtain the tail distribution of current beyond 4 to 6 sigma is nowadays a key issue in integrated circuit (IC) design and computer simulation is a popular tool to estimate the tail values. Since creating rare events via simulation is time-consuming, often the linear extrapolation methods (such as regression analysis) are applied to enhance efficiency. However, it is shown from past work that the tail values is likely to behave differently if the operating voltage is getting lower. In this study, a statistical method is introduced to deal with the lower voltage case. The data are evaluated via the Box-Cox (or power) transformation and see if they need to be transformed into normally distributed data, following by weighted regression to extrapolate the tail values. In specific, the independent variable is the empirical CDF with logarithm or z-score transformation, and the weight is down-weight in order to emphasize the information of extreme values observations. In addition to regression analysis, Extreme Value Theory (EVT) is also adopted in the research. The computer simulation and data sets from a famous IC manufacturer in Hsinchu are used to evaluate the proposed method, with respect to mean squared error. In computer simulation, the data are assumed to be generated from normal, student t, or Gamma distribution. For empirical data, there are 10^8 observations and tail values with probabilities 10^(-4),10^(-5),10^(-6),10^(-7) are set to be the study goal given that only 10^5 observations are available. Comparing to the traditional methods and EVT, the proposed method has the best performance in estimating the tail probabilities. If the IC current is produced from regression equation and the information of independent variables can be provided, using the weighted regression can reach the best estimation for the left-tailed rare events. Also, using EVT can also produce accurate estimates provided that the tail probabilities to be estimated and the observations available are on the similar scale, e.g., probabilities 10^(-5)~10^(-7) vs.10^5 observations.