The yield estimation of semiconductor products based on truncated samples

Abstract

Abstract. Product yield reflects the potential product quality and reliability, which means that high yield corresponds to good quality and high reliability. Yet consumers usually couldn't know the actual yield of the products they purchase. Generally, the products that consumers get from suppliers are all eligible. Since the quality characteristic of the eligible products is covered by the specifications, then the observations of quality characteristic follow truncated normal distribution. In the light of maximum likelihood estimation, this paper proposes an algorithm for calculating the parameters of full Gaussian distribution before truncation based on truncated data and estimating product yield. The confidence interval of the yield result is derived, and the effect of sample size on the precision of the calculation result is also analyzed. Finally, the effectiveness of this algorithm is verified by an actual instance.

Simulation of statistical mean and variance of normally distributed data $N_X(m_X,\sigma_X)$ transformed by nonlinear functions $g(X)=\cos X$, $e^X$ and their inverse functions $g^{-1}(X)=\arccos X$, $\ln X$

“…From the perspective of physical modelling, the range of dispersion of experimental values of BB is limited, therefore, a truncated normal distribution is considered. Thus, this approach is used to model the reliability of physical and technical systems [14], physical processes of charge transfer in electronic devices [15,16]. The corresponding theoretical model was built a long time ago, in the works of Einstein and Smolukhovsky [17,18].…”

Optimal Regularities of the Normal Distribution for Estimating the Sample Statistics of the Results of a Physical Experiment

“…Therefore, the truncated normal distribution is applied to model the reliability of physical and engineering systems [24][25][26][27], the physical processes of charge transfer in electronic devices [28,29], and other purposes.…”