Size distribution estimation of three-dimensional particle clusters in metal-matrix nanocomposites considering sampling bias

Abstract

Nanoparticle clustering phenomenon is a critical quality issue in metal-matrix nanocomposites (MMNCs) manufacturing. Accurate estimation of the 3D cluster size distribution based on the 2D cross section images is essential for quality assessment, quality control, and process optimization. The existing studies often draw conclusions with observable samples, which are inherently biased because large clusters are more likely to be intersected by scanning electron microscope (SEM) images compared with small ones. This paper takes into account this sampling bias and proposes two statistical approaches, namely, the maximum likelihood estimation (MLE) and the method of moments (MM), to estimate the distribution parameters accurately. Numerical studies and real case study demonstrate the effectiveness and accuracy of the proposed approaches.