Theoretical calculation of fundamental uncertainty region based on the maximum and/or the minimum size in the preparation of standard reference particles for particle size measurement

In order to confirm the reliability of particle size measurement technique and to prepare standard reference particles for calibrating particle size measurement devices, experimental and theoretical studies have been conducted through particle size measurement of silica particles having a size range of 0.1–1 μm. A new theoretical equation to calculate fundamental uncertainty region in the case that the maximum and/or the minimum particle size is known, is derived based on a log-normal distribution truncated by the maximum and/or the minimum. Fundamental uncertainty regions calculated based on these truncated size distributions are compared with that calculated based on the perfect log-normal distribution. The relationship between the parameter u to determine the reliability of size distribution and the truncate-parameter g is obtained to get 95% reliability of the measurement. Value of the parameter u is fairly reduced as the truncate-parameter g becomes smaller. Numerical simulation of uncertainty region agreed with the results calculated by the new theoretical equation. Calculations on the silica particles having a size range of 0.1–1 μm have been conducted showing that the uncertainty region based on the known maximum size is slightly smaller compared to that given in the previous paper.