Passive neutron multiplicity counting is widely used as a nondestructive assay technique to quantify mass of plutonium material. One goal of this technique is to achieve good precision in a short measurement time. In this paper, we describe a procedure to derive mass assay variance for multiplicity counting based on the threeparameter model, and analytical equations are established using the measured neutron multiplicity distribution.Monte Carlo simulations are performed to evaluate precision versus plutonium mass under a fixed measurement time with the equations. Experimental data of seven weapons-grade plutonium samples are presented to test the expected performance. This variance analysis has been used for the counter design and optimal gate-width setting at Institute of Nuclear Physics and Chemistry. Passive neutron multiplicity counting is widely used as a nondestructive assay technique to quantify mass of plutonium material. One goal of this technique is to achieve good precision in a short measurement time. In this paper, we describe a procedure to derive mass assay variance for multiplicity counting based on the threeparameter model, and analytical equations are established using the measured neutron multiplicity distribution. Monte Carlo simulations are performed to evaluate precision versus plutonium mass under a fixed measurement time with the equations. Experimental data of seven weapons-grade plutonium samples are presented This test has been used for the counter design and optimal gate-width setting at Institute of Nuclear Physics and Chemistry.