A method to measure the contribution of random joint clearances to mechanism output error, termed as Error Importance (EI), is presented in this paper. In this method, the 2-order original moment is used to characterize the deviation of mechanism output error and joint clearances from their ideal values, i.e. zero. Then the 2-order original moment of mechanism output error is decomposed into a series of fractions. These fractions are divided into two categories: individual effects and interaction effects. The total effect of one joint clearance is defined as the sum of the corresponding main effects and the interaction effects, and total importance index, i.e. EI index, is defined as the value of its total effect relative to 2-order original moment of mechanism output error. Similarly, the total importance index of a group of joint clearances are defined also. Then the mathematical and physical properties of the EI indices are discussed, and a Monte Carlo based evaluation method is offered. At last, the EI indices are applied to cabin door mechanism of aircraft landing gear. Simulation results revealed that the EI indices can reflect honestly the contribution of joint clearances to mechanism output error.