1. A production method for a semiconductor integrated circuit comprising: creating a model parameter of an element constituting a cell, wherein said model parameter is defined by a design value and a distribution function of variability from said design value; performing a circuit simulation using said model parameter to create a response function that expresses response of characteristic of said cell to said model parameter; creating a statistical cell library by using said response function, wherein said statistical cell library gives an expected value and statistical variation of said characteristic of cell, wherein said statistical variation is expressed by a product of said distribution function and sensitivity, wherein said sensitivity is calculated based on said response function; updating said statistical cell library when said model parameter is updated, wherein said statistical cell library is updated by using said model parameter after update and said response function without performing a circuit simulation; designing and verifying a semiconductor integrated circuit by using said statistical cell library; and manufacturing said designed semiconductor integrated circuit.