1. A production method for a semiconductor integrated circuit, the method 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 a response 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 a statistical variation of said response characteristic of said cell, wherein said statistical variation is expressed by a product of said distribution function and a sensitivity, wherein said sensitivity is calculated based on said response function; updating said statistical cell library when said model parameter is updated in accordance with a change of a manufacturing process of said semiconductor integrated circuit, wherein said statistical cell library is updated by using said model parameter after said update and said response function without performing a circuit simulation; designing and verifying a semiconductor integrated circuit by using said updated statistical cell library; and manufacturing said designed semiconductor integrated circuit.