Statistical studies of the robustness of the LHC main dipole mechanical structure

This paper describes two methods used to study the effect of the tolerances of the components on the structure of the LRC main dipole. The first metho d, called semi-statistical, is useful for the study of the effect of single different parameters and allows the determination of the acceptable varian ce of the dimensions of magnet components. The second one, fully statistica l, allows the study of the combined effect of many parameters. The use of t hese two methods allowed to evaluate with good confidence the robustness of two different dipole cross-section designs, featuring austenitic and alumi nium alloy collars, respectively.