A cylindrical part of diameter d is loaded by an axial force P. This causes a stress ofP/A, where A = nd²/4. If the load is known with an uncertainty of ±10 percent, the diameter is known within ±5 percent (tolerances), and the stress that causes failure(strength) is known within ±15 percent, determine the minimum design factor that will guarantee that the part will not fail.

Fig: 1