You need to make some decisions regarding the procurement of three different sup

Question

You need to make some decisions regarding the procurement of three different suppliers. You have requested that the shank diameter (above thread) have specifications of 1.500 plusminus 0.009 inches. The SPC studies done by the suppliers have indicated that their processes are behaving consistently in statistical control with the following process parameters: Supplier 1: x = 1.500 inches, sigma_x = 0.003 inch. Supplier 2: x = 1.500 inches, sigma_x = 0.0022 inch. Supplier 3: x = 1.4950 inches, sigma_x = 0.0015 inch Which supplier would you purchase from, why? Explain your logic and show calculations and graphical evidence to back it up.

Explanation / Answer

for tolerance region are 1.491 and 1.509 from above:

hence for supplier 1 propbabilty to be in tolerance region

P(1.491<X<1.509)=P((1.491-1.5)/0.003<X<(1.509-1.5)/0.003)=P(-3<Z<3)=0.9987-0.0013=0.9973

hence for supplier 2 propbabilty to be in tolerance region

P(1.491<X<1.509)=P((1.491-1.5)/0.0022<X<(1.509-1.5)/0.0022)=P(-4.0909<Z<4.0909)=0.99998-0.00002=0.99996

hence for supplier 3 propbabilty to be in tolerance region

P(1.491<X<1.509)=P((1.491-1.495)/0.0015<X<(1.509-1.495)/0.0015)=P(-2.667<Z<9.333)=1.000-0.0038=0.9962

as supplier 2 has highest probability to be in tolerance region , one should purchase from it

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