Question

Q410 pts].An appliance manufacturer wants to contract with a repair shop to ed repairs in Indianapolis. The of repair time of 55 minutes to 95 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 73 minutes with a standard deviation of 4.2 minutes and the other firm had a mean repair time of 72 minutes with a standard deviation of 5.7 minutes. Which firm would you choose and why? Assume that the manufacturer would like to have 4-sigma capability if possible

Answer 1

In this problem, Upper Specification Limit (USL) = 95 minutes and Lower Specification Limit (LSL) = 55 minutes.

Let x_A denote the mean repair time at A, x_B denote the mean repair time at B, σ_A denote the standard deviation at A, and σ_B denote the standard deviation at B. Then we have

x_A =73 , x_B =72

σ_A =4.2, σ_B =5.7

Cpk for A = min {( x_A - LSL/ 4 σ_A) , ( USL- x_A / 4 σ_A)} = min {(73 – 55 / 4*4.2) , ( 95-73/ 4*4.2)}

Cpk for A = min{1.07;1.31}

Cpk for A =1.07

Cpk for B = min {( x_B - LSL/ 4σ_B) , ( USL- xB/ 4 σ_B)} = min {(72 – 55 / 4*5.7) , ( 95-72/ 4 *5.7)}

Cpk for B = min{0.75;1.01}

Cpk for B =0.75

The company should choose A since it has a higher Cpk value