An appliance manufacturer wants to contract with a repair shop to handle authorized repairs. The company has an acceptable range of repair time from 50 minutes to 90 minutes. Two firms have submitted bids for the work. In the evaluation trail, one firm had a mean repair time of 74 minutes with standard deviation of 4.0 minutes, and the other firm had a mean repair time of 72 minutes with a standard deviation of 5.1 minutes. Which firm would you choose, and why? Show your calculations.

Answer:First VendorStep-by-step explanation:Givencompany acceptable rangeUpper control limit=90 minutesLower control limit=50 minutesMean of first vendor=74 minutesstandard deviation[tex](\sigma _1)=4 minutes[/tex]Mean of second vendor=72 minutesStandard deviation[tex](\sigma _2)=5.1 minutes[/tex]To find better vendor we use Process capability index which is given by[tex]C_{pk}=min. \left ( \frac{UCL-mean}{3\times Standard\ deviation},\frac{mean-LCL}{3\times Standard\ deviation}\right )[/tex][tex]C_{pk}=min\left ( \frac{90-74}{3\times 4},\frac{74-50}{3\times 4}\right )[/tex][tex]C_{pk}=min\left ( 1.33,2\right )[/tex]The Process capability index for first vendor is 1.33 For Second Vendor[tex]C_{pk}=min. \left ( \frac{UCL-mean}{3\times Standard\ deviation},\frac{mean-LCL}{3\times Standard\ deviation}\right )[/tex][tex]C_{pk}=min\left ( \frac{90-72}{3\times 5.1},\frac{72-50}{3\times 5.1}\right )[/tex][tex]C_{pk}=min\left ( 1.176,1.43\right )[/tex]The process capability index of Vendor 2 is 1.176Thus Vendor is chosen over vendor 2 because its Process capability index is higher