An appliance manufacturer wants to contract with a repair shop to handle authori

Question

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set an acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 74 minutes with a 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. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Which firm would you choose?

Explanation / Answer

Upper specification limit (USL)= 90. Lower specification limit (LSL) = 50.

Firm 1:

Mean = 74. standard deviation = 4. Cpl = (Mean-LSL)/3*standard deviation

(74-50)/3*4 = 24/12 = 2. Cpu = (USL-Mean)/3*standard deviation = (90-74)/3*4 = 16/12 = 1.33

Cpk = minimum of (Cpl, Cpu) = minimum of (2, 1.33) = 1.33

Firm 2:

mean = 72. standard deviation = 5.1

Cpl = (Mean-LSL)/3*standard deviation = (72-50)/3*5.1 = 22/15.3 = 1.44

Cpu = (USL-Mean)/3*standard deviation = (90-72)/3*5.1 = 18/15.3 = 1.18

Cpk = minimum of (Cpl, Cpu) = minimum of (1.44, 1.18) = 1.18

Thus firm 1 has a Cpk of 1.33 and form 2 has a Cpk of 1.18.

Hence firm 1 has a higher Cpk and will be selected.

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