The time to check out guests at a hotel was measured over the course of several weeks. Management believes that the target time for checking out guests should be between 2 and 4 minutes with a target of 3 minutes. The data gathered had a mean time of 2.75 minutes with a standard deviation of 0.4 minutes. Find and interpret Cp, Cpl, Cpu, and Cpk in the context of this situation
Cp = (USL - LSL)/6s = (4 - 2)/(6 x 0.4) = 0.833
Cpl = (µ- LSL)/3s = (2.75 - 2)/(3 x 0.4) = 0.625
Cpu = (USL - µ)/3 s = (4 - 2.75)/(3 x 0.4) = 1.041
Cpk = min(0.625, 1.04) = 0.625
The Cp value suggests that the process is not capable of meeting specifications. The value of Cpu is slightly greater than 1, indicating that the process can meet the upper limit target of 4 minutes nearly all the time. The value of Cpl (and thus Cpk) suggests that the process cannot meet the lower specification limit of 2 minutes. However, this must be viewed in the context of service, assuming that a shorter time is preferable from the perspective of guest satisfaction. Thus a value of Cpl< 1 in this situation is not bad, and in fact, means that the process is actually better than the target that management has specified.
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