The time taken for guests to check out at a hotel front desk was measured over the course of several weeks. The management believes that the target time for checking out guests should be between 2 and 3 minutes with a target of 2.5 minutes. The data gathered for the actual process had a mean time of 2.75 minutes with a standard deviation of 0.45 minutes. The process capability index will be:
A) less than or equal to 1.
B) more than 3 but less than or equal to 5.
C) more than 4 but less than or equal to 5.
D) more than 5.

Question

Quizplus · Accepted Answer

The process capability index (Cpk) can be calculated using the formula:
Cpk = min[(USL - Mean)/3*SD, (Mean - LSL)/3*SD]
where USL is the upper specification limit (3 minutes), LSL is the lower specification limit (2 minutes), Mean is the mean time taken for checkout (2.75 minutes) and SD is the standard deviation (0.45 minutes).

Substituting the values, we get:
Cpk = min[(3-2.75)/3*0.45, (2.75-2)/3*0.45]
Cpk = min[0.1667, 0.1667]
Cpk = 0.1667

Since the Cpk value is less than or equal to 1, the process is not capable of meeting the target time of 2.5 minutes. Therefore, the answer is A.

The Time Taken for Guests to Check Out at a Hotel