A health care system is trying to make its doctors’ offices more efficient. For

Question

A health care system is trying to make its doctors’ offices more efficient. For its primary care physicians it has decided that a patient visit with the physician must be at least 15 minutes and at the most 30 minutes. It has doctor’s offices at three different locations – A, B, and C. After a month-long study at each of these locations it has collected the following data:

Location A: average patient visit time 18 minutes, standard deviation: 2 minutes.

Location B: average patient visit time 22.5 minutes, standard deviation: 2.5 minutes.

Location C: average patient visit time 27 minutes, standard deviation: 1.5 minutes.

Calculate the process capabilities for the doctors at each of these locations. Which is the most capable and which is the least? Are any of them minimally capable?

Explanation / Answer

To check capability, Cp or Cpk can be used. The value must be greater than 1 to be capable

When Mean is centered, Cp = (UCL - LCL)/(6*standard deviation)

When Mean is not centered, Cpk = Min((UCL-Mean)/(3*standard deviation), (Mean - LCL)/(3*standard deviation))

UCL = 30

LCL = 15

Location A: Mean is not centered

Cpk = Min((30-18)/(3*2), (18-15)/(3*2)) = Min(2,0.5) = 0.5

Location B: Mean is centered

Cp = (30-15)/(6*2.5) = 1

Location C: Mean is not centered

Cpk = Min((30-27)/(3*1.5), (27-15)/(3*1.5)) = Min(0.67, 2.67) = 0.67

So, Location B is most capable

Location B is minimally capable

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