Improving public health waiting times. Statistical process

QUESTION:

Improving public health waiting times. Statistical process IIl control was utilized in an effort to improve the service wic1, delivery at a Women, Infants, and Children (WIC) health WIc2 clinic in Minnesota (American Journal of Public Health, Sep. 2009). The health department sampled patients for 10 consecutive days and recorded each patient's lobby waiting time (in minutes). The mean lobby waiting times were (in order): 25.5, 16.5,22.5, 18,13, 10.5, 14,4.5, 12.5, and 14 minutes. These means were plotted in an \(\bar{x}\)-chart to monitor the waiting time process.

a. Compute the value of the centerline for the \(\bar{x}\)-chart.

b. Critical boundaries for the \(\bar{x}\)-chart are listed as follows: UCL = 31.5, Upper A-B = 26, Upper B-C = 20.5, Lower B-C = 9.5, Lower A-B = 4, LCL = 0. Plot the 10 means in an \(\bar{x}\)-chart; include the critical boundaries on the chart.

c. Refer to part b. Apply pattern-analysis rules to the chart. Do you detect the presence of any special causes of variation?

d. After a 3-month time period, during which the clinic implemented new procedures, the health department conducted a second sampling of patients over 14 consecutive days. The mean lobby waiting times for these 14 days were (in order): 11.5, 12.5, 14.5, 11, 12.5,11.5, 13.5, 11.5, 7.5, 13.5,7, 10.5, 13.5, and 2 minutes. Critical \(\bar{x}\)-chart boundaries for the new data are listed as follows: UCL = 21.5, Upper A-B = 18, Upper B-C = 14.5, Lower     B-C = 7.5, Lower     A-B=4, LCL = .5. Construct an \(\bar{x}\)-chart for the new data. Do you detect the presence of any special causes of variation?

e. Place the two \(\bar{x}\)-charts side by side. The health department concluded that a process shift occurred after the clinic implemented its new procedures. Do you agree?