Various interventions are available for nurses to help relieve patients’ pain (e.g., heat/cold applications, breathing exercises, massage). The journal Research in Nursing & Health (Vol. 35, 2012) demonstrated the utility of statistical process control in determining the effectiveness of a pain intervention. The researchers presented the following illustration. Pain levels (measured on a 100-point scale) were recorded for a sample of 10 intensive care unit (ICU) patients 24-hours post-surgery each week for 20 consecutive weeks. The accompanying table provides the means and ranges for each of the 20 weeks. To establish that the pain management process is “in statistical control”, an x̅-chart is constructed.

a. Compute the value of the center line for the x̅-chart.

b. Compute the value of R̅.

c. Compute the UCL and LCL for the x̅-chart. 

d. Plot the means for the 20 weeks on the x̅-chart. Is the pain management process “in control”?

e. After the 20th week, a pain intervention occurred in the ICU. The goal of the intervention was to reduce the average pain level of ICU patients. To determine if the intervention was effective, the sampling of ICU patients was continued for eight more consecutive weeks. The mean pain levels of these patients were (in order): 71, 72, 69, 67, 66, 65, 64, and 62. Plot these means on the x̅-chart. Do you detect a shift in the mean pain level of the patients following the intervention? Explain.

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ICUPAIN Week Х-Bar Range 1 65 28 2 75 41 3 72 31 4 69 35 5 73 35 63 33 7 77 34 75 29 9 69 30 10 64 39 11 70 34 12 74 37 13 73 25 14 62 33 15 68 28 16 75 35 17 72 29 18 70 32 19 62 33 20 72 29