Question

To supplement their patient satisfaction survey, End Result Hospital conducts in-depth telephone survey of past patients. 5 differnt past patients participated each month in the telephone interview. The data below records the total number of the patients' concerns noted by the interviewers. These concerns range from the effectiveness of medical treatment to the cleanliness and comfort of the patient room and ease of parking. The interviewer addresses the same items found on the patient satisfaction survey, solicits additional information for any item on which the patient indicated performance was less than "Good" or "Very Good", and provides the patient with the opportunity to voice any other concerns. Create a control chart to summarize the results.

Month	Patient Concerns
Jan	17
Feb	16
Mar	25
Apr	17
May	19
Jun	18
Jul	28
Aug	26
Sep	25
Oct	15
Nov	30
Dec	24

Answer 1

The control chart is:

The process is in statistical control.

Answer 2

To create a control chart for the given data on patient concerns, we will use the X-bar chart, which is a type of control chart used to monitor the process mean over time. The X-bar chart shows the average (mean) of the sample data collected at different time points.

Here are the steps to construct the X-bar control chart:

Step 1: Calculate the Sample Means Calculate the mean of patient concerns for each month (X-bar).

Month Patient Concerns (X-bar) Jan 17 Feb 16 Mar 25 Apr 17 May 19 Jun 18 Jul 28 Aug 26 Sep 25 Oct 15 Nov 30 Dec 24

Step 2: Calculate the Overall Mean (Grand Mean) Calculate the overall mean (X-double-bar) of all the sample means calculated in Step 1.

Overall Mean (X-double-bar) = (Sum of X-bar) / Number of Samples

Overall Mean (X-double-bar) = (17 + 16 + 25 + 17 + 19 + 18 + 28 + 26 + 25 + 15 + 30 + 24) / 12 Overall Mean (X-double-bar) = 23.17 (rounded to two decimal places)

Step 3: Calculate the Range (R) Calculate the range (R) for each sample. The range is the difference between the highest and lowest values in each sample.

Month Patient Concerns (X-bar) Range (R) Jan 17 17-17=0 Feb 16 16-16=0 Mar 25 25-25=0 Apr 17 17-17=0 May 19 19-19=0 Jun 18 18-18=0 Jul 28 28-28=0 Aug 26 26-26=0 Sep 25 25-25=0 Oct 15 15-15=0 Nov 30 30-30=0 Dec 24 24-24=0

Step 4: Calculate the Average Range (R-bar) Calculate the average range (R-bar) of all the ranges calculated in Step 3.

Average Range (R-bar) = (Sum of R) / Number of Samples

Average Range (R-bar) = (0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0) / 12 Average Range (R-bar) = 0

Step 5: Calculate the Control Limits Calculate the control limits for the X-bar chart using the following formulas:

Upper Control Limit (UCL) = X-double-bar + A2 * R-bar Lower Control Limit (LCL) = X-double-bar - A2 * R-bar

Where A2 is a constant based on the sample size and is looked up from statistical tables or control chart constants.

For this case, since the sample size is 5, A2 = 0.729 (lookup value).

UCL = 23.17 + (0.729 * 0) ≈ 23.17 LCL = 23.17 - (0.729 * 0) ≈ 23.17

Step 6: Plot the Control Chart Now, plot the X-bar chart with the X-bar values (sample means) for each month and the calculated control limits.

The X-bar chart will have all data points falling on the overall mean (X-double-bar) of approximately 23.17, and the control limits will also be at this value, since the average range (R-bar) is 0. This indicates that the process is under control, and there is no significant variation in patient concerns over time.

Note: The control chart is based on the assumption that the process is in statistical control and there are no special causes of variation affecting the data. In a real-world scenario, further investigation might be needed if any data point falls outside the control limits or if there are any patterns or trends observed in the chart.