Thirty Patients Who Checked Out Of Rock Creek County Region

Thirty Patients Who Check Out Of The Rock Creek County Regional Hospit

Thirty patients who check out of the Rock Creek County Regional Hospital each week are asked to complete a questionnaire about hospital service. Since patients do not feel well when they are in the hospital, they typically are very critical of the service. The number of patients who indicated dissatisfaction of any kind with the service for each 30-patient sample over a 16-week period is provided. Construct a control chart to monitor customer satisfaction at the hospital using 3-sigma limits and determine if the process is in control.

Paper For Above instruction

In healthcare quality management, the application of control charts plays a crucial role in monitoring service processes and ensuring consistent patient satisfaction levels. Specifically, when assessing patient dissatisfaction, control charts can help identify variations that signify either common causes or special causes affecting service quality. In this context, we analyze the weekly dissatisfaction rates of patients at the Rock Creek County Regional Hospital through the construction of a p-chart, which is appropriate for monitoring proportions or percentages of dissatisfied patients in a process.

The data comprises the number of dissatisfied patients each week out of a fixed sample size of 30 patients over a 16-week period. To construct the control chart, we first need to calculate the proportion dissatisfied each week, denoted as p̂ (p-hat). Then, we compute the overall average proportion of dissatisfaction, \(\bar{p}\), along with the control limits, which are set typically at ±3 standard deviations (3-sigma) from the mean.

Calculating the proportions involves dividing the number of dissatisfied patients each week by the total sample size (30). To exemplify, suppose the weekly dissatisfaction counts are as follows: 5, 4, 6, 3, 5, 4, 7, 2, 6, 5, 3, 4, 5, 6, 4, 5. The corresponding proportions (p̂) are computed by dividing each weekly dissatisfied count by 30. The average proportion of dissatisfaction, \(\bar{p}\), is then obtained by summing all weekly p̂ values and dividing by 16.

Once \(\bar{p}\) is established, the control limits are calculated using the formulas:

UCL = \(\bar{p}\) + 3 * \(\sqrt{\frac{\bar{p}(1 - \bar{p})}{n}}\)


LCL = \(\bar{p}\) - 3 * \(\sqrt{\frac{\bar{p}(1 - \bar{p})}{n}}\)

where n = 30, the sample size each week. The control limits help identify whether weekly dissatisfaction rates are within expected variation or indicate a process shift warranting investigation. Any point beyond these limits or patterns such as runs or trends suggest that the process is out of control.

Constructing the p-chart involves plotting each weekly p̂ against the weeks, along with the central line (\(\bar{p}\)) and the calculated control limits. This visual allows hospital management to monitor the stability of patient satisfaction levels. If all points lie within the control limits and no non-random patterns are detected, the process can be considered in statistical control. Conversely, points outside the limits or systematic patterns suggest variability caused by assignable causes needing corrective action.

In conclusion, establishing a p-chart for patient dissatisfaction provides a powerful tool for continuous quality improvement at the hospital. It enables early detection of changes in patient perception and facilitates targeted interventions, ultimately enhancing the quality of hospital services and patient outcomes. Regular application of control charts in healthcare settings ensures a data-driven approach to maintaining and improving service quality over time.

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