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Homework answers / question archive / Section 1 – Short Answer (30 points – 5 points per question) Describe how Bayesian statistics differs from more traditional methods that use the frequency of outcomes from large studies

**Section 1 – Short Answer (30 points – 5 points per question)**

- Describe how Bayesian statistics differs from more traditional methods that use the frequency of outcomes from large studies.
- Briefly describe the problems of using the 6-Sigma framework to improve quality in Healthcare? Briefly describe the problems of using Lean to improve quality in Healthcare? Briefly describe how combining Lean and 6-Sigma is effective to improve quality in Healthcare.
- The below figure shows a process to treat a patient in an ER. It consists of three stages: Triage, Treatment, and Checkout. Assume that a patient comes every 30 mins. There is no randomness in the patient arrival rate or the service rate.

- What is the Throughput time (Do not include any waiting time)?
- What is the Cycle time of the entire Process (i.e. how fast do patients come out of this system)?
- If there is any waiting in this system between stages please identify where a que will form.
- Assume you have simple queuing system that models patients arriving and being treated in an ER. This is a simple system with a single que (M/M/1). A patient arrives on average every 20 minutes. A patient is served on average every 15 minutes.
- What is the Capacity Utilization of this Que?
- What is the Average total number of patients in this system
- Describe why a discrete event simulation of this simple queuing system is more useful to an operations manager?
- You are the manager of a Surgi-Center that performs minor surgical cases. The Center has 4 operating rooms and, on average, each case takes 30 minutes to perform. After each case clean-up requires 30 minutes. If the Center schedules its first case for 8:00 a.m., no cases are performed between 12:00 and 1:00 p.m., and the last case must be completed by 5:00, what is the daily capacity of the Center in cases? If the clean-up is reduced to 25 minutes does this increase the daily capacity? (If yes, what is the new capacity?) If the clean-up is reduced to 10 minutes does this increase the daily capacity? (If yes, what is the new capacity?).

Discuss John Snow’s study of cholera in 1854 in the context of how the display of information effects the interpretation. Discuss both the cause and effect data as illustrated in the bar graphs as well as the geographic location as shown in the maps of the problem. (Hint – think about Tufte’s work and the slides I showed from his book).

**Section 2 – Probability Analysis (20 points)**

1 – In class we discussed the probability of having cancer if your mammogram is positive using Bayesian methods. See the posted slides and reading. In class we discussed how to think about Bayesian methods using numbers. The tree we discussed in class is shown below.

The above tree is based on the following assumptions: The test is 80% accurate, the false-positive rate is 10%, and 1% of the patients tested have cancer.

A salesman is trying to sell your hospital a new mammogram that is 100% effective in detection. When you look at the specification you notice that while the test accuracy has been increased, the false positive rate has increased to 15%. When you question the salesman about this he claims this is not a problem because the test reliability has increased by 20% (from 80% to 100%) while the false positive rate has only increased 5% (from 10% to 15%), thus the probability that if your test is positive you have cancer is greater. To determine if the salesman is correct solve the below tree with the new assumptions (i.e. 100% test accuracy, 15% false rate).

- Probability of cancer with positive test is = G

**H (2 points)**what does the probability of having a false positive need to be if you want the probability of having cancer if you have a positive mammogram (i.e. G) to be = 8/107, which is the same as the above example = H

**Section 3 – Process Analysis (20 points)**

Using the data for Q3 to do a root cause analysis of the problem with rejected claims. You must use QI macros for this analysis, and you must include figures to illustrate the data and demonstrate the change. You must also describe the root cause and change. (Hint – I would start with a figure that shows the data with a time factor, and then I would show a figure that shows the distribution of the data, I would also include at least 3 more figures to show the root cause and the change.

**Section 4 – Data Visualization (30 points)**

Analyze the following data sets, 10 points for each data set. You must use Tableau to create charts to help explain the data on the last two question. You may use QI macros on Q1. . You may use more than one display technique for each question.

- Data set one is the number of complaints a hospital received each week. You may assume the number of patients per week is the same. Each patient may complain at most one time. For this data set assume management was not happy with the current # of complaints. They found and fixed one problem, they had a rude service provider that was asked to leave. Describe the data, where the change occurred, and how much has the problem improved.
- Data set two are patient satisfaction scores for two hospitals. The possible range of scores is 0 – 10. You are the manager for Hospital 1. Compare your patient satisfaction to that of Hospital 2.
- Data set three are the # of total falls from all patients in two Hospitals per week. Hospital # 1 has 50 patients; Hospital #2 has 25 patients. Each patient may fall 0 or more times. You are the manager for Hospital 1. Compare this quality metric to Hospital 2.