Portland Community College Engineering Statistic Questions

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Engineering Statistics Midterm Exam 1 Midterm Exam Note: Your submission must contain this cover. Please scan clearly. Unclear presentation may result in point deduction. Solve the problems using MS Excel, but do not submit your Excel file. Please, do submit one PDF file into the submission folder. Fill in the blanks with your solutions manually or electronically. NAME: SIGN: Total: /20 1-1 1-2 /2 3-1 1-3 /2 3-2 /2 1-4 /2 3-3 /2 2 /2 3-4 /2 /2 4-1 /2 /2 1 Engineering Statistics Midterm Exam 1 1. UPMC Hospital has been under recent pressure from stakeholders to improve cost efficiency and customer service. In response, the hospital calls in the Health Service Administration (HSA) Consulting Team of Robert Morris & Company (RMC). After initial analysis, we (HSA@RMC) decided to target the X-ray service process. We study the X-ray service process to recommend improvements. We identified the point of entry into the process as the instant that a patient leaves the physician’s office to walk to the X-ray lab. The point of exit is defined as the instant that both the patient and the completed X-ray film are ready to enter the physician’s office for diagnosis. The unit of flow is a patient. We examined the entire process in detail and broke it down into the 11 constituent activities identified as in the table of the next page. Note that a, c and b denote the optimistic time, the most likely time and the pessimistic time. The flow chart is as follows: 2 Engineering Statistics Midterm Exam 1 Activity Description /Event Start Patient leaves the physician’s office. 1 Patient walks to the X-ray lab. 2 The X-ray request travels to the X-ray lab by a messenger. 3 An X-ray technician fills out a standard form based on the information supplied by the physician. 4 The receptionist receives from the patient information concerning insurance, prepares and signs a claim form, and sends to the insurer. 5 Patient undressed in preparation for X-ray 6 A lab technician takes X-rays. 7 A darkroom technician develops X-rays. 8 A lab technician prepares X-rays for transfer. 9 Patient puts on clothes and gets ready to leave lab. 10 Patient walks back to the physician’s office. 11 The X-rays are transferred to the physician by a messenger. End Patient and X-rays arrive at the physician’s office. 3 Engineering Statistics Midterm Exam 1 1.1 (2 points) The duration of each activity is of Beta Distribution. Note that it is a BETA DISTRIBUTION. Fill in the following table. Activity/event a c b Mean Variance Start 1 5 15 30 2 5 15 25 3 10 20 30 4 5 10 15 5 10 20 40 6 10 15 30 7 10 30 40 8 15 40 55 9 5 10 30 10 3 7 10 11 15 20 40 End 4 Engineering Statistics Midterm Exam 1 1.2 (2 points) There are 4 paths as follows: Path 1: Start → 1 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End Path 2: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 → 10 → End Path 3: Start → 1 → 4 → 5 → 6 → 7 → 8 → 11 → End Path 4: Start → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 11 → End What are the mean and the variance of the duration of each path? What is the longest path in mean time? Fill in the following table and identify the longest path in mean time. Mean Variance Path 1 Path 2 Path 3 Path 4 Answer: The longest path in mean time is . 1.3 (2 points) What is the probability of completing the longest path within 185 minutes? Assume that the duration of the longest path is normally distributed. Answer: . 1.4 (2 points) What is the time T for which the probability to complete the longest path is 95%? Assume that the duration of the longest path is normally distributed. Answer: . 5 Engineering Statistics Midterm Exam 1 2. (2 points) In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.61. What is the probability of two or more deaths in a corps in three years? Answer: . 6 Engineering Statistics Midterm Exam 1 3. Consider the following system made up of functional components in parallel and series. C2 0.80 C1 C4 0.95 0.80 C3 0.95 3-1. (2 points) What is the probability that the system operates? Answer: . 7 Engineering Statistics Midterm Exam 1 3-2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. Answer: . 3-3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. Answer: . 8 Engineering Statistics Midterm Exam 1 3-4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.99 and when the probability that component C3 functions is improved to a value of 0.99. Which improvement increases the system reliability more? Answer: . 9 Engineering Statistics Midterm Exam 1 4. Wonder Shed Inc. is a manufacturer of storage sheds. The manufacturing process involves the procurement of sheets of steel that will be used to form both the roof and the base of each shed. The first step involves separating the material need for the roof from that needed for the base. Then the roof and the base can be fabricated in parallel, or simultaneously. Roof fabrication involves first punching and then forming the roof to shape. Base fabrication entails the punching-and-forming process plus a subassembly operation. Fabricated roofs and bases are then assembled into finished sheds that are subsequently inspected for quality assurance. A list of activities needed to fabricate a roof, fabricate a base, and assemble a shed is given in Table 4.1. A flowchart of the process is shown in Figure 4.1. 10 Engineering Statistics Midterm Exam 1 4.1 (2 points) We use a triangular distribution to represent an activity duration. (Note that it is a TRAIANGULAR DISTRIBUTION.) We assume that the activity durations are independent. We denote the optimistic, the most likely and the pessimistic times by a, c and b. Calculate the mean time and the variance of each activity duration and fill in the blanks of the table below. Activity a c b 1 3 4 6 2 5 7 8 3 4 5 7 4 3 7 10 5 3 5 6 6 5 6 8 7 2 3 6 8 7 8 12 Mean Variance 11
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Engineering Statistics
Midterm Exam 1

Midterm Exam

Note: Your submission must contain this cover. Please scan clearly. Unclear presentation may
result in point deduction. Solve the problems using MS Excel, but do not submit your Excel file.
Please, do submit one PDF file into the submission folder. Fill in the blanks with your solutions
manually or electronically.

NAME:
SIGN:
Total:

/20

1-1

1-2

/2

3-1

1-3

/2

3-2

/2

1-4

/2

3-3

/2

2

/2

3-4

/2

/2

4-1

/2

/2

1

Engineering Statistics
Midterm Exam 1

1. UPMC Hospital has been under recent pressure from stakeholders to improve cost efficiency
and customer service. In response, the hospital calls in the Health Service Administration (HSA)
Consulting Team of Robert Morris & Company (RMC). After initial analysis, we (HSA@RMC)
decided to target the X-ray service process. We study the X-ray service process to recommend
improvements.
We identified the point of entry into the process as the instant that a patient leaves the
physician’s office to walk to the X-ray lab. The point of exit is defined as the instant that both
the patient and the completed X-ray film are ready to enter the physician’s office for diagnosis.
The unit of flow is a patient. We examined the entire process in detail and broke it down into
the 11 constituent activities identified as in the table of the next page. Note that a, c and b
denote the optimistic time, the most likely time and the pessimistic time. The flow chart is as
follows:

2

Engineering Statistics
Midterm Exam 1
Activity

Description

/Event
Start

Patient leaves the physician’s office.

1

Patient walks to the X-ray lab.

2

The X-ray request travels to the X-ray lab by a messenger.

3

An X-ray technician fills out a standard form based on the information supplied by
the physician.

4

The receptionist receives from the patient information concerning insurance,
prepares and signs a claim form, and sends to the insurer.

5

Patient undressed in preparation for X-ray

6

A lab technician takes X-rays.

7

A darkroom technician develops X-rays.

8

A lab technician prepares X-rays for transfer.

9

Patient puts on clothes and gets ready to leave lab.

10

...


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