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EIND 477 – Exam 3 – 100 points

1. The exam is due on Thursday, April 16, 2020 – 9:00 am on D2L. There is a special drop box for the exam labeled Exam 3.
2. Please submit ONE word file (NO PDF as we will run a software to check for plagiarism). If you submit multiple files, only the first file uploaded will be graded. The rest of the files will be ignored. If you need help uploading only one document please let me know before 5 pm on Wednesday, April 15th.
3. No Excel or Minitab files will be graded.
4. Work individually. You may consult your book, notes, and use Excel and Minitab to validate your answers. However, you must submit a demonstration of your calculations in the submitted file to obtain full credit.
5. No questions will be answered during the exam period.

Part 1: Questions (20 points)

Question 1: Briefly explain the concept of statistical quality control. (4 points)

Question 2: What is an OCAP and why is it important? (3 points)

Question 3: What is an OC curve and what information can we infer from it? (3 points)

Question 4: Explain the principle of rational subgrouping and why is it important when you are constructing control charts. (3 points)

Question 5: Explain how do we monitor both the within and between sample variability in a set of X bar and s charts and why is it important to monitor both types of variabilities? (3 points)

Question 6: Briefly discuss the types of error (alpha and beta) associated with control charts (4 points)

Part 2: True or False (44 points)

1. Quality as a concept can be subdivided into quality of design and quality of conformance. _____
2. Statistical process control is concerned with quality of design._____
3. Deming is credited with creating the concept of the control chart and statistical process control. _____
4. Variation in a process can be partitioned between common causes and assignable causes. _____
5. Common cause variation is unnatural variation in a process. _____
6. Common cause variation is inherent in a process when it is operating as designed. _____
7. Assignable cause variation is unnatural variation in a process. _____
8. When common cause variation is present the process is said to be out of control. _____
9. The primary purpose of a control chart is to determine the type of variation present in a process. _____
10. Deming contended that only management can address common cause variation since it is inherent in the process. _____
11. Control charts by themselves will tell us much information about process capability. _____
12. SPC addresses the quality control process of Juran’s quality trilogy.
13. Variable and Attribute data are the two basic types of data used for control charts. _____
14. Attribute data are those data that can be measured on a continuous scale. _____

1. Variable data can be plotted on an x-bar chart and a rand chart. _____

1. The centerline on an x-bar chart is the grand mean. _____

1. One point falling outside the control limits on an x-bar chart means the process is in control and there is common variation. _____

1. Patterns in the plotted data on a control chart can sign that a process may be out of control. _____

2. Attribute control charts are based on some discrete distribution such as binomial or Poisson. _____
3. A Number defective chart is an alternative chart that can be substituted for the x-bar chart._____
4. The c-chart is used to control the average number of defects per inspection unit in the samples of fixed size. _____

Part 3: Exercises (36 points)

You may use Excel or Minitab for this part of the exam. However, make sure you demonstrate your calculations and the use of the formulas and include the tables generated in Excel and the charts as needed.

Exercise 1: (6 points)

A process is to be monitored with standard values m = 10 and s = 2.5.  The sample size is n = 2.

(a)  Find the center line and control limits for the  chart.

(b)  Find the center line and control limits for the R chart.

(c)  Find the center line and control limits for the s chart.

Exercise 2: (6 points)

The manufacturer wishes to set up a control chart at the final inspection station for a gas water heater.  Defects in workmanship and visual quality features are checked in this inspection.  For the past 22 working days, 176 water heaters were inspected and a total of 924 nonconformities reported.

(a)  What type of control chart would you recommend here, and how would you use it?

(b)  Using two water heaters as the inspection unit, calculate the center line and control limits that are consistent with the past 22 days of inspection data.

Exercise 3: (6 points)

A fraction nonconforming control chart with n = 400 has the following parameters: UCL = 0.0809, Center line = 0.0500, LCL = 0.0191.

(a)  Find the width of the control limits in standard deviation units.

(b)  What would be the corresponding parameters for an equivalent control chart based on the number nonconforming?

Exercise 4: (6 points)

A paper mill uses a control chart to monitor the imperfection in finished rolls of paper.  Production output is inspected for 20 days, and the resulting data are shown in Table 7E.13.  Use these data to set up a control chart for nonconformities per roll of paper.  Does the process appear to be in statistical control?  What center line and control limits would you recommend for controlling current production?

Exercise 5: (12 points)

The data in Table 9E.1 represent individual observations on molecular weight taken hourly from a chemical process.  The target value of molecular weight is 1,050 and the process standard deviation is thought to be about s = 25.

• Set up a tabular CUSUM for the mean of this process. Design the CUSUM to quickly detect a shift of about 1.0s in the process mean. HINT: d = 1s; H = 5s.
• Rework Exercise 5 using an EWMA control chart with l = 0.1 and L = 2.7. Compare your results to those obtained with the CUSUM.

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