The manager of a semiconductor production line wants to know if the manufacturin
ID: 3351882 • Letter: T
Question
The manager of a semiconductor production line wants to know if the manufacturing process of silicon wafer is stable or not. As a quality engineer, you collected one sample measurement from each of randomly selected three products every day, and you collected data for 25 days in a row. Data is attached.
1. If you want to develop control charts, what type of control charts would you plan to choose? Explain the reasoning behind your answer.
2. Are there any assumptions before using control charts? You do not have to test for these assumptions as part of this question.
3. Suppose the assumptions are met, construct the control chart using the original data. Is the process in control? Explain your findings.
4. What should you recommend the manager do next?
5. If the manager feels that any measurement over 60 or below 10 is not tolerable. What is the Cp and Cpk for this process? What is the DPMO level associated with this process?
6. Explain “common causes” and “special causes” and give at least one example for each. In this case, based on the control chart you developed, explain/identify the trends that can be associated with “common cause” and “special cause” variations.
Day Measurement 1 41 1 70 1 22 2 78 2 53 2 68 3 84 3 34 3 48 4 60 4 36 4 25 5 46 5 47 5 29 6 64 6 16 6 56 7 43 7 53 7 64 8 37 8 43 8 30 9 50 9 29 9 57 10 57 10 83 10 32 11 24 11 42 11 39 12 78 12 48 12 39 13 51 13 57 13 50 14 41 14 29 14 35 15 56 15 64 15 36 16 46 16 41 16 16 17 99 17 86 17 98 18 71 18 54 18 39 19 41 19 29 19 53 20 41 20 39 20 36 21 22 21 40 21 46 22 62 22 70 22 46 23 64 23 52 23 57 24 44 24 38 24 60 25 41 25 63 25 62Explanation / Answer
1) An X-bar and R (range) chart is a pair of control charts used with processes that have a subgroup size of two or more. The standard chart for variables data, X-bar and R charts help determine if a process is stable and predictable. The X-bar chart shows how the mean or average changes over time and the R chart shows how the range of the subgroups changes over time. It is also used to monitor the effects of process improvement theories. As the standard, the X-bar and R chart will work in place of the X-bar and s or median and R chart
2) We can use X-bar and R charts for any process with a subgroup size greater than one. Typically, it is used when the subgroup size falls between two and ten, and X-bar and s charts are used with subgroups of eleven or more
Use X-bar and R charts when you can answer yes to these questions:
4) Collect as many subgroups as possible before calculating control limits. With smaller amounts of data, the X-bar and R chart may not represent the variability of the entire system. The more subgroups you use in control limit calculations, the more reliable the analysis. Typically, twenty to twenty-five subgroups will be used in control limit calculations.
X-bar and R charts have several applications. When you begin improving a system, use them to access the system stability.
After the stability has been assessed, determine if you need to stratify the data. You may find entirely different results between shifts, among workers, among different machines, among lots of materials, etc. To see if variability on the X-bar and R chart is caused by these factors, collect and enter data in a way that lets you stratify by time, location, symptom, operator, and lots.
You can also use X-bar and R charts to analyze the results of process improvements. Here you would consider how the process is running and compare it to how it ran in the past. Do process changes produce the desired improvement?
Finally, use X-bar and R charts for standardization. This means you should continue collecting and analyzing data throughout the process operation. If you made changes to the system and stopped collecting data, you would have only perception and opinion to tell you whether the changes actually improved the system. Without a control chart, there is no way to know if the process has changed or to identify sources of process variability.
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