ISE235-HW3-solutions

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San Jose State University *

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235

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Industrial Engineering

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Jan 9, 2024

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pdf

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1 ISE 235 Homework Assignment #4 – Due 11:59 PM on October 26, 2020 NOTE: Most HW problems are exercises of the textbook. Some students may have the 7 th , 6 th or 5 th Edition while some others may have the 8 th Edition, which is the most recent edition and is the edition being sold at the Spartans Bookstore. Any of these four editions should suffice for the course. To avoid confusion, the first sentence of every HW problem assigned from the textbook will be stated as part of the HW problem specification. Problem #1 : (3-D Charts) In this problem, wafer is processed one at a time by a machine. (They are not processed in a group or lot.) Within-piece variability is important and is to be tracked by a within-piece range 𝑅 𝑊 chart. In addition, the process mean is to be monitored with an individual X chart and piece-to-piece variability is to be monitored with a moving range 𝑅 𝑃,𝑀 chart, with a moving window size of 2. Part (a) : Suppose that process mean 𝜇 is 100. Suppose also that the piece-to-piece variability follows a Normal distribution with mean 0 and standard deviation σ 𝑃 =2 . Finally, suppose that within-piece variability follows a Normal distribution with mean 0 and standard deviation σ 𝑊 =1 . Develop the control limits for the three charts.
2 Part (b) : Suppose now that none of three process parameters are known and that five measurements have been collected at five different locations on each of 30 wafers. The collected data are organized in a 30 by 5 matrix, as shown in a companion Excel file entitled ISE235-Problem#1-3D charts-with known parameters and with estimated parameters Develop the control limits for the three control charts. Also, plot on the three control charts the corresponding statistics for the 30 samples. Check if any of the plotted points fall outside of any of the control limits of the three control chart. Part (c): Now suppose that the five locational data are mistaken for data collected on five different wafers and the five phantom wafers constitute a subgroup (i.e., a sample of five wafers). Develop the control limits for the resulting 𝑋 ̅ and R charts. Then, plot on the two control charts the corresponding statistics for the 30 samples. Then, check if any of the plotted points fall outside of any of the control limits of the two control chart. If so, explain what led to the control limit violations. Solutions for part (b) and part (c): please refer to ISE235-HW4.1-3D charts-with known parameters and with estimated parameters-solution.xlsx ISE235-HW4.1-3D charts-with known parameters and with estimated parameters-solution-estimated parameters.doc ISE235-HW4.1-3D charts-with known parameters and with estimated parameters-solution-WRONG charts.doc Problem #2: Part (a): The data in the companion data table represent the results of inspecting all units of a personal computer produced for the past ten days. Does the process appear to be in control? Please use the Excel data table provided on this class website. ISE235-Problem#2-data-table-PC inspection
3 Part (b): Construct a standardized control chart for the data of Part (a). Problem #3: Surface defects have been counted on 25 rectangular steel plates, and the data are shown in the companion data table. Set up a control chart for nonconformities using these data. Does the process producing the plates appear to be in statistical control? Please use the Excel data table provided on this class website. ISE235-Problem#3-data-table-surface defects
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