Exam 26: Statistical Process Control

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In statistical process control, the range often substitutes for the standard deviation.

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Mean charts and range charts complement one another, one detecting shifts in process average, the other detecting shifts in process dispersion.

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Examine the Statistical Process Control outputs below. Answer the following questions. a. What is the sample size? b. What is the number of samples? c. What is the mean of sample 8; what is the range of sample 10? d. Is this process in control? Explain-a simple Yes or No is insufficient. e. What additional steps should the quality assurance team take? Mean Range UCL (Upper control limit) 12.6856 1.0193 CL (Center line) 12.36 0.67 LCL (Lower control limit) 10.0344 0 Sample Number Item 1 Item 2 Item 3 Item 4 Mean Range Sample 1 12.2 12.6 12 12.1 12.225 0.6 Sample 2 11.9 12.5 12.4 12.7 12.375 0.8 Sample 3 12 12.2 12.9 13.1 12.55 1.1 Sample 4 12.5 12.5 12.4 12.8 12.55 0.4 Sample 5 12.2 12.8 12.7 12 12.425 0.8 Sample 6 12.1 12.5 11.8 12.3 12.175 0.7 Sample 7 12.3 12.4 12.8 12.4 12.475 0.5 Sample 8 12 12.1 12.4 12.2 12.175 0.4 Sample 9 12.1 12.8 12.4 11.9 12.3 0.9 Sample 10 12.6 12.4 12.1 12.3 12.35 0.5

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A local manufacturer supplies you with parts, and you would like to install a quality monitoring system at his factory for these parts. Historically, the defect rate for these parts has been 1.25% (You've observed this from your acceptance sampling procedures, which you would like to discontinue). Develop ± 3σ control limits for this process. Assume the sample size will be 200 items.

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A Cp of 1.33 indicates how many sigma limits?

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The acceptable quality level (AQL) is the average level of quality we are willing to accept.

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A manufacturer uses statistical process control to control the quality of the firm's products. Samples of 50 of Product A are taken, and a defective/acceptable decision is made on each unit sampled. For Product B, the number of flaws per unit is counted. What type(s) of control charts should be used?

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The x-bar chart, like the c-chart, is based on the exponential distribution.

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What does it mean for a process to be "capable"?

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The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by a Cpk index of

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A department chair wants to monitor the percentage of failing students in classes in her department. Each class had an enrollment of 50 students last spring. The number of failing students in the 10 classes offered that term were 1, 4, 2, 0, 0, 0, 0, 0, 0, and 3, respectively. Compute the control limits for a p-chart at the 95% confidence level. Is the process in control?

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If μ = 9 ounces, σ = 0.7 ounces, and n = 9, calculate the 3-sigma control limits.

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Assignable variation

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The width of a gold bar is intended to be 0.42 cms. Inspection samples contain six bars each. The average range of these samples is 0.007 cms. What are the upper and lower control limits for the x-bar and R-chart for this process, using 3-sigma limits?

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A normal distribution is generally described by its two parameters: the mean and the range.

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The type of inspection that classifies items as being either good or defective is

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A city police chief decides to do an annual review of the police department by checking the number of monthly complaints. If the total number of complaints in each of the 12 months were 15, 18, 13, 12, 16, 20, 5, 10, 9, 11, 8, and 3 and the police chief wants a 90% confidence level, are the complaints in control?

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Pierre's Motorized Pirogues and Mudboats is setting up an acceptance sampling plan for the special air cleaners he manufactures for his boats. His specifications, and the resulting plan, are shown on the POM for Windows output below. Pierre wants acceptance sampling to remove ALL defects from his production of air cleaners. Explain carefully why this won't happen. Pierre's Motorized Pirogues and Mudboats is setting up an acceptance sampling plan for the special air cleaners he manufactures for his boats. His specifications, and the resulting plan, are shown on the POM for Windows output below. Pierre wants acceptance sampling to remove ALL defects from his production of air cleaners. Explain carefully why this won't happen.

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An operator trainee is attempting to monitor a filling process that has an overall average of 705 cc. The average range is 17 cc. If you use a sample size of 6, what are the upper and lower control limits for the x-bar and R chart?

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Can "in control" and "capable" be shown on the same chart?

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