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Chapter 14: Q4BSC (page 654)
Lake Mead Elevations What does the R chart tell us about Lake Mead?
The R-chart shows that variation in the process is out of control.
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In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.
What is the value of\(\bar \bar x\)? In general, how is a value of\(\bar \bar x\)found?
Heights On the basis of Data Set 1 “Body Data” in Appendix B, assume that heights of men are normally distributed, with a mean of 68.6 in. and a standard deviation of 2.8 in.
a. The U.S. Coast Guard requires that men must have a height between 60 in. and 80 in. Findthe percentage of men who satisfy that height requirement.
b. Find the probability that 4 randomly selected men have heights with a mean greater than 70 in.
In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.
What is the value of\(\bar R\)? In general, how is a value of\(\bar R\)obtained?
Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply
Car Batteries Defective car batteries are a nuisance because they can strand and inconvenience drivers, and drivers could be put in danger. A car battery is considered to be defective if it fails before its warranty expires. Defects are identified when the batteries are returned under the warranty program. The Powerco Battery corporation manufactures car batteries in batches of 250, and the numbers of defects are listed below for each of 12 consecutive batches. Does the manufacturing process require correction?
3 4 2 5 3 6 8 9 12 14 17 20
s Chart: In this section we described control charts for R and x based on ranges. Control charts for monitoring variation and center (mean) can also be based on standard deviations. An s chart for monitoring variation is constructed by plotting sample standard deviations with a centerline at s (the mean of the sample standard deviations) and control limits at B4s and B3s,where B4and B3 are found in Table 14-2 on page 660 in this section. Construct an s chart for the data of Table 14-1 on page 655. Compare the result to the R chart given in Example 3 “R Chart of Altimeter Errors.”
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