New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
statistics principles and methods

Elementary Statistical Quality Control 2nd Edition John T. Burr - Solutions

A system consists of N components of types 1 and 2: N1 is the number of components of type 1, N2 is the number of components of type 2, and N = N1 + N2. The components have a reliability each of p1 and p2, respectively. The failure of the system is defined as the failure of any n1 out of N1
For the system described in Problem 15.17, develop a fault tree model and evaluate the minimal cut set for N1 = 10, N2 = 20, n1 = 2, n2 = 3, p2 = 0.99, and p2 = 0.9. Determine the reliability of the system.
For the system described in Problem 15.17, develop a fault tree model and evaluate the minimal cut set for N1 = 10, N2 = 20, n1 = 5, n2 = 10, p2 = 0.99, and p2 = 0.9. Determine the reliability of the system.
For the system described in Problem 15.17, develop a fault tree model and evaluate the minimal cut set for N1 = 10, N2 = 20, n1 = 8, n2 = 15, p2 = 0.99, and p2 = 0.9. Determine the reliability of the system.
The accident probability at a new intersection is of interest to a traffic engineer. The engineer subjectively estimated the weekly accident probability as follows:Weekly Accident Probability Subjective Probability of Accident Probability 0.1 0.30 0.2 0.40 0.4 0.20 0.6 0.05 0.8 0.04 0.9 0.01 Solve
1. Section 8.6.2 reports data on reported hangover symptoms. For group 2, use the S-PLUS function rmanova to compare the trimmed means corresponding to times 1, 2, and 3.
2. For the data used in Exercise 1, compute confidence intervals for all pairs of trimmed means, using the S-PLUS function pairdepb.
3. Analyze the data for the control group reported in Table 6.1 using the methods in Sections 8.1 and 8.2. Compare and contrast the results.
4. Repeat Exercise 3 using the rank-based method in Section 8.5.1. How do the results compare to using a measure of location?
5. Repeat Exercises 3 and 4 using the data for the murderers in Table 6.1.
6. Analyze the data in Table 6.1 using the methods in Sections 8.6.1 and 8.6.3.
7. Repeat Exercise 6, only now use the rank-based method in Section 8.6.7.
1. Generate 20 observations from a standard normal distribution, and store them in the R or S-PLUS variable ep. Repeat this and store the values in x. Compute y=x+ep and compute Kendall’s tau. Generally, what happens if two pairs of points are added at (2.1, −2.4)? Does this have a large impact
2. Repeat Exercise 1 with Spearman’s rho, the percentage bend correlation, and the Winsorized correlation.
3. Demonstrate that heteroscedasticity affects the probability of a type I error when testing the hypothesis of a zero correlation based on any type M correlation and nonbootstrap method covered in this chapter.
4. Use the function cov.mve(m,cor=T)to compute the MVE correlation for the star data in Figure 9.2. Compare the results to the Winsorized, percentage bend, skipped, and biweight correlations as well the M-estimate of correlation returned by the S-PLUS function relfun.
5. Using the Group 1 alcohol data in Section 8.6.2, compute the MVE estimate of correlation and compare the results to the biweight midcorrelation, the percentage bend correlation using β = .1, .2, .3, .4, and .5, the Winsorized correlation using γ = .1 and .2, and the skipped correlation.
6. Repeat Exercise 5 using the data for Group 2.
7. The method of detecting outliers, described in Section 6.4.3, could be modified by replacing the MVE estimator with the Winsorized mean and covariance matrix. Discuss how this would be done and its relative merits.
8. Using the data in the file read.dat, test for independence using the data in columns 2, 3, and 10 and the S-PLUS (or R) function pball. Tryβ = .1, .3, and .5. Comment on any discrepancies.
9. Examine the variables in Exercise 8 using the R function mscor.
10. For the data used in Exercises 8 and 9, test the hypothesis of independence using the function indt. Why might indt find an association not detected by any of the correlations covered in this chapter?
11. For the data in the file read.dat, test for independence using the data in columns 4 and 5 and β = .1.
12. The definition of the percentage bend correlation coefficient, ρpb, involves a measure of scale, ωx, that is estimated with ωˆ = W(m), where Wi = |Xi − Mx| and m = [(1 − β)n], 0 ≤ β ≤ .5. Note that this measure
13. If in the definition of the biweight midcovariance, the median is replaced by the biweight measure of location, the biweight midcovariance is equal to zero under independence. Describe some negative consequences of replacing the median with the biweight measure of location.
14. Let X be a standard normal random variable, and suppose Y is contaminated normal with the probability density function given by Eq. (1.1).Let Q = ρX + 1 − ρ2Y, −1 ≤ ρ ≤ 1. Verify that the correlation between X and Q is
1. The average LSAT scores (x) for the 1973 entering classes of 15 American law schools and the corresponding grade point averages (y) are as follows.
2. Discuss the relative merits of βˆch.
3. Using the data in Exercise 1, show that the estimate of the slope given byβˆch is 0.0057. In contrast, the OLS estimate is 0.0045, and βˆm = 0.0042.Comment on the difference among the three estimates.
4. Let T be any regression estimator that is affine equivariant. Let A be any nonsingular square matrix. Argue that the predicted y values, yˆi, remain unchanged when xi is replaced by xiA.
5. For the data in Exercise 1, use the S-PLUS function reglev to comment on the advisability of using M regression with Schweppe weights.
6. Compute the hat matrix for the data in Exercise 1. Which x values are identified as leverage points? Relate the results to Exercise 5.
7. The example in Section 6.6.1 reports the results of drinking alcohol for two groups of subjects measured at three different times. Using the group 1 data, compute an OLS estimate of the regression parameters for predicting the time 1 data using the data based on times 2 and 3.Compare the results
8. For the data used in Exercise 7, compute the .95 confidence intervals for the parameters using OLS as well as M regression with Schweppe weights.
9. Referring to Exercise 6, how do the results compare to the results obtained with the S-PLUS function reglev?
10. For the data in Exercise 6, verify that the .95 confidence intervals for the regression parameters, using the S-PLUS function regci with M regression and Schweppe weights, are (−0.2357, 0.3761) and(−0.0231, 1.2454). Also verify that if regci is used with OLS, the confidence intervals are
11. The file read.dat contains reading data collected by L. Doi. Of interest is predicting WWISST2, a word identification score (stored in column 8), using TAAST1, a measure of phonological awareness stored in column 2, and SBT1 (stored in column 3), another measure of phonological awareness.
12. For the data used in Exercise 11, compute the hat matrix and identify any leverage points. Also check for leverage points with the S-PLUS function reglev. How do the results compare?
13. For the data used in Exercise 11, RAN1T1 and RAN2T1 (stored in columns 4 and 5) are measures of digit-naming speed and letternaming speed, respectively. Use M regression with Schweppe weights to estimate the regression parameters when predicting WWISST2. Use the function elimna, described in
14. For the data in Exercise 13, identify any leverage points using the hat matrix. Next, identify leverage points with the function reglev. How do the results compare?
15. Graphically illustrate the difference between a regression outlier and a good leverage point. That is, plot some points for which y = β1x + β0, and then add some points that represent regression outliers and good leverage points.
16. Describe the relative merits of the OP and MGV estimators in Section 10.10.
17. For the star data in Figure 6.3, which are stored in the file star.dat, eliminate the four outliers in the upper left corner of the plot by restricting the range of the x values. Then using the remaining data, estimate the standard error of the least squares estimator, the M-estimator with
1. For the data in Exercise 1 of Chapter 10, the .95 confidence interval for the slope, based on the least squares regression line, is (0.0022, 0.0062).Using R, the .95 confidence interval for the slope returned by lsfitci is (0.003, 0.006). The .95 confidence interval returned by both R and the
2. Section 8.6.2 reports data on the effects of consuming alcohol on three different occasions. Using the data for group 1, suppose it is desired to predict the response at time 1 using the responses at times 2 and 3. Test H0: β1 = β2 = 0 using the S-PLUS function regtest and βˆm.
3. For the data in Exercise 1, test H0: β1 = 0 with the functions regci and regtest. Comment on the results.
4. Use the function winreg to estimate the slope and intercept of the star data using 20% Winsorization. (The data are stored in the file star.dat.See Section 1.8 for how to obtain the data.)
5. For the Pygmalion data in Section 11.2.1, use the function reglev to determine which points, if any, are regression outliers. (The data for the control group are stored in pygc.dat, and the data for the experimental group are stored in pyge.dat.)
6. Use runmean to plot a smooth of the Pygmalion data using f = .75 and 20% trimmedmeans. Create a plot for both the control and experimental groups when the goal is to predict post–IQ scores with pretest scores.Comment on how the results compare to using f = 1.
7. Based on the results of Exercise 6, speculate about what a nonrobust smoother might look like. Check your answer with the smoother lowess in S-PLUS.
8. Use the function ancova and the Pygmalion data to compare the control group to the experimental group using means. What might be affecting power?
9. For the reading data in file read.dat, let x be the data in column 2(TAAST1), and suppose it is desired to predict y, the data in column 8 ?
10. For the reading data in the file read.dat, use the S-PLUS function runm3d to investigate the shape of the regression surface when predicting the 20% trimmed mean of WWISST2 (the data in column 8) with RAN1T1 and RAN2T1 (the data in columns 4 and 5).
11. The data in the lower left panel of Figure 11.5 are stored in the file agegesell.dat. Remove the two pairs of points having the largest x value, and create a running-interval smoother using the data that remain.
12. Using the Pygmalion data, compare the slope of the regression line of the experimental group to the control group using the biweight midregression estimator.
13. For the reading data in the upper left panel of Figure 11.5, recreate the smooths. If you wanted to find a parametric regression equation, what might be tried? Examine how well your suggestions perform.
14. For the experimental group of the Pygmalion data in Section 11.2.1, create a plot of the smooth using f = 1 and the function rungen. Recreate the plot, but this time omit the scatterplot of the points by setting the argument scat to F, for false. What does this illustrate?
15. Generate 25 observations from a standard normal distribution and store the results in the S-PLUS variable x. Generate 25 more observations and store them in y. Use rungen to plot a smooth based on the Harrell–Davis estimator of the median. Also create a smooth with the argument scat=F.
16. Generate 25 pairs of observations from a bivariate normal distribution having correlation zero and store them in x. Generate 25 more observations and store them in y. Create a smooth using runm3d. and compare it to the smooth produced by run3bo.
2.1 Hardness Rockwell 15 T: 72, 72, 66, 67, 68, 71, specifications being 66–72 on carburetor tubes.
2.2 Tube diameters: 0.2508, 0.2510, 0.2506, 0.2509, 0.2506 in.
2.3 Dimension on a rheostat knob: 142, 142, 143, 140, 135 in 0.001 in.
2.4 Dimension on an igniter housing: 0.534, 0.532, 0.531, 0.531, 0.533 in.
2.5 Eccentricity or distance between center of cone and center of triangular base on needle valves: 50, 35, 36, in 0.0001 in.
2.6 Number of nonconformities on subassemblies: 2, 8, 3, 3, 7, 1.
2.7 Density of glass: 2.5037, 2.5032, 2.5042 g=cm3.
2.8 Percent of silicon in steel castings: 0.94, 0.89, 0.98, 0.87.For the following two samples of raw data, choose appropriate numerical classes and tabulate the data into a frequency table. Draw an appropriate frequency graph. Comment on the data.
2.9 Data on eccentricity of needle valves, conical point to base, in 0.0001 in. units. Maximum specification limit 0.0100 in.Suggest 0–9, 10–9, and so on for classes.32 30 30 37 18 37 50 35 36 57 24 75 49 6 24 67 25 25 52 56 53 18 39 47 40 51 51 31 61 28 15 10 35 27 49 19 51 34 40 19 32 10 39
2.10 Chemical analyses for manganese in 80 heats of 1045 steel. Data in 0.01% units. Suggest 66–68, 69–71, and so on for classes. Specifications: 70–90.74 79 77 81 72 66 75 80 76 86 84 70 80 62 74 71 68 79 81 76 79 79 84 78 74 88 71 80 79 74 76 75 81 80 80 78 76 81 70 76 79 80 79 84 75 75 76
2.11 The frequency distribution obtained in Problem 2.9.
2.12 The frequency distribution obtained in Problem 2.10
2.13 Density of glass in g=cm3 Density Frequency Density Frequency 2.5012 2 2.5052 19 2.5022 6 2.5062 10 2.5032 25 2.5072 4 2.5042 33 Total: 99
2.14 Over-all height of bomb base Height (in.) Frequency Height (in.) Frequency 0.830 1 0.834 13 0.831 3 0.835 11 0.832 11 0.836 6 0.833 14 0.837 6 Total: 65
2.15 Spring tension in pounds Tension (lb) Frequency Tension (lb) Frequency 50.0 2 53.0 32 50.5 2 53.5 12 51.0 4 54.0 18 51.5 6 54.5 2 52.0 9 55.0 1 52.5 12 Total: 100
2.16 For problem 2.1, calculate the % out of specification that one could expect to find in the production of carburetor tubes assuming that this sample has been representative of production.
2.17 For problem 2.9, determine the % of needle valves exceeding the maximum specification limit in the production lot assuming that this sample represents the lot.
2.18 For problem 2.10, determine the % of all heats that are beyond the specification limits assuming that this sample represents the population.
2.19 For problem 2.13, calculate the % out of specification when the limits are 2.5050 0.0030 g=cm3.
2.20 For problem 2.14, calculate the % out of specification when the limits are 0.8300 and 0.830þ0.010 in.
2.21 For problem 2.15, calculate the % of springs in the lot when the specification calls for a minimum tension of 50 pounds.
3.1 Toss a coin 100 times, keeping track of the number of heads thrown. After each 10 tosses, calculate the occurrence ratio of heads up to that point. Describe the approach to the assumed po¼0.50 for a balanced coin. About how far from the expected 50 heads (in 100 tosses) might we expect our
3.2 Proceed as in Problem 3.1, but roll a die and count the number of times that 6 shows. Using po¼1=6 as the expected probability.
3.3 Given a process with a fraction nonconforming po¼0.02 and taking a random sample of n¼2 pieces, find P(2 good), P(1 good) and P(0 good).
3.4 Same as Problem 3.3 but with po 0.01
3.5 Given as in Example 1 that po¼0.08 for the fraction nonconforming and we take n¼3, find P(3 good), P(2 good), P(1 good) and P(0 good).
3.6 From a lot of N¼8 gauges, of which D¼1 is slightly off, find the distribution of d for results from a random sample of n¼2. Show graphically.
3.7 Same as Problem 3.6, but with n¼3. Show graphically.
3.8 Same as Problem 3.6, but with D¼2 and n¼2.Show graphically.
3.9 Same as Problem 3.8, but with n¼3. Show graphically.
3.10 If the fraction nonconforming for a process is po¼0.10 on minor nonconformities and random sample of 400 is taken, how many can be expected to be nonconforming pieces. How far from this expectation would be a reasonable deviation (sd)?What is about the very worst discrepancy we could
3.11 Find the value of 10C4, 10C6, 10P4.
3.12 From a standard deck of 52 cards, four are drawn without replacement.a. How many different possible hands are there?b. In how many of these will all four be of the same one rank?c. In how many will there be three cards of the same rank and one of some other rank?d. What then is the probability
3.13 Past data have shown an average of co¼1.2 typographical error per magazine page of print. (a)Find the probability of one or fewer typographical errors on a page. (b) Find the probability of three or more errors on a page.
3.14 Past data have shown an average of co¼3.6 leak points per radiator on the initial check test. (a)Find the probability of three or fewer leaks on a radiator. (b) Of five or more.
3.15 At final inspection of trucks, an average of co¼2.0 nonconformities is found. (a) Find the probability of two or fewer nonconformities. (b) Of exactly two nonconformities. (c) Of two or more.
3.16 Over a test area of painted surface, an average of co¼5.4 pinholes is standard for a process. (a) Find the probability of two or fewer pinholes. (b) Of over seven pinholes.
3.17 An executive picks up a sample of five brass bushings from a tote pan containing 1000 of them, of which 100 have at least slight burrs. (a)What is the probability that none in the sample have any burrs? (b) Which distribution is formally correct to use? (c) Which is the simplest distribution
3.18 An automatic screw machine is producing spacers with po¼0.01 for off-diameter pieces. A sample of n¼10 is taken randomly. (a) What is the probability of no off-diameter pieces in the sample?(b) Which distribution is formally correct?(c) Can you approximate with the Poisson distribution?
3.19 A process has produced a lot of 1000 temperature controls for automatic hot water tanks. The fraction nonconforming has been running at po¼0.0020. (a) In a sample of 100, approximate the probabilities of none, one and two nonconforming controls. (b) Which distribution is formally correct? (c)
3.20 Problem 3.14.find sc and find the probability of cco 3sc.

Showing 4700 - 4800 of 6202

First
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved