Questions and Answers of Statistics Engineers Scientists

Repeat Exercise 3, using the S chart in place of the R chart. Repeat Exercise 3 The means are X̅ = 2.505, R̅ = 0.1395, and s̅ = 0.057. a. Calculate the 3σ control limits for the R̅ chart. Is
Someone constructs an X̅ chart where the control limits are at ±2.0σX̅ rather than at ±3σX̅ .a. If the process is in control, what is the ARL for this chart?b. If the process mean shifts by
The target fill weight for a box of cereal is 350 g. Each day a sample of 300 boxes is taken, and the number that are underweight is counted. The number of underweight boxes for each of the last 25
The article ??Influence of Supplemental Acetate on Bioremediation for Dissolved Polycyclic Aromatic Hydrocarbons?? (T. Ebihara and P. Bishop, Journal of Environmental Engineering, 2002:505??513)
Fluid inclusions are microscopic volumes of fluid that are trapped in rock during rock formation. The article ??Fluid Inclusion Study of Metamorphic Gold-Quartz Veins in Northwestern Nevada, U.S.A.:
The following MINITAB output presents a power calculation. a.?What is the power requested by the experimenter? b. To guarantee a power of 0.864138, how many observations must be taken for all
The article cited in Exercise 19 provides measures of electrical conductivity (in Î¼S/cm). The results are presented in the following table.Can a one-way analysis of variance be used to determine
The article??Withdrawal Strength of Threaded Nails?? (D. Rammer, S.Winistorfer, and D. Bender, Journal of Structural Engineering, 2001:442??449) describes an experiment comparing the withdrawal
Refer to Exercise 17. It turns out that the measurements of operator 2 were taken in the morning, shortly after the balance had been powered up. A new policy was instituted to leave the balance
The Williamsburg Bridge is a suspension bridge that spans the East River, connecting the boroughs of Brooklyn and Manhattan in New York City. An assessment of the strengths of its cables is reported
The article ??The Lubrication of Metal-on-Metal Total Hip Joints: A Slide Down the Stribeck Curve?? (S. Smith, D. Dowson, and A. Goldsmith, Proceedings of the Institution of Mechanical Engineers,
The article referred to in Exercise 15 also presents measurements of Young??s modulus for side members of T-braced assemblies. The following table presents data in which the factors are the length of
For some data sets, the F statistic will reject the null hypothesis of no difference in mean yields, but the Tukey–Kramer method will not find any pair of means that can be concluded to differ. For
Refer to Exercise 14.a. Compute the quantity s = √MSE, the estimate of the error standard deviation σ.b. Assuming s to be the error standard deviation, find the sample size necessary in each
Refer to Exercise 12. a. Compute the quantity s =??MSE, the estimate of the error standard deviation σ. b. Assuming s to be the error standard deviation, find the sample size necessary in each
The article ??Use of Taguchi Methods and Multiple Regression Analysis for Optimal Process Development of High Energy Electron Beam Case Hardening of Cast Iron?? (M. Jean and Y. Tzeng, Surface
In an experiment to determine the effect of curing time on the compressive strength of a certain type of concrete, the mean strengths, in MPa, for specimens cured for each of four curing times were
The article ??Enthalpies and Entropies of Transfer of Electrolytes and Ions from Water to Mixed Aqueous Organic Solvents?? (G. Hefter, Y. Marcus, andW.Waghorne, Chemical Reviews, 2002:2773??2836)
In a 25??1design (such as the one in Exercise 12) what does the estimate of the main effect of factor A actually represent? i. The main effect of A. ii. The sum of the main effect of A and the BCDE
Four different types of solar energy collectors were tested. Each was tested at five randomly chosen times, and the power (in watts) was measured. The results were as follows. a. Construct an ANOVA
The article ??An Application of Fractional Factorial Designs?? (M. Kilgo, Quality Engineering, 1988:19??23) describes a 25??1design (half-replicate of a 25design) involving the use of carbon dioxide
The article ??Anodic Fenton Treatment of Treflan MTF?? (D. Saltmiras and A. Lemley, Journal of Environmental Science and Health, 2001:261??274) describes a two-factor experiment designed to study the
Refer to Exercise 18 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for annularly threaded and smooth shank nails. b. Use the
A process that manufactures vinyl for automobile seat covers was studied. Three factors were varied: the proportion of a certain plasticizer (A), the rate of extrusion (B), and the temperature of
Refer to Exercise 10. Is it plausible that the brands of spark plug all have the same mean lifetime? Refer to Exercise 10. One-way Analysis of Variance Analysis of Variance Source Brand Error Total
An experiment to compare the lifetimes of four different brands of spark plug was carried out. Five plugs of each brand were used, and the number of miles until failure was recorded for each.
In a small-disc test a small, disc-shaped portion of a component is loaded until failure. The article €œOptimizing the Sensitivity of the Small-Disc Creep Test to Damage and Test Conditions€
An engineering professor wants to determine which subject engineering students find most difficult among statistics, physics, and chemistry. She obtains the final exam grades for four students who
The lifetime of a tool was investigated under three settings for feed rate and three settings for speed. Four tools were tested under each combination of settings. The results (in hours) were as
The article ??Impact of Free Calcium Oxide Content of Fly Ash on Dust and Sulfur Dioxide Emissions in a Lignite- Fired Power Plant?? (D. Sotiropoulos, A. Georgakopoulos, and N. Kolovos, Journal of
In a 2pdesign with one replicate per treatment, it sometimes happens that the observation for one of the treatments is missing, due to experimental error or to some other cause. When this happens,
The article €œMulti-objective Scheduling Problems: Determination of Pruned Pareto Sets€ (H. Taboada and D. Coit, IIE Transactions, 2008:552€“564), presents examples in
Refer to Exercise 9 in Section 9.1.a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for temperatures of 70°C and 90°C.b. Use the
Vermont maple sugar producers sponsored a testing program to determine the benefit of a potential new fertilizer regimen. A random sample of 27 maple trees in Vermont were chosen and treated with one
Adding glass particles to clay brick may improve the structural properties of the brick. The article ??Effects of Waste Glass Additions on the Properties and Durability of Fired Clay Brick?? (S.
Refer to Exercise 3 in Section 9.1. a. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for treatments B and D. b. Use the Tukey??Kramer method to
The article ??Case Study Based Instruction of DOE and SPC?? (J. Brady and T. Allen, The American Statistician, 2002:312??315) presents the result of a 24??1 factorial experiment to investigate the
The article ??Stability of Silico-Ferrite of Calcium and Aluminum (SFCA) in Air-Solid Solution Limits Between 1240?C and 1390?C and Phase Relationships within the Fe2O3-CaO-Al2O3-SiO2(FCAS) System??
Archaeologists can determine the diets of ancient civilizations by measuring the ratio of carbon-13 to carbon-12 in bones found at burial sites. Large amounts of carbon-13 suggest a diet rich in
A metal casting process for the production of turbine blades was studied. Three factors were varied. They were A: the temperature of the metal, B: the temperature of the mold, and C: the pour speed.
The article €œSprinkler Technologies, Soil Infiltration, and Runoff€ (D. DeBoer and S. Chu, Journal of Irrigation and Drainage Engineering, 2001:234€“239) presents a
The article €œVariance Reduction Techniques: Experimental Comparison and Analysis for Single Systems€ (I. Sabuncuoglu, M. Fadiloglu, and S. C¸ elik, IIE Transactions, 2008:538€“551)
Refer to Exercise 1 in Section 9.1. A scientist wants to determine whether the mean strength of specimens cured at 30°C differs from the mean strengths of specimens cured at 0°C, 10°C, and
The antibiotic gentamicin sulphate is often blended with acrylic bone cement to help prevent infection following joint replacement surgery. The article ??Incorporation of Large Amounts of Gentamicin
The following MINITAB output is for a two-way ANOVA. Something went wrong with the printer, and some of the numbers weren??t printed. Fill in the missing numbers in the table for (a) through (l).
The article €œEfficient Pyruvate Production by a Multi-Vitamin Auxotroph of Torulopsis glabrata: Key Role and Optimization of Vitamin Levels€ (Y. Li, J. Chen, et al. Applied
Three different corrosion-resistant coatings are being considered for use on iron pipes. Ten pieces of pipe are marked off in six equal segments. For each pipe, two segments received coating A, two
The effect of curing pressure on bond strengthwas tested for four different adhesives. There were three levels of curing pressure. Five replications were performed for each combination of curing
Refer to Exercise 2 in Section 9.1.a. Use the Bonferroni method to determine which means, if any, differ from the mean of the control group at the 5% level. b. Use the Tukey??Kramer method to
The article referred to in Exercise 1 also considered the effect of gypsum on the electric conductivity (in dS m??1) of soil. Two types of soil were each treated with three different amounts of
The article ??Nutrient Deprivation Improves Field Performance of Woody Seedlings in a Degraded Semi-arid Shrubland?? (R. Trubata, J. Cortina, and A. Vilagrosaa, Ecological Engineering,
Give an example of a factorial experiment in which failure to randomize can produce incorrect results.
A study was done to see which of four machines is fastest in performing a certain task. There are three operators; each performs the task twice on each machine. A randomized block design is employed.
A machine shop has three machines used in precision grinding of cam rollers. Three machinists are employed to grind rollers on the machines. In an experiment to determine whether there are
The article €œOptimum Design of an A-pillar Trim with Rib Structures for Occupant Head Protection€ (H. Kim and S. Kang, Proceedings of the Institution of Mechanical Engineers,
Indicate whether each of the following quality characteristics is a continuous, binary, or count variable.a. The number of flaws in a plate glass window.b. The length of time taken to perform a final
The thickness specification for aluminum sheets is 0.246–0.254 mm. Data from an X̅ chart, based on samples of size 6, that shows that the process is in control, yield values of X̅ = 0.248 and s̅
True or false:a. Control charts are used to determine whether special causes are operating.b. If no special causes are operating, then most of the output produced will meet specifications.c.
The specification for the diameters of ball bearings is 15.40–15.60 mm. Data from an X̅ chart, based on samples of size 8, that shows that the process is in control, yield values of X̅ = 15.52
The following X̅ chart depicts the last 50 samples taken from the output of a process. Using the Western Electric rules, is the process detected to be out of control at any time? If so, specify at
Fill in the blank. The choices are: is in control; has high capability.a. If the variability in a process is approximately constant over time, the process.b. If most units produced conform to
Fill in the blank: Once a process has been brought into a state of statistical control,i. It must still be monitored continually.ii. Monitoring can be stopped for a while, since it is unlikely that
Refer to Exercise 3. In the last 50 samples, there were a total of 622 defective items. The largest number of defectives in any sample was 24, while the smallest number was 6. Is this enough
Refer to Exercise 1.a. To what value should the process mean be set to maximize the process capability?b. Is it possible to make the process capability acceptable simply by adjusting the process
Repeat Exercise 3, using the S chart in place of the R chart. Repeat Exercise 3. Samples of three resistors are taken periodically, and the resistances, in ohms, are measured. The following table
True or false:a. When a process is in a state of statistical control, then most of the output will meet specifications.b. When a process is out of control, an unacceptably large proportion of the
A newly designed quality-control program for a certain process involves sampling 20 items each day and counting the number of defective items. The numbers of defectives in the first 10 samples are 0,
A process has mean 12 and standard deviation 3. The process is monitored by taking samples of size 5 at regular intervals. The process is declared to be out of control if a point plots outside the
Fill in the blank: When sampling units for rational subgroups,i. it is more important to choose large samples than to sample frequently, since large samples provide more precise information about the
A process that produces mirrors for automobiles is monitored by taking samples of 1500 mirrors and counting the total number of visual flaws on all the sample mirrors. Let cibe the total number of
A quality-control apprentice is preparing a CUSUM chart. The values calculated for SL and SH are presented in the following table. Three of the values have been calculated incorrectly. Which are
A process is monitored for flaws by taking a sample of size 70 each hour and counting the total number of flaws in the sample items. The total number of flaws over the last 50 samples is
A process has mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ
To set up a p chart to monitor a process that produces computer chips, samples of 300 chips are taken daily, and the number of defective chips in each sample is counted. The numbers of defective
Each hour, a 10 m2section of fabric is inspected for flaws. The numbers of flaws observed for the last 20 hours are as follows: a. Compute the upper and lower 3σ limits for a c chart. b. Is the
Samples of eight bolts are taken periodically, and their diameters (in mm) are measured. The following table presents the means, ranges, and standard deviations for 25 consecutive samples. The means
A certain type of integrated circuit is connected to its frame by five wires. Thirty samples of five units each were taken, and the pull strength (in grams) of one wire on each unit was measured. The
Refer to Exercise 4. Assume that the cost of repairing an assembly whose clearance is too little is $2, and the cost of repairing an assembly whose clearance is too much is $3. a. Express the total
The lifetime, in years, of a certain type of pump is a random variable with probability density function.a. What is the probability that a pump lasts more than two years?b. What is the probability
Refer to Exercise 18.a. Find Cov(X, Y).b. Find ρX,Y.c. Find the conditional probability density function fY |X(y | 0.5).d. Find the conditional expectation E(Y | X = 0.5). Refer to Exercise 18. 3
The lifetime of a certain component, in years, has probability density function.Two such components, whose lifetimes are independent, are available. As soon as the first component fails, it is
Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen
A certain delivery service offers both express and standard delivery. Seventy-five percent of parcels are sent by standard delivery, and 25% are sent by express. Of those sent standard, 80% arrive
Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.a. Given that the test is positive, what is the probability that the person has the
A system consists of four components connected as shown in the following diagram:Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10, and
A system contains two components, C and D, connected in parallel as shown in the diagram.Assume C and D function independently. For the system to function, either C or D must function.a. If the
In an experiment to determine the effect of ambient temperature on the emissions of oxides of nitrogen (NOx) of diesel trucks, 10 trucks were run at temperatures of 40°F and 80°F. The
If the level α remains the same, and the sample size increases, then the power will. Options: increase, decrease.
It is suspected that using premium gasoline rather than regular will increase the mileage for automobiles with a particular engine design. Sixteen cars are used in a randomized experiment. Eight are
A certain manufactured product is supposed to contain 23% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2. If the mean
The pH of an acid solution used to etch aluminum varies somewhat from batch to batch. In a sample of 50 batches the mean pH was 2.6, with a standard deviation of 0.3. Let μ represent the mean pH for
When the light turns yellow, should you stop or go through it? The article “Evaluation of Driver Behavior in Type II Dilemma Zones at High-Speed Signalized Intersections” (D. Hurwitz, M. Knodler,
The article €œAbyssal Peridotites > 3,800 Ma from Southern West Greenland: Field Relationships, Petrography, Geochronology, Whole-Rock and Mineral Chemistry of Dunite and Harzburgite
Five different variations of a bolt-making process are run to see if any of them can increase the mean breaking strength of the bolts over that of the current process. The P-values are 0.13, 0.34,
A test is made of the hypotheses H0 :μ ≤ 10 versus H1 :μ > 10. For each of the following situations, determine whether the decision was correct, a type I error occurred, or a type II error
The article €œTime Series Analysis for Construction Productivity Experiments€ (T. Abdelhamid and J. Everett, Journal of Construction Engineering and Management,
A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The variance of the amount in each can is 0.01. The machine is moved to a new location. To determine whether
A new material is being tested for use in the manufacture of electrical conduit, to determine whether it will reduce the variance in crushing strength over the old material. Crushing strengths are
The article “Wired: Energy Drinks, Jock Identity, Masculine Norms, and Risk Taking” (K. Miller, Journal of American College Health, 2008:481–489) reports that in a sample of 413 male college
If P = 0.50, which is the best conclusion?i. H0 is definitely false.ii. H0 is definitely true.iii. There is a 50% probability that H0 is true.iv. H0 is plausible, and H1 is false.v. Both H0 and H1

Showing 400 - 500 of 790