PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 13.2, Problem 18E
Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article “Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys” (J. of Engineering for Gas Turbines and Power, 2002: 161–176) gave the accompanying data and fit a nonlinear regression model in order to predict strain amplitude from cycles to failure. Fit an appropriate model, investigate the quality of the fit, and predict amplitude when cycles to failure 5 5000.
| Obs | Cycfail | Strampl | Obs | Cycfail | Strampl |
| 1 | 1326 | .01495 | 11 | 7356 | .00576 |
| 2 | 1593 | .01470 | 12 | 7904 | .00580 |
| 3 | 4414 | .01100 | 13 | 79 | .01212 |
| 4 | 5673 | .01190 | 14 | 4175 | .00782 |
| 5 | 29516 | .00873 | 15 | 34676 | .00596 |
| 6 | 26 | .01819 | 16 | 114789 | .00600 |
| 7 | 843 | .00810 | 17 | 2672 | .00880 |
| 8 | 1016 | .00801 | 18 | 7532 | .00883 |
| 9 | 3410 | .00600 | 19 | 30220 | .00676 |
| 10 | 7101 | .00575 |
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a. Fit a multiple regression model to describe the rela-tionship between weight and the predictors length and age. y^5 2 511 1 3.06 length 2 1.11 ageb. Carry out the model utility test to determine whether at least one of the predictors length and age are useful for predicting weight.
2. The authors of the paper "Age, Spacing and Growth Rate of Tamarix as an Indication of
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51) used a simple linear regression model to describe the relationship between y = vigor
(average width in centimeters of the last two annual rings) and x
(stems/m?). Data on which the estimated model was based is as follows.
4
= stem density
6
9
14
15
15
19
21
22
y
.75
1.20
.55
.60
.65
.55
.35
.45
.40
Construct a scatter plot for the data.
a)
b) Find the estimated regression line and draw it on your scatter plot.
Determine and interpret the coefficient of determination.
c)
d) What is your estimate of the average change in vigor associated with a 1-unit increase in
stem density?
What would you predict vigor to be for a plant whose density was 17 stems/m2?
e)
An article described an experiment carried out to assess the impact of the
variable x₁ = force (gm), x₂ = power (mW), x3 = temperature (°C), and
time (msec) on y
ball bond shear strength (gm).
X4 =
=
The estimated regression equation is
y = -37.48 +0.2117x₁ +0.4983x2 +0.1297x3 +0.2583x4
Interpret b3 and b4.
● What is the expected value of strength (y) from a force of 35 gm,
power of 75 mW, temperature of 200 °C, and time of 20 msec ?
Chapter 13 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
Ch. 13.1 - Suppose the variables x = commuting distance and y...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - As the air temperature drops, river water becomes...Ch. 13.1 - The accompanying scatterplot is based on data...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Consider the following four (x, y) data sets; the...Ch. 13.1 - a. Show that i=1nei=0 when the eis are the...
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - If there is at least one x value at which more...Ch. 13.2 - No tortilla chip aficionado likes soggy chips, so...Ch. 13.2 - Polyester fiber ropes are increasingly being used...Ch. 13.2 - The following data on mass rate of burning x and...Ch. 13.2 - Failures in aircraft gas turbine engines due to...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Mineral mining is one of the most important...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Kyphosis refers to severe forward flexion of the...Ch. 13.2 - Prob. 25ECh. 13.3 - The following data on y 5 glucose concentration...Ch. 13.3 - The viscosity (y) of an oil was measured by a cone...Ch. 13.3 - Prob. 29ECh. 13.3 - The accompanying data was extracted from the...Ch. 13.3 - The accompanying data on y 5 energy output (W) and...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The following data resulted from an experiment to...Ch. 13.3 - The article The Respiration in Air and in Water of...Ch. 13.4 - Cardiorespiratory fitness is widely recognized as...Ch. 13.4 - A trucking company considered a multiple...Ch. 13.4 - Let y = wear life of a bearing, x1 = oil...Ch. 13.4 - Let y = sales at a fast-food outlet (1000s of ),...Ch. 13.4 - The article cited in Exercise 49 of Chapter 7 gave...Ch. 13.4 - The article A Study of Factors Affecting the Human...Ch. 13.4 - An investigation of a die-casting process resulted...Ch. 13.4 - Prob. 43ECh. 13.4 - The accompanying Minitab regression output is...Ch. 13.4 - The article Analysis of the Modeling Methodologies...Ch. 13.4 - A regression analysis carried out to relate y =...Ch. 13.4 - Efficient design of certain types of municipal...Ch. 13.4 - An experiment to investigate the effects of a new...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - The article Optimization of Surface Roughness in...Ch. 13.4 - Utilization of sucrose as a carbon source for the...Ch. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.5 - The article The Influence of Honing Process...Ch. 13.5 - Prob. 56ECh. 13.5 - In the accompanying table, we give the smallest...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Pillar stability is a most important factor to...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13 - Curing concrete is known to be vulnerable to shock...Ch. 13 - Prob. 66SECh. 13 - The article Validation of the Rockport Fitness...Ch. 13 - Feature recognition from surface models of...Ch. 13 - Air pressure (psi) and temperature (F) were...Ch. 13 - An aeronautical engineering student carried out an...Ch. 13 - An ammonia bath is the one most widely used for...Ch. 13 - The article An Experimental Study of Resistance...Ch. 13 - The accompanying data on x = frequency (MHz) and y...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - The article Chemithermomechanical Pulp from Mixed...Ch. 13 - Prob. 77SECh. 13 - Prob. 78SECh. 13 - Prob. 79SECh. 13 - Prob. 80SECh. 13 - Prob. 81SECh. 13 - Prob. 82SECh. 13 - Prob. 83SE
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