Part – A : (5 X 16 = 80 Marks) (Answer any five from the following)
1. a. Discuss the different types of scales of measurement and its properties with suitable examples from aerospace engineering related data sets. CO1 U
b. The cruising altitudes of a fleet of aircraft were recorded and grouped as follows:
Altitude (km)
8 -9
9 -10
10 -11
11-12
12 -13
No of aircraft
5
12
18
10
5
Find the average altitude of aircraft. Also find the median and mode. CO1 A
2. a. The reliability of different units in a hydraulic system is given below. Determine the reliability of the system: CO2 An
b. An electronic system has 10 identical components. It is desired that the system reliability to be 0.95. Determine how good each component should be if the components are connected in (i) series (ii) parallel. CO2 An
3. a. During a pre-flight inspection, 30 turbine blades are tested for micro-cracks. Each blade has a 0.05 probability of having a defect (independently of others). What is the probability that there are (i) no defective blades (ii) 1 defective blade (iii) less than 2 defective blades, in the batch? CO2 A
b. The life time of a wind speed measuring sensor in an aircraft is known to be normally distributed with a mean of 8000 flying hours and standard deviation 400 hours. Find the probability that (i) the life time of a sensor is greater than 7700 hours (ii) the sensor fails before 7500 hours of use (iii) the life time of a sensor is between 7400 and 8200 hours. CO2 A
4. a. Two different models of aircraft engines were tested for fuel efficiency (in km per liter). Test whether there is a significant difference in the mean fuel efficiency of the two engine types, at 5% significance level.
Type of engines Sample size
Type of engines
Sample size (test runs)
Mean
SD
A
50
5.6
0.4
B
60
5.4
0.5
b. In an experiment on engine performances at high and low temperatures, the following results were obtained:
Standard performance
Poor performance
High temperature
60
120
Low temperature
80
40
Determine whether the performance of engines is independent of temperature. CO3 E
5. The following data resulted from an experiment to compare three jet engine models A, B and C. The Latin square design experiment was set up and the tests were made on the three engines, using different fuels and ignition systems.
Fuels
Ignitions
1
2
3
1
A-16
B-17
C-20
2
B-16
C-21
A-15
3
C-15
A-12
B-13
Test the hypothesis that there is no significant difference between the engines. CO3 An
6. The following data was recorded by an aerospace test engineer for a jet engine at different operating conditions:
Thrust (kN)
40
50
60
70
80
90
Fuel flow rate (kg/s)
0.8
1
1.3
1.4
1.6
1.8
Determine the correlation coefficient between thrust and fuel flow rate. Interpret what the correlation indicates about engine performance efficiency. Also find the regression equation of fuel flow over thrust. Estimate the thrust of the engine if the fuel flow rate is 2.1 kg/s. CO4 An
7. a. The following are the recorded values of drag coefficient Cd for an experimental UAV over 7 test flights:
Test flight no
1
2
3
4
5
6
7
Drag coefficient
0.28
0.30
0.27
0.32
0.31
0.29
0.33
Compute a 3-point moving average; plot the actual and trend values on a graph. Comment on the trend. CO5 A 8 b. By the method of least square fit a straight line to the following data. Also estimate the data for the years 1997, and 2000.
Year
1990
1992
1993
1994
1995
Data
60
80
102
121
137
Part – B : (1 X 20 = 20 Marks) [Compulsory Question] 8. a. (i) A doctor wants to predict an astronaut systolic blood pressure (Y) based on two factors: the astronaut age(X1) and BMI(X2). He developed a multiple linear regression model for the same; Y= 0.48X1 +2.102X2+ 60.64. Predict the systolic blood pressure of a 38-year-old astronaut with a BMI of 27 using the MLR model.
(ii) In a tri variate distribution, it is found that R12 = 0.7, R13 = 0.61, and R23 = 0.4. Find the partial correlation coefficients and multiple correlation co efficient R1.23. CO6 A
b. In a study of aircraft performance, engineers collected data on the cruise speed (y) of several aircraft and two predictor variables: x: Engine thrust (kN), z: Wing loading (N/m²). The correlation coefficients among these variables are as follows: Ryx = 0.85, Ryz = 0.78, Rxz = 0.65. Compute the multiple correlation co efficient Ry.xz. Interpret the result in terms of how strongly the aircraft’s cruise speed depends on the combination of engine thrust and wing loading. Calculate R2 and find how much cruise speed variation depends on thrust and wing load. CO6 An
Course Outcomes: • CO1 Understand nature of data, and measurements. • CO2 Relate predictive analysis using probability distributions. • CO3 Construct the comparative analysis using testing of hypothesis • CO4 Measure the relationship between variables. • CO5 Analyze data trends using graphical method • CO6 Estimate using multiple correlation models
