The North-South Airline

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Case Background

In 2008, Northern Airlines merged with Southeast Airlines to create the fourth largest U.S.

carrier. Company was headed by Stephan Ruth, who concern is to create a financially strong company

and he believes that it can be possible by reducing the maintenance costs. It is noted that, Southeast

airline had new/ young fleet compared to northern airlines. In concern to this Ruth has noted that there

has been significant difference between in reported B737-200 maintenance cost both in airframe and

engines areas between Northern Airlines and Southeast Airlines. To ascertain this issue Ruth assigned

Peg Young, vice president for operations and maintenance. The task of the Peg Young is to report Ruth

with answer along with quantitative and graphical descriptions about the following:

1) Whether the average fleet age was correlated to direct airframe maintenance cost

2) Whether there was a relationship between average fleet age and direct engine maintenance

costs.

The fleet data are shown in the following table. Airframe cost data and engine cost data are both shown

paired with fleet average age.

Yogesh N Luhar EMBA – Operations Roll No : 22035 Page 1

It is known that fleet ages of southeast airline are lesser than the Northern fleet. Hence, we will check

the correlation between average ages of fleet with maintenance cost for both the airline separately.

Correlation is measure of the degree of relatedness of variable. Correlation between two variables is

represented with r, called as Pearson product – moment correlation co-efficient. The correlation

between two variables falls between -1.0 to 0 to 1. If the correlation is positive, we have a positive

relationship. If it is negative, the relationship is negative.

Correlation Co-Efficient: Correlation(r) = [NΣXY - (ΣX)*(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])] where N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores ΣY2 = Sum of square Second Scores

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There are total five different degrees of correlations.

1) Represents strong negative correlation2) Represents moderate negative correlation3) Represents moderate positive correlation4) Represents strong positive correlation5) No correlation

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PART A)

1) Correlation between average age of fleet and airframe maintenance cost for Northern airline.

Northern Airline

Year Avg age in hrs

Airframe cost/Airline

x y X2 y2 XY2001 6512 51.8 42406144 2683.24 337321.62002 8404 54.92 70627216 3016.2064 461547.682003 11077 69.7 122699929 4858.09 772066.92004 11717 68.9 137288089 4747.21 807301.32005 13275 63.72 176225625 4060.2384 8458832006 15215 84.73 231496225 7179.1729 1289166.952007 18390 78.74 338192100 6199.9876 1448028.6

ΣX = 84590 ΣY = 472.51 ΣX2 = 1118935328 ΣY2 = 32744.1453 ΣXY = 5961316.03

r = 0.87715

The Value of Pearson product moment correlation co-efficient represents strong positive relationship between average fleet age and Airframe cost in case of Northern Airlines.

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2) Correlation between average age of fleet and airframe maintenance cost for Southeast airline.

Southest Airline

Year Avg age in hrs

Airframe cost/Airline

x y X2 y2 XY2001 5107 13.29 26081449 176.6241 67872.032002 8145 25.15 66341025 632.5225 204846.752003 7360 32.18 54169600 1035.5524 236844.82004 5773 31.78 33327529 1009.9684 183465.942005 7150 25.34 51122500 642.1156 1811812006 9364 32.78 87684496 1074.5284 306951.922007 8259 35.56 68211081 1264.5136 293690.04

ΣX = 51158 ΣY = 196.08 ΣX2 = 386937680 ΣY2 = 5835.825 ΣXY = 1474852.48

r = 0.625

1000090008000700060005000

35

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Avg age in hrs_Southeast Airline

Airfr

am

e c

ost

_South

east

Airlin

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Scatterplot of Airframe cost vs Avg age in hrs

The Value of Pearson product moment correlation co-efficient represents moderate positive relationship between average fleet age and Airframe cost in case of Southeast Airlines.

Yogesh N Luhar EMBA – Operations Roll No : 22035 Page 5

PART B)

3) Correlation between average age of fleet and engine maintenance cost for Northern airline.

In this section relationship between Northern Airlines fleet age and direct engine maintenance cost is evaluated.

To check the relationship between these variables, we have to do simple regression analysis. Simple regression analysis is a process of constructing a mathematical model or function that can be used to predict one variable by another variable.

In Regression analysis there are two variables,

1) Dependent variable – Designated as Y2) Independent variable – Designated as X

In this case there are two variables; hence simple regression is the best method to generate the mathematical model. We will find the straight line relationship between average fleet age of Northern Airlines and direct engine maintenance cost.

The simple regression line equation is

Regression Equation(y) = a + bx

Or simplified as y=b0 + b1x ----------------------------------(1)

Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)Intercept(a) = (ΣY - b(ΣX)) / N

where x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores

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Avg age in hrs for

Northern Airline

Engine cost / Airline

for Northern

Airlinex y X2 xy

6512 43.49 42406144 283206.888404 38.58 70627216 324226.32

11077 51.48 122699929 570243.9611717 58.72 137288089 688022.2413275 45.47 176225625 603614.2515215 50.26 231496225 764705.918390 79.6 338192100 1463844

ΣX = 84590 ΣY = 367.6 ΣX2 = 1118935328 ΣXY = 4697863.55

20100-10-20

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70605040

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Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Engine cost / Northern Airline

The regression equation is Engine cost / Northern Airline = 20.6 + 0.00264 Avg age in hrs_Northern Airline. The slope of the line is 0.00264, that means every unit increase in x (avg fleet age) , Avg engine maintenance cost is predicted to be increased by factor 0.00264 plus fixed cost 1.636.

Yogesh N Luhar EMBA – Operations Roll No : 22035 Page 7

Ssxy 255680.1214SSxx 96725599.43b1 0.002643355b0 20.57122558

4) Correlation between average age of fleet and engine maintenance cost for Southeast airline.

Avg age in hrs for

Southeast Airline

Engine cost / Airline

for Southeast

airlinex y X2 xy

5107 18.86 26081449 96318.028145 31.55 66341025 256974.757360 40.43 54169600 297564.85773 22.1 33327529 127583.37150 19.69 51122500 140783.59364 32.58 87684496 305079.128259 38.07 68211081 314420.13ΣX =

51158ΣY = 203.28 ΣX2 = 386937680 ΣXY = 1538723.62

100-10

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3632282420

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7654321

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Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for Engine cost / Southeast Airline

The regression equation is Engine cost / Southeast Airline = - 0.7 + 0.00407 Avg age in hrs_Southeast airline. Since, it is know that fleet age of southeast airline are low, engine cost will be low and with increase in age, there is a small increase in the maintenance cost.

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sxy 53095.3SSxx 13060399.43b1 0.004065366b0 -0.670854144