Aviation Accidents Reports Example

 INTRODUCTION ON THE STATISTIC ANALYSIS:

The first attempts to build an airplane were made in the XIX century; in particular, aeronautic shell (aircraft) was built in full size in 1882, by Russian engineer Mozhaysky. However, his design was not able to rise into the air. The reasons for this were: weight was too big and the law abilities of the engines of that time (steam engines), the lack of theory of flight and the lack of engineering experience in many aviation pioneers.
The first aircraft, which could alone get off the ground and make a controlled level flight, became the "Flyer 1", built by brothers Orville and Wilbur Wright in the United States. The First World War served as a powerful stimulus to the development of the aircraft industry worldwide. In the first months of fighting aircraft proved to be a highly effective form of military equipment, and the government of the belligerent countries began to allocate more funds for the development of aviation. During the war it was built about 200 thousand aircraft. By 1918, in the aviation industry employed 700 thousand people. Aircraft industry has become a major industry.
What was a "typical" plane in 1918? It was a biplane with racks and wire braces between the wings. This spatial design provides efficient perception of the forces acting on the wing, and has high strength with relatively low weight. The fuselage also had a truss design-power circuit. The main material used to make airplanes, there was a tree. Then his snug cloth, and recently varnished to provide moisture and airtight casing. The speed of the aircraft during the First World War did not exceed 200 km / h, and the perfection of aerodynamic shapes of aircraft has not been given much attention. The challenge to the development of aviation has been a search for new aircraft applications. After the horrors of bloody battles 1914-1918 beginning of a new war seemed impossible and budgets on the military dramatically reduced. Since the second half of the XIX century in transport engineering process began crowding wood metal. First there were metal vessels and then the metal was used in the construction of car bodies, cars and other land vehicles. Advantages of metal lay in the homogeneity of its physical and mechanical properties, ease of use of machine methods of production, longer life. Unlike metal wood does not rot, its weight does not change with increasing humidity. He is non-flammable, does not split upon impact; Metal parts can have virtually any shape and size.
After the end of World War I, many years has started to revive the romantic fascination with aviation. Indomitable passion man with his own hands to build a "flying machine" and go up to her in the sky again, as in the beginning of the century, captured the imagination of many enthusiasts. Again began to rise into the air homemade planes with extremely simple design, with low-power motors, often taken from a car or a motorcycle. New area of ​​application is the use of light aircraft in agricultural work. The first of these experiments took place in August 1921 in Ohio, USA, at the request of local agricultural management. They were unsuccessful and were continued in the next year.
Passenger transportation in airplanes began shortly after the end of World War I. For this type of use of aviation high expectations, because during the war years the quality and reliability of aircraft has increased significantly increased their capacity. In the arsenals of western countries there is now a huge number of unnecessary combat aircraft, which was believed to be easily be converted into a civilian. By the early 20s in Western Europe was formed a network of overhead lines. The abundance of aircraft and engines, the presence of a large number of demobilized pilots and mechanics encourage governments and private companies to open up opportunities for the use of air lines.
World War II led to the need for a sharp increase in the rate of improvement of the aircraft and production. All countries involved in the war developed, modernized and made airplanes and aircraft weapon, and the new types of aircraft, such as long-range bombers. Escorts fighters have become essential for the success of heavy bombers, significantly reducing losses in the battle against enemy fighters. After the Second World War a commercial aircraft was quickly developed.
The first plane crash occurred almost immediately after the beginning of the era of ballooning, i.e. at the end of the XIX century. As the number of accidents themselves, and the number of victims was relatively small before the massive use of aircraft in combat and as a civilian transport. With the development of international air services, a system of registration and classification of accidents began to develop international standards for aviation security. Thomas Selfridge became the first person killed in the crash of the aircraft 17 September 1908, when a plane piloted by Orville Wright and the passenger who was Selfridge, crashed during a test of a contract with the US Army at Fort Mayr in Virginia. Since the beginning of the era of mass air travel in the second half of 1940 the number of aircraft accidents and the number of victims began to soar. Increase the reliability of aircraft and improving safety standards have led to a decrease in these indicators in the first half of the 1950s. However, the beginning of the jet age and the expansion of air transport in the Third World countries led to a new increase in the number of accidents, which ceased only in the mid-1960s. By this time the market were withdrawn new, more reliable jetliners, been established with respect to aviation safety worldwide.
The research sets to determine the statistical analysis of aviation accidents within the aviation industry by providing all the statistical elements to provide a clear variation of the data for the period between 1908 and 1943.

Introducing Data

We are given with the data of fatalities in aviation accidents from 1908 to 1947. There are 5 sets in the data. Each set represents the month of the year, when the accident has happened: August, September, October, November, December. There are three variables characterizing observations in the data:

Aircraft type / Registration – the type of aircraft caught an accident.

Fatalities – the number of victims in an accident.
Our goal is to analyze the number of fatalities by month. There were 97 accidents in August, 81 accidents were happened in September, 104 in October, 103 in November and 101 in December.

For each data set I have developed a frequency histogram:

We can see that the distribution of the variables is similar to each other. The data is positively skewed an close to the Gaussian distribution.

Descriptive Statistics

Run descriptive statistics using SPSS:
We can see that the averages of fatalities are not significantly different between months. The deviation of the data is also approximately equal.

Probability Distribution Plots

QQ plot is used to compare the distribution forms, providing a graphical view of properties such as location, scale and asymmetry in the two distributions. QQ plot can be used to compare the data set or theoretical distribution. Using graphics QQ to compare two sets of data can be viewed as a non-parametric approach to compare their major distributions. QQ plot is more powerful approach than the common method of histograms comparing two samples, but requires more skills to interpret. QQ plot is generally used to compare the data with the theoretical model. This can give graphical evaluation. It also used to compare two theoretical distributions. As the graph compares distributions QQ, then there is no need for values ​​that will occur as pairs, as in the scattering patterns, or even the number of values ​​in the two comparison groups should be equal.
The term "probabilistic graph" sometimes refers specifically to the QQ plot, and sometimes to a more general class diagrams, sometimes, rarely used PP plot.
The linearity of points on the graph suggests that the data are distributed normally. The closer points to the straight line, the better it fits normal distribution.

Confidence Intervals

The tables in Descriptive Statistics chapter have the information about 95% confidence intervals for mean values:
We are 95% confident that the population average of fatalities in august is between 6.7841 and 10.5673, in September – between 8.0188 and 11.9812, in October – between 5.7567 and 9.8109, in November – between 7.3932 and 12.0392, in December – between 5.6261 and 9.455.

Test for Independents

In this chapter I want to test if the data is independent. I’m given with the frequency distribution of fatalities in aviation accidents by months. I’m interested if the data is significantly different from each other. To check this Chi-square test is appropriate. The following observed frequencies (sums of fatalities numbers) are given:

Create a table for Chi-square test:

Perform testing:
Thus, the difference is significant.
Regression Analysis
The mean values and the months are given below in the table:
Plot the data on a scatterplot and add a trend line with equation and R-squared.
This “relationship” shows that there is a negative association between the month and number of fatalities. On average, the number of fatalities decreases from August till December.

Analysis of Variance

In this chapter I will perform ANOVA to see if there is a significant difference in mean values of fatalities between months.
H0: μ1=μ2=μ3=μ4=μ5Ha:not all means are equal

Set level of significance alpha:

a=0.05

Perform testing:

Since p-value of the test is 0.366>0.05, we failed to reject the null hypothesis. There is no enough evidence to say that the number of fatalities is different between the months (at 5% level of significance).

Conclusion

In this paper the basics of the statistical techniques related to a real world problem have been shown. The data of fatalities appeared to be not significantly different between the months, however, on average, in August the number of fatalities is a little bit larger than in other months. There is a weak tendency of decreasing the number of fatalities from August to December.

References

Archdeacon, Thomas J. Correlation and Regression Analysis: A Historian's Guide. Madison, Wis.: University of Wisconsin Press, 1994.
Weiss, N. A., and Matthew J. Hassett. Introductory Statistics. Reading, Mass.: Addison-Wesley Pub., 1982.