Tried Analysis and Forecast for Aviation Accident from a selective period of time and concluded my results through trend analysis, Mann Kendall abrupt and observed ACF and PACF of stationary series and analysis for the model accuracy. also used ARIMA model to forecast the time series of number of fatalities of civil aviation accidents.

1. AFAA
Analysis and
Forecast of Aviation
Accident
Swet ha M ( 2 1 3 7 5 06 3)
A t hira U nnikrishnan ( 2 1 3 7 50 12 )

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INTRODUCTION
Aviation safety is one of the most studied domains today. Recent
commercial aviation incidents and accidents are, however, becoming
more and more complex issues, which makes this commitment quite a
challenge. As more and more people use airplanes as a means of
transportation, the number of passengers and flight routes have
expanded in recent years . Aviation accidents can occur during all
phases of flight, including takeoff, climb, cruise, descent, approach,
and landing. The number of airplane crashes has decreased over the
last few decades; 104 crashes with 2,937 fatalities in 1972 declined to
39 crashes with 158 fatalities in 2022.
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Causes and Impacts :
Causes:
Aviation accidents can have multiple causes, including technical failures, pilot error, air traffic control
errors, weather conditions, sabotage, and other factors.
Impact:
The most obvious impact of aviation accidents is the loss of human lives. The loss of even a single life is
tragic, but aviation accidents can involve hundreds of casualties, which can be devastating to families
and communities.
Safety Concerns: Aviation accidents can create safety concerns among the public and aviation industry
stakeholders. This can lead to increased scrutiny and regulatory measures, which can impact the
operations and profitability of airlines.
Economic Impact: Aviation accidents can have a significant economic impact, particularly in the
aviation industry. Airlines may face financial losses due to grounded planes, cancelled flights, and
reduced bookings in the aftermath of an accident. This can also impact the broader economy, particularly
in areas where aviation is a major source of employment and revenue.

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Objective:
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• Find some factors that contribute to airplane crashes,
• Analyze patterns of the data collected from all over the world in the past
decades,
• Find replicable solutions for both aviation industry and customers,
• Through time series research the variation law in the historical data of long-
term aviation accidents and predicted the possible changes of future aviation
accidents, providing data reference for aviation safety research.

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Time-Series Analysis :
Time series analysis is an important statistical analysis and forecast method that describes the
statistical characteristics of a variable and reveals the law of change in data according to the
statistical relationship between data. The Autoregressive Moving Average (ARMA) model consists
of the autoregressive (AR) model and the moving average (MA) model. The ARMA stationary
time series model is defined as follows:
where p and q refer to the order of autoregressive (AR) part and moving average (MA) part,
respectively. When 𝜑0 = 0 , through introduction of the delay operator B, the centralized
ARMR(p, q) model is as follows:

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Hypothesis:
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Null Hypothesis 𝑯𝟎 : If failed to be rejected, it suggests the time series has a unit root,
meaning it is non-stationary. It has some time dependent structure.
Alternate Hypothesis 𝐇𝟏 : The null hypothesis is rejected; it suggests the time series does not
have a unit root, meaning it is stationary. It does not have time-dependent structure.
• p-value > 0.05: Fail to reject the null hypothesis 𝐻0 , the data has a unit root and is non-
stationary.
• p-value <= 0.05: Reject the null hypothesis 𝐻0 ,the data does not have a unit root and is
stationary.
Decision Rule:
• If test statistic value < critical value or p-value < 0.05, we reject the null hypothesis
𝐻0 , that is, time series does not have a unit root or it is stationary. Or, in other words, it does
not have a time-dependent structure.
• If the null hypothesis is failed to be rejected, this test may provide evidence that the series
is non-stationary.

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Methodology:
• Based on the Mann-Kendall trend analysis and mutation analysis methods, the change trend
of accidents and casualties in different flight stages of civil aviation and built ARIMA
(Autoregressive Integrated Moving Average model) time series analysis model to predict the
number of civil aviation accidents and casualties by the long-term data in the world.
• Mann-Kendall trend Analysis:
Mann-Kendall trend analysis is a nonparametric statistical method for rank
correlation test on the rank of statistic series and time series; dependent variables may be
nonnormally distributed, so it applies to analysis of the trend in statistical variables. Given that
H0 is the sample of the time series as independent identically distributed random
variables, then the statistic S is given by

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where 𝑅𝑖 and 𝑅𝑗 refer to the rank of 𝑋𝑖 and 𝑋𝑗, respectively. When n > 10, S is normally
distributed with the mean and variance as follows:
where E(S) refers to the mean and var(S) refers to the variance.
The statistic Z is Mann-Kendall’s rank correlation coefficient. Positive Z or negative Z,
respectively, means that there is an upward or downward trend. The absolute value of Z
reflects the significance level of trend. When the significance level is consistent with a
99%, 95%, or 90% confidence interval.

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About Dataset:
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Aboard and Fatalities from 2000 – 2008:

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Count of Total Accidents by year and ration of both Aboard and
Fatalities:

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Total Count by Operator:
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Here we can see the Fatalities rate by the operators:

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Mann-Kendall test of the number of global aviation casualties
at different stages:
Interpretation:
In the approach phase, curve UF exceeded the upper limit of the critical value in around 1960, from
when the fatalities increased significantly; it moved downward and was lower than the upper limit of
the critical value in around 2006, from when the fatalities decreased significantly. There was no obvious
abrupt change in the fatalities in the approach phase.

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The actual value and forecast value of global aviation
casualties:

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The correlation chart and partial correlation graph after
global aviation accident time series difference:

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Comparison of parameters of different ARIMA models in global
aviation accidents:

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The actual value and fitting value of global aviation
accidents:
Interpretation:
The ARIMA model is used to forecast the fatalities of civil aviation accidents worldwide, which
will not be discussed here due to limited space. ARIMA (1,0,1) is finally selected as the optimum
model through natural logarithm transformation, in which case AIC=-146.57, C=50.92%, R=0.71,
and the residual error sequence is white noise.

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Time Series Modeler and Summary:

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The actual value and forecast value of global aviation
accidents and causalities:

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Conclusion:
• The number of aviation accidents worldwide reduced in a fluctuant way. In 1942-2016, there were
two periods of change in the number of accidents. The number increased by 70 in the first period
(1942 -1948) and by 30 in the second period (1983-1989) .There was a significant difference
between the trends of change in the number of fatalities of accidents worldwide. The fatalities first
increased and then reduced, showing a parabolic trend, and 1972 was the year when the fatalities
reached the maximum.
• The number of aviation accidents was different, which was maximum in Air Taxi ; there was a
large difference between different flight phases in the fatalities rate by Operators.
• The result of Mann-Kendall abrupt change analysis, there was no abrupt change in the number and
fatalities of accidents in the approach phase. 2013, 1980, 2012, and 2006 were the years when there
was an abrupt change in the fatalities, the number of accidents in the en-route phase, the number of
accidents in the approach phase, and the fatalities in the en-route phase, respectively.
• The observation of the ACF and PACF of stationary series and analysis of the model accuracy, the
ARIMA (1,0,1) model is selected to forecast the time series of the number and fatalities of civil
aviation accidents worldwide, obtaining the forecasted values of the two by the end of year 2025.

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References:
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 https://www.kaggle.com/datasets/saurograndi/airplane-crashes-since-1908
 https://www.sciencedirect.com/science/article/pii/S2666691X21000439
 https://www.sciencedirect.com/science/article/pii/S2666691X21000439
 https://www.hindawi.com/journals/mpe/2019/5710984/
 https://medium.com/analytics-vidhya/interpreting-acf-or-auto-correlation-plot-d12e9051cd14
 G. Tamasi and M. Demichela, “Risk assessment techniques for civil aviation security,” Reliability
Engineering & System Safety, vol. 96, no. 8, pp. 892–899, 2011. (Google Scholar)
 https://www.statisticshowto.com/mann-kendall-trend-test/
 https://www.bing.com/videos/search?q=arima+model+using+spss&docid=6035374888867117
25&mid=34EBF330AED2EF7B1EE834EBF330AED2EF7B1EE8&view=detail&FORM=VIRE
 file:///C:/Users/HP/Desktop/Presentation/Time_series_analysis_and_modelling_.pdf

25. Thank You.