Abstract
Earthquake in recent years has increased tremendously. This paper outlines an evaluation of Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charting technique to determine if the frequency of earthquake in the world is unusual. The frequency of earthquake in the world is considered from the period 1973 to 2016. As our data is auto correlated we cannot use the regular control chart like Shewhart control chart to detect unusual earthquake frequency. An approach that has proved useful in dealing with auto correlated data is to directly model time series model such as Autoregressive Integrated Moving Average (ARIMA), and apply control charts to the residuals. The EWMA control chart and the CUSUM control chart have detected unusual frequencies of earthquake in the year 2012 and 2013 which are state of statistically out of control.
Highlights
Earthquake is one of the most horrific and devastating natural phenomena in the world
An approach that has proved useful in dealing with auto correlated data is to directly model time series model such as Autoregressive Integrated Moving Average (ARIMA), and apply control charts to the residuals (Montgomery and Mastrangelo, 1991)
To detect shift in number of earthquake, we identify an appropriate ARIMA model to the earthquake data and apply the residuals of this ARIMA model to Cumulative Sum Control Chart (Page, 1961) and Exponentially Weighted Moving Average (Roberts, 1959)
Summary
Earthquake is one of the most horrific and devastating natural phenomena in the world It is the sudden, rapid shaking of the earth, caused by the breaking and shifting of subterranean rock as it releases strain that has accumulated over a long time. Earthquakes may damage household items, building to move off foundations or collapse, damage roads, bridges and dams, cause fires and explosions. They may trigger landslides, avalanches and tsunamis. Chen et al (2010) analysed earthquake data with the help of frequency time analysis. Besides the analysis of earthquake data, there are some studies that predict the occurrences of large scale earthquakes. Amei et al (2012) predicted a total number of 12 large scale earthquakes based on the worldwide earthquake data during 1986 to 2009. Alam (2015) forecasted the earthquake behaviour in Indonesia based on the earthquake data during the year 1980 to 2007. Last et al (2016) predicted the magnitude of the earthquakes in the area of Israel and its neighbouring countries using the earthquake data from the year 1983 to 2010
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