Stress-strength analysis by time series models and a risk study on water consumption

In stress-strength analysis, reliability which is the probability of endurance against the strain that an object is exposed and risk (failure) which is the probability of not being able to endure are the parameters of stress-strength analysis. In this study, the scope of examination is the results of the analysis when time bound stress and strength variables have univariate linear time series models. In line with these results, a generalization has been obtained to achieve maximum likelihood estimators of these parameters in case they have the model of Seasonal Integrated Autoregressive Moving Average (SARIMA). While this generalization is made, induction method has been used. In the implementation study, It has been observed that risk estimations of agricultural droughts calculated monthly for Turkey in general and as to the geographical regions in 2008 match with the actual droughts. When it is studied according to the geographical regions, it has been found out that risk measures show difference from one season to another depending on the climatic characteristics. In accordance with the stress-strength analysis carried out in Ankara by time model, it is estimated that the risk of water consumption will be highest in August 2010 and will be least in April. According to the data obtained, unless it is not summer season, risk of water consumption is not expected in Ankara in 2010 with high probabilities. In the light of the risk measures, the first signals of risk in Ankara will be received in May-June 2010 and the most serious signals will be received in August. Results of the analysis are in compliance with the estimations in terms of climatic parameters monitored in Ankara in 2010.