Model Assisted Statistics and Applications

An engineered system is a functionally related group of components, and thus estimation of its reliability depends on the estimation of the reliability of its components. The component reliabilities are estimated usually under a laboratory set up while the system may be installed to work under a different condition, called field condition. The difference may arise due to the change in temperature, humidity, voltage, friction, etc. The cause of the difference may be attributed to a random variable, known as an environmental variable, which affects the functioning of the system. The presence of this variable makes the component failure-times dependent, and hence they behave differently from what they would have behaved under independent set up. Naturally, this change in the behavior of the components affects the estimates of system reliability. Thus, under such situation, if the reliability of a system is not estimated considering the conditions under which it actually works, there will be an upward or downward bias in estimation. Here we make an attempt to study the effect of an environmental variable on the reliability estimation of a complex coherent system, and try to find out the conditions under which the system performance is optimized. A simulation study has been included to see the crossing behavior of the reliability function, which describes the nature of the reliability curves under laboratory and field conditions, at different time points, in particular, when they cross each other.

Recently there has been a growing interest in using stochastic volatility models in option pricing. A proposed option pricing valuation method is to use characteristic function. In this paper, we present a theory to obtain closed-form expressions of conditional characteristic functions for option pricing for several stochastic volatility models, based on partial differentiation equation. We also compare the option prices from our presented method and a recursive method introduced by Heston and Nandi [8]. Our method significantly reduces the computation time by avoiding the recursive process.

Generally, response surface designs are used (in quality improvement experiments) in estimating the optimal level combinations of the process parameters. In an industrial process, the most important problem is to predict the operating condition that optimize a response of interest, and simultaneously minimizes the process variability. In modern quality engineering, dual response surface approach was introduced to achieve this goal. Some researchers have proposed to use the generalized linear models to derive the joint mean and variance models, instead of separate mean and variance models as in the dual response surface approach. This article illustrates (based on two real examples) how the generalized linear models approach can be used to achieve the goal. The present analyses and interpretations (related to these two examples) are completely different from all the earlier research findings.

We continued investigation of variation of blood pressure and heart rate characteristics of patients groups from different blood pressure categories in the present research. We analyze dynamical features of considered data sets by means of power spectrum regression, detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MF-DFA). We aim to compare dynamical characteristics of analysed data in different blood pressure categories. Special interest is the comparison of these characteristics in normal and high normal blood pressure categories.

Based on the results of our analysis we show that scaling features of considered data sets are different in different blood pressure categories. The most interesting is the fact that by their dynamical features normal and high normal categories are different for all considered physiological characteristics. The obtained results point to the fact that important quantitative and qualitative changes occur in these looking close guidelines categories, which finally lead to transition of dynamical system to pathological condition typical for grade I hypertension category.

We formalize a guaranteed solution notion for a non-cooperative game of n persons under uncertainty. This notion is based on the appropriate modification of maximin and the Berge equilibrium. We obtain existence conditions for the guaranteed solution in the class of mixed strategies (probability measures). We prove existence of such solution in mixed strategies under standard (for the mathematical game theory) restrictions, such as continuity of payoff functions and compactness of the sets of players' strategies. We use a new method for construction of guaranteed solutions in pure and mixed strategies. We reduce construction of a guaranteed solution to construction of a saddle point of a special convolution of payoff functions.

We propose two recently developed iterative algorithms for solving large scale linear programming problems: the first one is based on the gravitation centers method, which in its turn widely uses Monte Carlo statistical test method, and the second one is realized on the basis of the constant step gradient method. Though the developed iterative algorithms are approximate, it is rather worthwhile in most cases to apply them when solving large scale linear problems, as they are characterized by positive properties, such as simplicity of the algoritm and the program, high-speed performance, and besides the appropriate software is free of such an unpleasant, specific for the simplex method event as a “loop”. We present some computational results. We assess the both developed algorithms with respect to a high-speed performance criterion and compare their high-speed performance with the one of the simplex method.

In this paper two identical parallel units have been analyzed by using discrete distribution and regenerative point technique. The distribution for repair time and inspection policy for detecting the kind of failures (minor or major) are taken as geometric distribution. Various reliability measures of system effectiveness such as mean time to system failure, steady state availability and busy period for both inspection and repairman were obtained. Graphs has been plotted for the system, that concluded the behaviour of profit function which increase along with increase in rate of repair mechanism and decreases with increase in failure rate.

We considered system-analytical and statistical approach for solving the problem of analysis and predicting terrorist attacks. Intervals between attacks have been the objectives of our research. This study can help us to predict next terrorist activities and consider counter-terrorism action plan. Proposed methodology was illustrated on the examples of terrorist activities in Afghanistan, Algeria, India, Iraq and the USA. We used for calculations statistical data for the time frame 2000–2010.