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Set-Membership Filter (SMF) has been extensively studied for state estimation in the presence of bounded noises with unknown statistics. Since it was first introduced in the 1960s, the studies on SMF have used the set-based description as its mathematical framework. One important issue that has been overlooked is the optimality of SMF. In this work, we put forward a new mathematical framework for SMF using concepts of uncertain variables. We first establish two basic properties of uncertain variables, namely, the law of total range (a non-stochastic version of the law of total probability) and the equivalent Bayes' rule. This enables us to put forward a general SMFing framework with established optimality. Furthermore, we obtain the optimal SMF under a non-stochastic Markov condition, which is shown to be fundamentally equivalent to the Bayes filter. Note that the classical SMF in the literature is only equivalent to the optimal SMF we obtained under the non-stochastic Markov condition. When this condition is violated, we show that the classical SMF is not optimal and it only gives an outer bound on the optimal estimation., 8 pages, 3 figures

Traditional simulation-based method for resilience assessment of distribution systems is very time consuming since the network topology is characterized with a large number of scenario-specific optimization models. In this paper, we propose a methodology for fast resilience assessment of distribution systems with a non-simulation-based, which can significantly improve the assessment accuracy and computational efficiency. First, a probabilistic metric is proposed to assess the system resilience against extreme events, which quantifies the system performance starting from the pre-event stage to the post-event stage. Then, a mixed-integer linear programming (MILP) is proposed to model the energization paths (EPs) with binary decision variables. Subsequently, the resilience metric-related probability events are built using the EPs. Last, the probabilistic resilience metric is explicitly expressed based on the total probability formula, conditional probability formula and EP-topology simplification methods. In the proposed method, the topology evolution along with the system degradation, restoration (part healed) and recovery (all healed) is characterized with a non-simulation-based method, rather than the multiple scenarios in traditional methods. The numerical tests validate the effectiveness of the proposed method and superiority over the simulation-based approach

The fusion of temporal consistency and semantic information with limited foreground information for background segmentation using deep learning is an underinvestigated problem. In this paper, we explore the relation between temporal consistency and semantic information based on the law of total probability. A highly concise framework is proposed to fuse these two types of information. A theoretical proof is given to show that the proposed framework is more accurate than either the temporal consistency-based model or the semantic information-based model and that each model is a special case of the proposed framework. The proposed framework is a white-box framework that can easily be embedded into a deep neural network as a merging layer. In the proposed model, only a few parameters must be learned, which substantially reduces the need for a large dataset. In addition, these interpretable parameters reflect our understanding of the background and can be applied to a wide range of environments. Extensive evaluations indicate the promising performance of the proposed method. Our code and trained weights for the experiments are available at GitHub. (We encourage the reader to run the program for a better understanding of the proposed method).

The numerical strength of the evidence of matching DNA profiles is conveyed by a likelihood ratio. This is the probability under one hypothesis, generally from the Prosecution, divided by the probability of the evidence under an alternative hypothesis, generally from the Defense. The probabilities can be calculated to reflect the effects of population structure or of relatedness between individuals listed under the alternative hypotheses.

An integrated probabilistic framework is proposed with a set of probabilistic models that are compatible with the reliability methods used in resilience-based design (RBD). Previous seismic resilience estimation frameworks primarily have used conditional probabilities and total probability integration to compute the expected seismic resilience index while considering the effects of only a few types of uncertainty. However, a high level of uncertainty is associated with seismic resilience estimation. This study presents a probabilistic framework and models that can consider the effect of unlimited uncertainties when calculating the probability distribution of the seismic resilience index for generating resilience curves. These curves reveal the probability of a building resilience index falling below a specific value and can be used in RBD for a building by considering its resilience. Probabilistic models that are compatible with the reliability methods are proposed for the ground motion intensity, building response, building damage, loss of functionality, recovery, and resilience of a building. The proposed models have been validated using information from HAZUS and were implemented in Rt software. The proposed framework and software are demonstrated through generation of a resilience curve for a typical four-story concrete moment-resisting frame building and the results are compared with outputs of conventional methods.

For nonlinear discrete-time systems where measurements can be randomly delayed by multiple sampling periods, measurements are dependent conditioned on the state trajectory, and the dependence becomes more complicated with the increase of step of random delay. A particle filtering for this system is developed, which is novel in that the likelihood is computed allowing multi step of delay and dependence of measurements. Multi step of delay is dealt with through utilizing the formula of total probability skillfully, and dependence is dealt with through estimating the filtering probability distribution of random delay. The novel particle filtering is applied to two examples to validate its effectiveness and superiority.

The disjunction effect is an interesting phenomenon of the violation of the law of total probability, and many studies have shown that the categorization decision-making experiment (CDME) can produce the disjunction effect. Recently an Evidential Markov decision making modeling (EM) has been proposed to predict the disjunction effect in CDME. A critical step in EM is that it uses Deng entropy to measure the amount of information of mass function. However, Deng entropy just considers the partial amount of information, which results in information loss in the prediction of the disjunction effect. To address this problem, an Improved Evidential Markov decision making model, named IEM, is proposed in this paper. Instead of Deng entropy, another method, i.e., Information volume of mass function (IV), is applied by the proposed IEM. IV can measure the total amount of information by superposing information volume at different orders. Hence IV is more reasonable than Deng entropy in measuring information volume. Experimental results show that IEM can predict the disjunction effect more accurately than the existing methods.

Since their inception in the 1980s, simplified procedures for the analysis of liquefaction hazards have typically characterized seismic loading using a combination of peak ground acceleration and earthquake magnitude. However, more recent studies suggest that certain evolutionary intensity measures (IMs) such as Arias intensity or cumulative absolute velocity may be more efficient and sufficient predictors of liquefaction triggering and its consequences. Despite this advantage, widespread hazard characterizations for evolutionary IMs are not yet feasible due to a relatively incomplete representation of the ground motion models (GMMs) needed for probabilistic seismic hazard analysis (PSHA). Without widely available hazard curves for evolutionary IMs, current design codes often rely on spectral targets for ground motion selection and scaling, which are shown in this study to indirectly result in low precision of evolutionary IMs often associated with liquefaction hazards. This study presents a method to calculate hazard curves for arbitrary intensity measures, such as evolutionary IMs for liquefaction hazard analyses, without requiring an existing GMM. The method involves the conversion of a known IM hazard curve into an alternative IM hazard curve using the total probability theorem. The effectiveness of the method is illustrated by comparing hazard curves calculated using the total probability theorem to the results of a PSHA to demonstrate that the proposed method does not result in additional uncertainty under idealized conditions and provides a range of possible hazard values under most practical conditions. The total probability theorem method can be utilized by practitioners and researchers to select ground motion time series that target alternative IMs for liquefaction hazard analyses or other geotechnical applications. This method also allows researchers to investigate the efficiency, sufficiency, and predictability of new, alternative IMs without necessarily requiring GMMs.

U završnom radu definirane su osnove vjerojatnosti koje čine temelj Bayesovu teoremu. Pojašnjene su operacije na prostoru događaja i De Morganov zakon. Definirani su aksiomi vjerojatnosti, klasična definicija vjerojatnosti te svojstva vjerojatnosti. Uvjetna vjerojatnost i nezavisni događaji objašnjeni su matematičkom definicijom i svojstvima, te primjenom u primjerima. Pokazani su potpun sustav događaja i zakon potpune vjerojatnosti, te njihova primjena. Objašnjenje Bayesova teorema dano je matematičkom definicijom i raznim primjerima koji opisuju njegovu praktičnu primjenu., In final thesis there are defined basis of probability that are foundation of Bayes' theorem. There are explained operations on sample space and De Morgan's law. Probability axioms, probability space and classical definition of probability are defined. Conditional probability and indepedent events are clarified with its mathematical definition and properties, as well as its application in examples. Sample space, and law of total probability are illustrated and applied. Explenation of Bayes' theorem is given with mathematical defiinition and various examples that describe its practical application.

In the early Meiji period, the mathematical probability concept will be supposed to be very difficult to understand or accept at Japanese Army. In this paper, we investigate how the Japanese had understood or accepted the classical probability theory founded by Laplace, comparing several Japanese text books on probability theory with those of some European ones. Especially we focus on the words“ total probability” which is a little bit curious words from the point of view in the modern probability theory., "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

The coefficient of consolidation (ch) of clay interpreted based on piezocone penetration test (CPTU) usually deviates from the actual values. This can be due to the inherent variability of ch, model uncertainty in the CPTU-based interpretation model, and test errors. Considering the importance of ch in designing the structures over clays, Bayesian inference approach combined with total probability theorem was proposed in this study to integrate the prior knowledge of ch with the project-specific test data to obtain the site-specific distributions of ch. Subsequently, a large number of equivalent samples were generated from the updated distributions of ch by Markov Chain Monte Carlo simulation. Then, Bayesian model comparison approach was developed to quantitatively compare the model proposed by Torstensson (model M1) with the model proposed by Teh and Houlsby (model M2). Finally, a sensitivity analysis was performed to study the effect of model uncertainty and data quantity on the updated distributions of ch. The results showed that model M2 was significantly better than model M1 after considering the rigidity index (Ir). The updated distributions of ch approximately exhibited the log-normal distribution, especially for model M2, which was less affected by the model uncertainty and data quantity than model M1. The proposed Bayesian approach in this study gives the updated distributions of ch from a limited number of test data and recommends model M2 for calculating ch.

Risk analysis is vital for reservoir flood control operation considering forecast because forecast uncertainties may create risks of multiple hazard events, including the single-hazard events, the union and intersection of single-hazard events (UHE and IHE). The probability of UHE and IHE are the major concern of decision-makers. This research proposes an analytical flood risk probability calculation framework for single-hazard event, UHE and IHE caused by uncertainties in flood forecasting and takes Dahuofang Reservoir, located in the Hunhe River basin, Northeast China, as a case study. In the framework, the risk is calculated by the integral of the joint probability density function (Pdf) of the risk sources over the hazard domain, which is the collection of the values of risk sources that cause hazards. The determination method of the hazard domain and the Pdf of risk sources and the procedure of risk analysis are elaborated. Results of single-hazard events show that the proposed methodology is of higher precision compared with the risk analysis method based on the law of total probability. Meanwhile, the flood risks of UHE and IHE are calculated for the reservoir operation under different levels of flood limit water level. The study provides a new method of flood risk analysis for flood control reservoir operation.

Previous studies have developed plenty of mathematical models for assessing indoor environment quality. Literature reviews that most of them presented a mean value of perception of a population and ignored the interaction effects of multiple environmental factors on occupants' perceptions. In this regard, the aim of our paper is to develop a comprehensive indoor physical environment quality (IPEQ) index which could present a whole picture of perception of a population by taking the combined effects (i.e., main, crossed and interaction effects) into consideration. The hypothesis and methodology of quantitation were firstly proposed according to Probability Theory. Our quantitation was performed based on the subjective perception votes that collected from 216 experimental conditions in a controlled laboratory. Three 3-input 7-output Artificial Neural Network models were subsequently developed for predicting probability mass functions (PMFs) of 7-point sensation votes under the combined effects of temperature, illuminance, and sound level. Thereafter, the PMFs of 3-point satisfaction votes were expressed and calculated by using Law of Total Probability. Finally, a comprehensive IPEQ index-Predicted Probability Overall Dissatisfied (PPOD) index, which provides an estimate of how many occupants in a space would feel dissatisfied with the overall physical environment, was developed. The predicted expected value of overall satisfaction distribution (average overall satisfaction) was validated to be roughly in accordance with previous studies and more reasonable when at least one kind of environmental factor was far away from expectation. The new quantitative measure also indicated that the minimum PPOD is 17.55% (air temperature = 24.3°C, illuminance = 910Lx, sound level = 35 dB) within common ranges of environmental parameters. It was also discussed that our new quantitative measure could provide quick and direct suggestions for controlling or designing the indoor environment.

The recent claim of Google to have brought forth a breakthrough in quantum computing represents a major impetus to further analyze the foundations for any claims of superiority regarding quantum algorithms. This note attempts to present a conceptual step in this direction. I start with a critical analysis of what is commonly referred to as entanglement and quantum nonlocality and whether or not these concepts may be the basis of quantum superiority. Bell-type experiments are then interpreted as statistical tests of Bohr’s principle of complementarity (PCOM), which is, thus, given a foothold within the area of quantum informatics and computation. PCOM implies (by its connection to probability) that probabilistic algorithms may proceed without the knowledge of joint probability distributions (jpds). The computation of jpds is exponentially time consuming. Consequently, classical probabilistic algorithms, involving the computation of jpds for n random variables, can be outperformed by quantum algorithms (for large values of n). Quantum probability theory (QPT) modifies the classical formula for the total probability (FTP). Inference based on the quantum version of FTP leads to a constructive interference that increases the probability of some events and reduces that of others. The physical realization of this probabilistic advantage is based on the discreteness of quantum phenomena (as opposed to the continuity of classical phenomena).

The total probability formula for continuous random variables is the integral of product of two probability density functions that defines the unconditional probability density function from the conditional one. The need for calculation of such integrals arises in many applications, for instant, in statistical decision theory. The statistical decision theory attracts attention due to the ability to formulate the problems in a strict mathematical form. One of the technical problems solved by the statistical decision theory is the problem of dual control that requires calculation of integrals connected with the multivariate probability distributions. The necessary integrals are not available in the literature. One theorem on the total probability formula for vector Gaussian distributions was published by the authors earlier. In this paper we repeat this theorem and prove a new theorem that uses more familiar form of the initial data and has more familiar form of the result. The new form of the theorem allows us to obtain the unconditional mathematical expectation and the unconditional variance-covariance matrix very simply. We also confirm the new theorem by direct calculation for the case of the simple linear regression.

In this paper, we propose a two-level difference scheme for solving the two-dimensional Fokker–Planck equation. This equation is a parabolic type equation which governs the time evolution of probability density function of the stochastic processes. In addition, these equations preserve positivity and conservation. The Chang–Cooper discretization scheme is used, which ensures second-order accuracy, positiveness, and satisfies the conservation of the total probability. In particular, we investigate a two-level scheme with factor-three coarsening strategy. With coarsening by a factor-of-three we obtained simplified inter-grid transfer operators and thus have a significant reduction in CPU time. Numerical experiments are performed to validate efficiency of the proposed Chang–Cooper two-level algorithms to stationary and time-dependent Fokker–Planck equations, respectively.

In this paper, we discuss the modeling and stabilization problems for a class of discrete-time stochastic networked systems (DSNSs) subject to successive packet losses. The system under consideration is transformed into a stochastic one with bounded stochastic delay. Considering that the stochastic delay is characterized by nonuniform distribution, a new equivalent model is then constructed that enables the DSNS’s controller design to benefit from knowing the probability characteristic of packet losses. Specially, to verify this feature, the probabilities of the delay can be explicitly obtained by utilizing the formula of total probability, which is critical to model transformation and analyze practical problems that exist in DSNSs. Based on the proposed model, sufficient conditions are established under which the globally mean-square asymptotic stability of resulting stochastic delay closed-loop system is guaranteed, and a delay-distribution-dependent design procedure is then proposed. A numerical example with simulation is provided to validate the analytical results and demonstrate the effectiveness of the design procedure.

The reliability of power grids has always received high level concerns, since a high quality of power supply is generally required in both daily life and industrial applications, thus an appropriate reliability assessment is instructive for the design and troubleshooting of power grids. In this work, to improve the sampling efficiency of assessing processes, a pseudo-analytical mix sampling strategy is proposed for reliability assessment of power grids, which is mainly based on the ideas of average-and-scattered sampling and total probability formula method. The proposed scheme is evaluated in both IEEE reliability test system (RTS) and modified IEEE reliability test system (MRTS). The superiority of the proposed scheme is confirmed by comparison, since the results of which indicate that the sampling times can be reduced by more than 3/4 than those obtained by traditional ways.

To define inspection intervals that ensure the continuous and safe operation of a damage-tolerant component, such as a railway axle, a reliable estimation of its fatigue crack growth life is required. Due to the uncertainties involved in the fatigue process, inspections have to be devised not only considering the uncertainties in the performance of the inspection technique, but also based on a probabilistic lifespan prediction. From this premise, this paper presents a procedure for determination of inspection intervals that uses a conservative fatigue crack growth life estimation based on the lifespan probability distribution. A practical example to illustrate the reliability-based inspection planning methodology in a railway axle under random bending loading is given. The inspection intervals are further assessed in terms of total probability of detecting cracks in successive inspections, taking into account the probability of detection curve of the non-destructive testing technique. The procedure developed provides recommendation for the definition of inspection intervals and associated inspection techniques.

The article is devoted to the study of the seals of fixed joints. The mechanisms of leakage occurrence at different values of roughness and pressure on the joint surfaces are considered taking into account the real contact area. The estimation of deformations and forces in the contact zone was carried out taking into account the profile of surfaces, limit deviations of shape and location of surfaces, as well as physical and mechanical properties of materials of the sealed joint. The obtained theoretical dependence allows to evaluate the tightness of the fixed connection depending on the main parameters of the seal roughness, manufacturing errors and the location of the interfaces, their physical and mechanical properties and characteristics of sealed liquid, including differential pressure and the nominal pressure in the joint. A new law of probability density distribution is proposed, which more adequately describes the considered boundary conditions of the experiment. Relations for the probabilistic evaluation of the contact area and surface deformations taking into account the characteristics of the material are obtained. Simple engineering relations for the estimation of probability of contact of the projections and offset surfaces for the two profiles are obtained. The simulation of the process of leakage depending on these conditions is carried out. It is shown that the complete tightness of rigid joints is insufficient even with low roughness provided by the finishing methods of processing and in the absence of deviations in the shape of the joint surfaces. The comparison of experimental data with the obtained theoretical results showed that the proposed engineering dependences provide a good match with the experimental data.

Emergency situations, that cause risks for human life and health, dictate elevated requirements to completeness and accuracy of the presentation of information about current ground environment. Modern robotic systems include sensors, that operate on different physical principles. This causes incrementation of information entering control system. Computing resources and technical capabilities of robotic systems are limited in range and detection probabilities of appearing objects. In case of insufficient performance of the on-board computer system and high uncertainties of ground environment, robotic systems are not able to perform without combining information from robotic group and producing a single view of ground environment. Complex information from a group of robotic systems occurs in real time and a non-deterministic environment. To solve the problem of identifying attribute vectors related to a single object, as well as to evaluate the effectiveness of obtained solutions, is possible using known formulas of the theory of statistical hypothesis testing and probability theory only under the normal distribution law with the known mathematical expectation of an attribute vector and a correlation matrix. However, these conditions are usually not met in practice. Problems also arise when methods of nonparametric statistics are used with an unknown law of probability distribution. The new method of identifying attribute vectors is proposed, that does not rely on a statistical approach and, therefore, does not require knowledge of the type of distribution law and the values of its parameters. Proposed method is based on the idea of combining cluster analysis and fuzzy logic, and is relatively simple to the basic methods of multidimensional nonparametric statistics. The results of modeling information processes are presented. The advantages of proposed method are shown. The comparative values for the number of false recognitions are given. The recommendations are given for constructing fuzzy inference rules when creating an expert system knowledge base.

Armaments are characterized by groups of technical and operational characteristics, each of which is divided into separate indicators. These include effectiveness, ranges of use; combat capability, reliability, operational safety. Under the effectiveness of the missile’s warhead it shall be understood the amount of damage that can cause an explosion in combat environment. The aim of the work is to evaluate the effectiveness of the blast-fragmentation warhead by modeling and analyzing the damaging of injurious effects. Primary blast-fragmentation warhead effects are a shock wave, which is characterized by a specific air pressure on its front and a specific impulse, as well as fragments that move at high speed. Determining the effectiveness of target neutralization by the fragmentation effect of the warhead is described by a set of positions of the j units, each of which is characterized by the fractional volume, the angle of inclination, the type of losses. Due to the independent impact on the target of several effects, their whole impact can be estimated by the total probability of individual injurious effects. The effectiveness of warhead is assessed by the probability of hitting the target. It is most rational to achieve the goal by reducing the distance to the explosion while increasing accuracy. This is a global development trend. Other ways are either to increase its explosive power or structurally - the number of fragments. It is necessary to indicate experimental data on the number of holes per unit area for a given distance and characteristics of the warhead of the missile. Assessing the probability of the debris impact requires clarification of the characteristics of the warhead, the characteristics of the vulnerable spots of the target and the angle of the missile approach. It is advisable to make the trajectory of the missile approach guided, taking into account the modularity of the configuration. This reduces ammunition consumption and increases the efficiency of the warhead.

The problem of forecasting emergency situations at hydraulic facilities of a hydroelectric complex, forming its pressure waterfront, based on the application of a logical-probabilistic approach is considered. The relevance of the studies and their practical significance are determined by the need to assess the compliance of the safety of hydraulic facilities with international safety standards and current national legislation. Therefore, the reports on the environmental impact assessment of hydraulic facilities should present the results of assessing the additional risk of emergency situations at the hydroelectric complex. This assessment, in turn, requires an analysis of the probability of accidents at the hydroelectric complex before and after new construction. In the present study, using the example of the Kakhovka hydroelectric complex (Ukraine), the systemic nature of possible causes of accidents at pressure hydraulic facilities as part of hydroelectric complexes is found. An accident at a hydroelectric complex is considered as a complex natural and man-made event, which can be associated with various natural and man-made factors. The total (generalized) probability of an accident at the hydroelectric complex is estimated by the logical-probabilistic method of failure and fault trees based on a deductive approach. The upper limit estimates of the probability of accidents at individual hydraulic facilities of the hydroelectric complex and the generalized estimate of the probability of an accident at the hydroelectric complex as a whole are calculated. It is found that the probability of an accident depending on the hydraulic facility of the hydroelectric complex can vary. In the case of the Kakhovka hydroelectric complex, it varies from 2.1×10–6, year–1, at the run-of-river earth dam, to 5.6×10–6, year–1, at the spillway dam. The total probability of an accident at the hydroelectric complex is 2.35×10–5emergency events per year. However, these estimates do not exceed the permissible value of 5×10–5, year–1, which is regulated for hydraulic facilities of the corresponding consequence class. Thus, it is concluded that the current reliability and safety of the hydraulic facilities of the Kakhovka hydroelectric complex can be recognized as sufficient

The article summarizes research results of the study on the problem of assessing the differentiation level of socio-economic development of territorial units of the Russian Federation. The authors propose an approach to measuring differentiation using mixtures of probability distributions.This technique was developed and tested on real data that allows one to determine the presence or absence of interregional differentiation. The research hypothesis, that interterritorial differentiation is estimated by a specific statistical indicator selected based on a content, qualitative analysis, served as a theoretical platform of this methodology. Differentiation is practically absent if the entire statistical population is described by a single law of probability distribution. If the statistical population is described by a mixture of probability distributions, then one should expect the presence of a significant level of differentiation by the considered indicator.In mathematical statistics, the problem of separating a mixture of probability distributions (estimating parameters of distribution densities and weighting coefficients) is traditionally solved using several similar methods. For example, the expectation-maximization (EM) algorithm, median modifications of the EM-algorithm, SEM-algorithm, taking into account the specifics of the selected object (constituent entities of the Russian Federation a small sample). To solve this problem, the authors used the SEM algorithm. As the information base of the empirical study, official statistics were used (open data from the Federal State Statistics Service).The typologies of the constituent entities of the Russian Federation were identified based on two characteristics within 2005-2017-time interval. The first one being the level of violence (using the “homicide rate” indicator the number of homicides and attempted murders per 100000 population). And second average per capita income, which made it possible, among other things, to additionally test the hypothesis of the traditional use of differentiation trends in the level of violence as an indicator of economic inequality. According to the authors, the results of this study can be used as instrumental and informational support for managerial decisions aimed at regulating the differentiation of Russian regions by the level of violence and economic inequality.

This paper argues that the path integral formulation of quantum mechanics suggests a form of holism for which the whole (total ensemble of paths) has properties that are not strongly reducible to the properties of the parts (the single trajectories). Feynman’s sum over histories calculates the probability amplitude of a particle moving within a boundary by summing over all the possible trajectories that the particle can undertake. These trajectories and their individual probability amplitudes are thus necessary in calculating the total amplitude. However, not all possible trajectories are differentiable, thus suggesting that they are not physical possibilities, but only mathematical entities. It follows that if the possible differentiable trajectories are taken to be part of the physical system, they are not sufficient to calculate the total probability amplitude. The conclusion is that the total ensemble is weakly non-supervenient upon the physically possible trajectories.

Performance is a very important factor in determining success in assessing work quality. Good performance is the hope of all parties in an institution, including agricultural institutions. The Sukaraja Agricultural Extension Service Technical Unit (UPT BPP) always supports to improve the performance of extension workers in order to improve the quality of extension workers. Evaluation of broadcasting performance is carried out from the beginning of the activities carried out, starting from the preparation, implementation, evaluation and reporting. Evaluation of instructor performance at UPT BPP Sukaraja is carried out every three months and six months. So far, the evaluation is done manually, so it does not need to be done in a timely manner because of constrained inadequate labor. The method used in the evaluation study is the use of agricultural instructors using the Bayes method. The Bayes method is first performed by calculating the value of each criterion, total weighting, probability perriterian, calculating the total probability, calculating the threshold of each criterion and calculating the threshold value then comparing the total value with the threshold value of each criterion. The results of this method produce a good agriculture instructor ranking ranking, namely with initial Sdn with a total value of probability 31.38 and those requiring guidance are extension agents with Sjn and Dsm with a total probability of 24.13, and a total probability of 24.

When analyzing typical assault aviation combat missions, the most common objects for each aircraft actions should be identified, a preliminary estimate of their distance from the front line has to be provided, and one of the objects should be selected as the typical target for evaluating the aircraft effectiveness. A destruction of a typical target by an aircraft with a certain probability is one of the main components of the assault aviation aircraft effectiveness, but it does not fully characterize the effectiveness of the aircraft. In the course of assault aircraft combat mission accomplishment, the generally accepted approach is identification the four aircraft flight phases with a purpose of destruction a surface target. As a combat mission for assault aircraft the striking for destruction an enemy airfield or division of guided missiles can be considered. The choice of flight route and profile is related to the assessment of the enemy's actual areas of engagement to determine the line of maneuvering. The feature of devastating effect of attack ammunition is the conditional law of target destruction. For the means of destruction of a remote action the feature of devastating effect of attack ammunition is a cumulative effect of each munitions at known coordinates of impact points. For the means of destruction which are used in cluster bombs, as a result of small caliber live ammunition scattering the total area of destruction is created. The cover area for single cluster bomb is ellipse shaped. Thus, in order to evaluate the effectiveness of the assault aviation aircraft employment it is advisable to use an indicator such as the effectiveness of the aircraft in one combat sortie. Evaluation of aircraft effectiveness in one sortie consists of estimates of the probability for penetration the means of air defense, the probability of target detection, the probability of target attack, the probability of target destruction and reliability of aviation equipment. For assault aviation, the effectiveness of an aircraft in a single combat sortie has the notion of a total probability of a target destruction or a mathematical expectation of a target destruction.

Signal classification plays an important role in cognitive communication networks to identify and avoid interference. Contrary to traditional cooperative spectrum sensing based on binary hypothesis testing, we study a network of cognitive radios that jointly perform linear cooperation based signal classification via $M$ -ary hypothesis testing. To maximize the probability of successful classification subject to constraints on individual probabilities of misclassification, we divide the problem into $M$ independent binary hypothesis testing subproblems in parallel before selecting the hypothesis that is most likely true. Furthermore, we consider a problem that maximizes the probability of successful classification subject to a constraint on the total probability of misclassification. We reformulate such an optimization problem into two different subproblems, where the optimal solution is obtained by alternating the two optimization sub-problems iteratively. Numerical simulations demonstrate the near-optimality of the proposed methods with low computational complexity for the cooperative signal classification problems.

Most research studies on the reliability of oil derrick structures have focused on static reliability analysis. Strength degradation with time of oil derrick structures and mechanism failure should also be considered in reliability analysis. In order to address this issue, we propose a new time-dependent reliability analysis method for oil derrick structures in mechanism failure mode and apply it to a tower derrick structure. We used the Monte Carlo finite element method to compute the static failure probability of each derrick component, and steps were employed to determine the main failure mechanisms. The time-dependent failure probabilities of each derrick component in the main failure mechanisms were calculated by the total probability theorem. The time-dependent reliability of a derrick structure system was obtained by considering the system as a series of parallel subsystems. A tower derrick example was used to demonstrate the accuracy and applicability of the proposed method. The results revealed that the proposed method is accurate and reliable.

Stochastic tools have been developed to estimate the potential for tsunami generation in a particular region under consideration. This paper identifies 13 probable zones on the earth where there is a high likelihood for tsunami generation in the future. The conditional probabilities for future tsunami and earthquake occurrences are estimated for all the identified zones. Also, total probabilities for future tsunami events are computed. Forecasting is done on the basis of conditional probability obtained using the best fit model among Lognormal, Gamma, Log-Logistic and Weibull distributions. The obtained probabilities of tsunami are validated by calculating the region-specific threshold probabilities. Also, a country wise expectation of anticipated tsunami is developed for each zone. Zones 5 (Northwest U.S.A and Bering Sea Islands), 6 (Kuril & Kamchatka Islands) and 7 (Japan, Northeast China and Korea) have the highest ratio of tsunamigenic earthquakes to the total number of earthquakes. The zone 7 has the highest probability of tsunami occurrence in the near future as calculated from the total probability theorem. However, zones 1 (Southwest coast of South American continent), 7 and 11 (Papua New Guinea and Solomon Islands) are expected to experience a tsunami in the near future (before 2022) as per the current forecasting study.

This paper studies a finite Markovian queue with customer interjections. Arriving customers are dispersed into normal customers and interjecting customers, the normal customers join the queue at the end and the interjecting customers try to cut in line and occupy a position as close to the head of the queue as possible. The behavior of interjecting customers is described by the percentage of customers interjecting and the tolerance level of interjection by individual customers who are already waiting in the queue. Customers in different positions in the waiting line have different tolerance levels on customer interjection. By using the theory of the exponential distribution, the Laplace–Stieltjes transform and the formula of the total probability, we obtain the mean and variance of waiting time of a customer in position n, a normal customer and an interjecting customer. Further, numerical results show that these means and variances of waiting times increase with increase of the arrival process, and are sensitive to the percentage of customers interjecting and the tolerance level of interjection. It is found that eliminating customer interjection would be beneficial to normal customers.

A simple scheme is presented for mapping the 2D probability density for an observer's position, defined by any number of lines of position (LOPs) on the surface of the Earth, assuming that the LOPs result from uncorrelated observations that have normally distributed errors. Although the mapping can be used to determine the position fix corresponding to the LOPs (which is consistent with other methods), its intended use is computing the total probability that the observer is located within (or outside) some specified area of interest, such as a zone of avoidance around a navigational hazard. Numerical experiments with areas where the average total interior probability is known, such as the triangles and polygons formed by nearly convergent LOPs, show that the method provides correct answers. The numerical experiments also revealed that theoretical probabilities associated with commonly used error ellipses are overstated for navigational solutions based on small numbers of LOPs.