Hallmark professionalism in probabilistic analysis is to quantify the uncertainties involved in construction materials subject to intrinsic randomness in its physical and mechanical properties and is now gaining popularity in civil engineering arena. As well, knowledge of behaviour of materials is continuously evolving and its statistical descriptors are also changing when more and more data collected or even data updated and hence reliability analysis has to be carried out with the updated data as a continuous process. As per the committee report ACI 544.2R, it is found that there is no attempt made for probabilistic relation between cube compressive strength and cylinder compressive strength for fiber reinforced concrete. In consequence of this report, a robust relation between cube and cylinder of experimentally conducted compressive strength was established by Monte-Carlo simulation technique for different types of fibrous concrete like steel, alkali resistant glass and polyester fibrous concrete before and after thermoshock considering various uncertainties. Nevertheless simulated probabilistic modals, characteristic modals, optimized factor of safety and allowable designed cylinder compressive strength have been developed from the drawn probability of failure graph, which exhibits robust performance in realistic Civil Engineering materials and structures.

The article discusses the evolution of Marian Smoluchowski’s reasoning in his research on causality and understanding the essence of chance. Initially, Smoluchowski focused on the epistemic study of causality, looking for evidence supporting the kinetic-molecular theory. In proving the causes of Brownian motion, he used the concepts of physical causality. The fundamental change in Polish physicist's perception of causality was the understanding of the position of chance on the cause-effect line. Introducing mathematical relations into his considerations, he analyzed the aspect of the occurrence of the effect. The chance suitable for calculating probability was distinguished from the chance in a broader sense by the essential regularity of the frequent recurrence of the phenomenon, regardless of the knowledge of the cause. Smoluchowski's merit was the distinction between the philosophical and physical understanding of causality, chance and probability theory. Shifting the considerations on the nature of chance to the ontological plane moved the study of chance into the area of science, thus leading to the practical application of probability theory in physics.

Biological diversity within a mixture field allows for better use of habitat and agro-technical conditions by the mixtures, which can be seen by higher and more stable yields than varieties sown separately. Our studies were conducted in the growing seasons 2011/2012–2014/2015 as field experiments with four winter barley varieties (Bombaj, Gil, Gregor, Bażant) and three, two- and three-component mixtures (Bombaj/Gil, Bombaj/Gregor, Gil/Gregor/Bażant). Seven different chemical treatments with fungicides were applied. The aim of this study was to compare the different varieties of winter barley with their mixtures for resistance to powdery mildew infection. To achieve this aim the logistic model for the analysis of data was used. Of the varieties under consideration, the best and the most resistant variety was Gregor, while the weakest and the most susceptible to diseases (powdery mildew) was Gil. This variety was also significantly weaker than any of the other mixtures taken into account. Moreover, it was so weak that when it was included in mixtures with other varieties, it weakened these mixtures as well.

Currently, the Republic of Kazakhstan is developing a new standard for symmetric data encryption. One of the candidates for the role of the standard is the Qamal encryption algorithm developed by the Institute of Information and Computer Technologies (Almaty, Republic of Kazakhstan). The article describes the algorithm. Differential properties of the main operations that make up the Qamal cypher are considered in the questions of stability. We have shown that for a version with a 128-bit data block and the same secret key size for three rounds of encryption it is difficult to find the right pairs of texts with a probability of 2–120, which makes differential cryptanalysis not applicable to the Qamal cypher.

The paper evaluates the relationship between the selection of the probability density function and the construction price, and the price of the building's life cycle, in relation to the deterministic cost estimate in terms of the minimum, mean, and maximum. The deterministic cost estimates were made based on the minimum, mean, and maximum prices: labor rates, indirect costs, profit, and the cost of equipment and materials. The net construction prices received were given different probability density distributions based on the minimum, mean, and maximum values. Twelve kinds of probability distributions were used: triangular, normal, lognormal, beta pert, gamma, beta, exponential, Laplace, Cauchy, Gumbel, Rayleigh, and uniform. The results of calculations with the event probability from 5 to 95% were subjected to the statistical comparative analysis. The dependencies between the results of calculations were determined, for which different probability density distributions of price factors were assumed. A certain price level was assigned to specific distributions in 6 groups based on the t-test. It was shown that each of the distributions analyzed is suitable for use, however, it has consequences in the form of a final result. The lowest final price is obtained using the gamma distribution, the highest is obtained by the beta distribution, beta pert, normal, and uniform.

Rammed earth significantly reduces intrinsic energy compared to concrete construction and has an environmental benefit throughout the life cycle of the building: phases of construction, operation, maintenance, renovation, and demolition. Several studies have recently been carried out to study this material. However, the seismic behavior of rammed earth constructions is still an important topic that needs to be studied in more detail. Through the analysis of non-linear behavior of the rammed earth construction for different wall thicknesses according to the Moroccan earthquake regulation RPS2011, we were able to assess the seismic performance under the corresponding conditions (loads, seismic zone). The results show that the walls studied can have good resistance in areas of seismicity ranging from “very low” to “moderate” and acceptable performance in areas of high seismicity. Furthermore, fragility analysis shows that rammed construction with a wall thickness equal to 50 centimeters exhibits better seismic performance and a low probability of damage, particularly in the case of moderate, severe, and complete damage states.

Civil engineering is one of the many fields of occurrences of uncertain parameters. The present paper in an attempt to present and describe the most common methods used for inclusions of uncertain parameters . These methods can be applied in the area of civil engineering as well as for a larger domain. Definitions and short explanations of methods based on probability, interval analysis, fuzzy sets, and convex sets are presented. Selected advantages, disadvantages, and the most common fields of implementation are indicated.

An example of a cantilever beam presented in this paper shows the main differences between the methods. Results of the performed analysis indicate that the use of convex sets allows us to obtain an accuracy of results similar to stochastic models. At the same time, the computational speed characteristic for interval methods is maintained.

This paper investigates the effect of explicitly informing participants about the objective probability of winning a lottery on the illusion of control. In a procedure based on Experiment 3 from Langer’s 1975 seminal paper, participants were faced with lotteries based on familiar vs. unfamiliar stimuli and either explicitly informed about the objective probability of winning or not (the probability could be derived from other data). Results indicated that stating the objective probability of winning the lottery reduced, but not eliminated the illusion of control. Moreover, Langer’s effect of stimulus familiarity was not replicated. Experiment 2, which included a lottery based on the full set of Polish alphabet letters, confirmed the same effects. Results indicate that illusion of control may be explained by the control heuristic (Thompson et al., 1998) – in absence of explicitly stated probability, participants estimate their chances of winning based on perceived control, even though calculating the objective probability is possible.

Rainfall is one of the main components of the hydrologic cycle; thus, the availability of accurate rainfall data is fundamental for designing and operating water resources systems and infrastructure. This study aims to develop an empirical model of rainfall intensity ( I_t,p) as a function of its probability ( p) and duration ( t). In 1999–2020, data on the hourly duration of rainfall were collected from automatic rainfall recorder (ARR) gauges. The empirical model has been developed using a statistical approach based on duration ( t) and probability ( p), and subsequently they have been validated with those obtained from ARR data. The resulting model demonstrates good performance compared with other empirical formulas (Sherman and Ishiguro) as indicated by the percent bias ( PBIAS) values (2.35–3.17), ratio of the RMSE (root mean square error) between simulated and observed values to the standard deviation of the observations ( RSR, 0.028–0.031), Nash–Sutcliffe efficiency ( NSE, 0.905–0.996), and index of agreement (d, 0.96–0.98) which classified in the rating of “very good” in model performance. The reliability of the estimated intensity based on the empirical model shows a tendency to decrease as duration ( t) increases, and a good accuracy mainly for the rainfall intensity for shorter periods (1-, 2-, and 3-hours), whereas low accuracy for long rainfall periods. The study found that the empirical model exhibits a reliable estimate for rainfall intensity with small recurrence intervals ( Tr) 2-, 5-, 10-, and a 20-year interval and for a shorter duration ( t). Validation results confirm that the rainfall intensity model shows good performance; thus, it could be used as a reliable instrument to estimate rainfall intensity in the study area.

Usually, cellular networks are modeled by placing each tier (e.g macro, pico and relay nodes) deterministically on a grid. When calculating the metric performances such as coverage probability, these networks are idealized for not considering the interference. Overcoming such limitation by realistic models is much appreciated. This paper considered two- tier twohop cellular network, each tier is consisting of two-hop relay transmission, relay nodes are relaying the message to the users that are in the cell edge. In addition, the locations of the relays, base stations (BSs), and users nodes are modeled as a point process on the plane to study the two hop downlink performance. Then, we obtain a tractable model for the k-coverage probability for the heterogeneous network consisting of the two-tier network. Stochastic geometry and point process theory have deployed to investigate the proposed two-hop scheme. The obtained results demonstrate the effectiveness and analytical tractability to study the heterogeneous performance.

The paper discusses service load measurements (weight of construction materials, small equipment and workers) conducted on 120 frame scaffoldings all over Poland in 2016‒2018. Despite the fact that the scaffolding should ensure the safety of its users, most accidents on construction sites are caused by fall from height. Service loads are one of the elements affecting the safety of scaffolding use. On the basis of the studies, maximum load on one platform and maximum load on a vertical scaffolding module for one day were obtained. They were treated as the random variables of the maximum values. Histograms and probability density functions were determined for these variables. The selection of a probability distribution consisted in the selection of a probability density function by means of fitting curves to the study result histograms using the method of least squares. The analysis was performed for distribution Weibull and Gumbel probability density functions which are applied for maximum values of random variables. Parameters of these functions can be used for the purposes of the reliability analysis to calibrate partial safety factors in simulation of service load during the scaffolding failure risk assessment. Besides, the probability of not exceeding the standard loads provided for frame scaffoldings for 120 weeks was established on the aforementioned basis. The results of the presented research show that in Poland there is a high probability of exceeding the permissible service loads in one year and thus there is a high risk of scaffolding damage.

The paper contains synthetic and analytical test results and model solutions for technical maintenance and wear problems of apartment houses traditionally structured. The crucial methodological aspect of the research is striving to minimize the subjectivity of expert assessment while technical investigation of old buildings. The cause and effect between the occurrence of damage to the elements of the rental houses, treated as an expression of the conditions for their maintenance, and the size of the technical process of wear of these elements was determined on a representative, purpose-appropriate, sample of 102 residential buildings erected in the second half of the 19th and early 20th centuries in downtown Wrocław (Poland) district. Rational maintenance of existing buildings is nowadays significant issue for their proprieties. Therefore, there is constant need to find a research method that may lead to well thought out building maintenance management. The goal of undergone research was to search influence of apartment houses maintenance on the grade and intensity of their deterioration. As to fulfil the research objective the group of engineers identified symptoms of the technical wear growth, which means performed identification of causes and effects responsible for the defects appearance. The range of the work demanded elaboration of a new qualitative model of detected defects and its transfer into a quantitative model. Therefore, such approach enabled to establish the reason - effect connection ‘defect - technical wear’ related to the crucial structural parts of investigated apartment houses.

An advanced evaluation technique, helpful in the fire resistance assessment of a simple steel structure exposed to fire is presented and discussed in detail on the example of an unrestrained and uniformly heated steel beam. The proposed design methodology deals with the generalised probability-based approach in which the most probable failure point is formally identified. The random nature of all variables considered in the detailed analysis is taken into account. The critical temperature of the steel from which the considered beam is made of is accepted here as the authoritative safety measure. This temperature value is associated with the fire resistance limit state defined for the maximum acceptable value of failure probability. When forecasting the failure probability, not only the risk of a potential fire being initiated but also not being effectively extinguished is included in the calculation. Various levels of the target failure probability may be assumed in such the analysis, depending on the selected reliability class. They are specified in general by setting an appropriate value of the required reliability index β fire req. In the presented design algorithm no representative values of the considered random variables are specified. The critical temperature estimates obtained from these calculations are always less restrictive in comparison with the corresponding solutions computed after applying the conventional standard procedure.

In this paper we derive mathematical description of TCP (Transmission Control Protocol) retransmission probability based on Jacobson’s smoothing algorithm that belongs to EWMA (Exponentially Weighted Moving Average) category. This description is parametrized on the probability density function (pdf) of RTT (Round Trip Time) samples and α, β – two primary parameters of Jacobson’s algorithm. Although it is not a close form expression, it is formulated as an effective algorithm that let us to explicitly calculate the values of RTO (Retransmission Time Out) probability as a function of α, β and the pdf of RTT samples. We achieve the effectiveness of this approach by applying smart discretization of the state space and replacement of continuous functions with discrete approximate equivalents. In this way, we mitigate the cardinality of discrete distributions we deal with that results in linear (n+m) instead of multiplicative (n⋅m) growth of computational complexity. We provide the evaluation of RTO probability for a wide set of α, β parameter values and differently shaped Normal and Laplace pdfs the RTT samples are taken from. The obtained numerical results let us to draw some conclusions regarding the choice of optimal values of α, β parameters as well as the impact of pdf the RTT samples are taken from.

In this paper we present the Bayesian model selection procedure within the class of cointegrated processes. In order to make inference about the cointegration space we use the class of Matrix Angular Central Gaussian distributions. To carry out posterior simulations we use an alorithm based on the collapsed Gibbs sampler. The presented methods are applied to the analysis of the price – wage mechanism in the Polish economy.

The paper formulates some objections to the methods of evaluation of uncertainty in noise measurement which are presented in two standards: ISO 9612 (2009) and DIN 45641 (1990). In particular, it focuses on approximation of an equivalent sound level by a function which depends on the arithmetic average of sound levels. Depending on the nature of a random sample the exact value of the equivalent sound level may be significantly different from an approximate one, which might lead to erroneous estimation of the uncertainty of noise indicators. The article presents an analysis of this problem and the adequacy of the solution depending on the type of a random sample.

This paper presents the statistical modelling of the monitoring data on oxygen indicators in the Rega River, collected in years of 1992-97. In the first part, the six probability distributions are examined to fit the experimental data. The results indicate that the lognormal and Gamma distributions give an adequate description for all considered data series, as measured by P-P probability plots, and a Kolmogorov-Srnirnov goodness of fit test. In the second part, the detailed statistical analysis was performed based on lognormal distribution. This study showed that the approximation of monitoring data with the appropriate probability distribution could be very useful for evaluating of water quality.

The paper presents an analysis of the voicing of the phoneme /v/ in modern spoken Macedonian. The phoneme /v/ in the standard Macedonian language is classifi ed as a fricative, but some of its characteristics separate it from the other phonemes in this group. This is due to the fact that this phoneme was once a sonorant. In a part of the Macedonian dialects this phoneme is pronounced with marked voicing to this day. This phenomenon is then refl ected in the pronunciation of standard Macedonian. Our analysis is based on a selected corpus of examples that have been spoken by speakers from various dialect origins, in order to assess the any differences in pronouncing of the phoneme /v/ when placed in different phoneme contexts in the word.

The paper presents the method of determination of two-dimensional probability distribution P_f of crack initiation versus fatigue life N and the fatigue damage parameter : P_f − N − ϭ. The proposed distribution P_f uses parameters of the standard fatigue characteristics and allows calculating fatigue life of elements with heterogeneous stress fields at any probability level. The model was successfully verified on experimental test results.

To reliably calibrate suitable partial safety factors, useful for the specification of global condition describing structural safety level in considered design case, usually the evaluation of adequate failure probability is necessary. In accidental fire situation, not only probability of the collapse of load-bearing structure, but also another probability related to the people staying in a building at the moment of fire occurence should be assessed. Those values are different one from another in qualitative sense but they are coupled because they are determined by similar factors. The first one is the conditional probability with the condition that fire has already occured, whereas the second is the probability of failure in case of a potential fire, which can take place in the examined building compartment, but its ignition has not yet appeared. An engineering approach to estimate such both probabilities is presented and widely discussed in the article.

The aim of the study was to model the operation of a wastewater treatment plant using the Monte Carlo method and selected probability distributions of random variables. Pollutant indices in treated wastewater were analysed, such as: biological oxygen demand ( BOD ₅), chemical oxygen demand ( COD _Cr), total suspended solids ( TSS), total nitrogen (N _tot), total phosphorus (P _tot). The preliminary analysis of pollution indicators series included the: calculation of descriptive statistics and assessment of biological degradability of wastewater. The consistency of the theoretical distributions with the empirical ones was assessed using Anderson–Darling statistics. The best-fitting statistical distributions were selected using the percent bias criterion. Based on the calculations performed, it was found that the analysed indicators of pollution in treated wastewater were characterised by an average variability of composition for BOD ₅, COD _Cr and TSS, and a high variability of composition for N _tot and P _tot. The best fitted distribution was log-normal for BOD ₅, TSS, N _tot and P _tot and general extreme values for COD _Cr. The simulation carried out using the Monte-Carlo method confirmed that there may be problems associated with the reduction of nutrients (N _tot and P _tot) the analysed wastewater treatment plant. Results of values obtained of the risk values of negative control of wastewater treatment plant operation for biogenic compounds, different from 1, indicate that the number of exceedances at the outflow may be higher than the acceptable one.