V. I. Piterbarg, I. V. Rodionov

Certain modern developments in stochastic extreme value theory, on occasion of 110th birthday of Boris Vladimirovich Gnedenko 

 

We present a short overview of developments of the last decade in asymptotic analysis of extrema of families of random variables. We focus on the methods of investigating the quality of approximations as given by Gnedenko’s extreme value theorem, and its generalizations to the case of dependent random variables.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-16-25

 

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Andrei V. Zorine

Mikhail Andreevich Fedotkin: A Nonstatistical Analysis Of The First 80 Years Of His Life

 

Professor of the Lobachevsky University of Nizhni Novgorod celebrated his 80th anniversary in May 2021. This paper touches some of his personal histories, and his scintific contributions. This paper is dedicated to the life and scientific achievements of Mikhail Andreevich Fedotkin, on the occasion of his 80th anniversary. It is not an easy task to present the topic better than the protagonist did himself in his autobiographical book. No one has a more complete knowledge of his life facts than he does. So, we may only revew several turning points in his biography, maybe in a half-joking tone sometimes, with all our love and respect to the man of the hour.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-26-31

 

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P. Vijaya Laxmi, E. Girija Bhavani

Multi-Server Markovian Queue With Successive Optional Services

 

In this study, we analyze a multi-server queueing model with two successive optional services. Each server provides FES as well as two optional services to each arriving customer, for a total of  servers. Every new customer requires the first essential service (FES). The customer may quit the system with probability  or choose optional services supplied by the same server after finishing the FES. With probability , customer chooses the first optional service (OS - 1). Following that, the customer has the option of joining the second optional service (OS - 2) with probability  or leave the system with probability . We obtain the steady-state probability distributions by applying matrix-geometric method. We also derive a number of performance measures of the queueing model. Sensitivity analysis is used to investigate the impact of various parameters on performance of the queueing model.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-32-43

 

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Victor Yu. Itkin

Markov Reliability Model Of A Wind Farm

 

A Markov reliability model of a wind farm has been built using the example of Anholt wind farm, Denmark. Reliability indicators of wind turbine equipment are calculated as wind speed functions. Basing hourly measurements of the wind speed and the consumed electricity, two samples of duration time of the met and unmet demand of electricity were obtained. It has been found that these samples can be approximated with exponential mixture model of the probability distributions. The wind farm operation process has been approximated with a continues-time 5-states Markov process. As a result, stationary and non-stationary probabilities that the electricity demand will be met by wind power were estimated.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-44-57 

 

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Abhimanyu S. Yadav, H. S. Bakouch, S. K. Singh1 and Umesh Singh

Estimation procedures for a flexible extension of Maxwell distribution with data modeling

 

In this paper, we introduce a flexible extension of the Maxwell distribution for modeling various practical data with non-monotone failure rate. Some main properties of this distribution are obtained, and then the estimation of the parameters for the proposed distribution has been addressed by maximum likelihood estimation method and Bayes estimation method. The Bayes estimators have been obtained under gamma prior using squared error loss function. Also, a simulation study is gained to assess the estimates performance. A real-life application for the proposed distribution have been illustrated through different lifetime data.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-58-72

 

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Achyutha Krishnamoorthy

A Reliability-Inventory Problem Under N-policy of Replenishment of Component

 

In this paper a new process is introduced. To some extent it has resemblance with Queueing-Inventory (Inventory with positive service time) (see Sigman and Simchi-Levy and Melikov and Molchanov. We consider a k - out - of - n: G system of identical components, each of which has exponentially distributed lifetime with parameter l, independent of the others. When the number of working components goes down to N (k ≤ N ≤ n) due to failures, an order for n − k + 1 items is placed. Replenishment time is exponentially distributed with parameter b. On replenishment, all failed components are instantaneously replaced by the new arrivals, subject to a maximum of n − k + 1. This process is investigated and its long run system state distribution derived explicitly. An associated optimization problem is discussed. Throughout this paper the k - out - of - n system is assumed to be COLD.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-73-87 

 

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Jens Braband, Hendrik Schäbe

Safety Vs. Security – Why Architecture Makes The Difference

 

Cybersecurity plays an increasing role. This also holds true for safety systems. Hence, it is necessary to combine systems that fulfill security and safety requirements. These requirements are partially contradictory. Safety related software will not be changed in an ideal world, whereas security software needs almost permanent updates. This leads to problems that are hard to solve. Different approaches have been proposed by different authors. In this paper we will show, how a suitable architecture can be applied to satisfy the security as well as the safety requirements. We consider some examples of such architectures and show, how systems can be constructed that on the one hand side contain a “golden” code for safety that is not changed and on the other hand side security software that can easily be patched, not touching the “golden” code.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-88-93

 

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Victor Netes

Effectiveness Retention Ratio And Multistate Systems

 

This paper analyzes approaches to dependability assessment of multistate systems in which partial failures can occur. It is shown that for many multistate systems it is advisable to use the effectiveness retention ratio as a dependability measure. The paper explains the meaning and advantages of this measure and presents methods for its calculation for two classes of systems covering typical situations. They are additive systems in which the output effect is obtained by summing the output effects of the subsystems, and multimode systems that can perform some function or task in different modes depending on their state. Besides that, the presence and use of the effectiveness retention ratio in international and regional Euro-Asian standards are considered.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-94-104

 

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Ram Milan, Diwakar Shukla

Kernel Sampling Based Parameter Estimation in Detected Community in Weighted Graph in Big Data

 

The social media platforms are such examples of big-data where the volume, velocity, and variety are visualized over time domain.  Registered users of such platforms bear frequent communication with others and that could be identified as a community. Many methods (algorithms) exist in literature to detect such likely groups of frequent communication. This paper presents contribution to estimate parameters of detected communities using sampling procedure. A Kernel sampling procedure is suggested in the setup of detected community environment. A method is suggested whose efficiency has been estimated using calculations of confidence interval. Simulation procedure is used to obtain the lower and upper limits of confidence intervals with the help of multiple samples.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-105-120

 

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Baranov L. A., Ermolin Y.A., Shubinsky I. B.

Reliability Of A Big City Sewer Network

 

The ramified sewerage system for receiving and transferring household and industrial sewage typical for a large city is considered. Consideration is restricted to the sub-system of sewage conveyance (sewer network). A sewer network is defined as a combination of underground pipes (sewers) passing sewage through the force of gravity. A review of the literature reveals that there is currently no universally acceptable definition or measure for the reliability of urban sewer network. The aim of this article is to propose the physically obvious reliability index, and to develop an engineering methodology for its calculating. The relative raw sewage volume that could be potentially discharged to the environment as a result of component failures in the sewer network is proposed as a measure of overall system reliability. A simple method for quick and proper calculation of this volume is presented. The basis for this method is a representation of the sewer network by a combination of Y-like fragments. Each such fragment is formally substituted by a fictitious equivalent sewer that has a failure rate leading to the same output for the same input. A sequential application of this approach reduces the problem of estimating the discharged sewage volume to an elementary sub-problem with a simple solution is. The proposed approach is based on the reliability theory. The notions “failure flow” and “repair flow” are used. These flows are taken stationary with known parameters. Numerical examples are used to demonstrate the proposed approach.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-121-136

 

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Kambiz Ahmadi

Reliability analysis for a class of exponential distribution based on progressive first-failure censoring

 

Based on progressively first-failure censored data, the problem of estimating parameters as well as reliability and hazard rate functions for a class of an exponential distribution is considered. The classic and Bayes approaches are used to estimate the parameters. The maximum likelihood estimates and exact confidence interval as well as exact confidence region for parameters are developed based on this censoring scheme. Also, when the parameters have discrete and continuous priors, several Bayes estimators with respect to different symmetric and asymmetric loss functions such as squared error, linear-exponential (LINEX) and general entropy are derived. Finally, two numerical examples are presented to illustrate the methods of inference developed in this paper.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-137-149

 

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K.M. Sakthivel, K. Dhivakar

Transmuted Sine-Dagum Distribution and its Properties

 

In this paper, we introduce a new four parameters continuous probability distribution called transmuted sine-Dagum distribution obtained through the transmuted Sine-G family introduced by Sakthivel et al. [13]. We have obtained some distributional properties including moments, inverted moments, incomplete moments, central moments, and order statistics for proposed model. The reliability measures such as reliability function, hazard rate function, reversed hazard rate function, cumulative distribution function, mean waiting time and mean residual lifetime are studied in this paper. Further, we have discussed some income inequality measures including Lorenz curve, Bonferroni index and Zenga index. The maximum likelihood method is used to estimate the parameters of the proposed probability distribution. Finally, we demonstrated goodness of fit the proposed model with other suitable models in the literature using real life data sets.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-150-166

 

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V. Sai Jyothsna Devi, K. Srinivasa Rao

EPQ Models With Mixture Of Weibull Production Exponential Decay And Constant Demand

 

This paper deals with an economic production quantity (EPQ) model in which production is random and having heterogeneous units of production. The production process is characterized by mixture of Weibull distribution. It is assumed that the demand is constant and the lifetime of the commodity is random and follows an exponential distribution. Assuming that the shortages are allowed and fully backlogged the instantaneous state of inventory in the production unit is derived. The minimizing the expected total production cost, the optimal production quantity, the production uptime and downtime are derived. Through sensitivity analysis it is observed that the random production with mixture distribution have a significant influence on the optimal production schedules and production quantity. It is also observed that the rate of deterioration can tremendously influence the optimal operating policies of the system. This model also includes some of the earlier models as particular cases. The model is extended to the case of without shortages. A comparison of the two models reveals that allowing shortages will reduce expected total cost of the model.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-167-185 

 

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Farhadzadeh E.M., Muradaliyev A.Z., Abdullayeva S.A.

Estimation, Comparison And Ranking Of Operational Reliability Indicators Of Overhead Transmission Lines Of Electric Power Systems

 

The regular increase in relative number of units of equipment, devices and installations (further - objects) electric power systems, which service life exceeds normative value and the consequences connected with this fact, including, including unacceptable ones, demand acceptance of drastic measures on increase of efficiency of their work. The main efforts today aimed at improving the methods of recognition and control of their technical condition. In other words, the problems of increasing the reliability of work and the safety of service brought to the fore quite justifiably. In the article, it is propos to carry out monitoring of the technical condition of overhead lines with a rated voltage of 110 kV and above monthly on the basis operational reliability parameters. New methods and algorithms for their estimation, comparison and ranking presented. As the operational reliability parameters are multidimensional, the existing methods for comparing and ranking one-dimensional statistical estimates for them are unacceptable, as the neglect preconditions of these methods conducts to essential growth of risk of the erroneous decision. The proposed new methods based on the fiducial approach, imitating modeling and the theory of statistical hypothesis testing. The cumbersomeness and laboriousness of manual calculation of operational reliability parameters, the science intensity of calculation methods is compensated by the transition to automated systems that provide information and methodological support with information about the technical condition of overhead lines. The recommended methods are included in the group of risk-focused approaches of increase the efficiency of the electric power systems.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-186-196  

 

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Aminu Suleiman Mohammed, Fidelis Ifeanyi Ugwuowo

On Transmuted Exponential-Topp Leon Distribution with Monotonic and Non-Monotonic Hazard Rates and its Applications

 

For the last decade, inspired by the increasing demand for probability distributions in numerous fields, many generalized distributions have been studied. Most of these distributions are developed by adding one or more parameter(s) to the standard probability distributions to make them flexible in capturing the sensitive parts of a dataset. The Topp-Leone distribution (TL) is one of the continuous probability distributions used in modelling lifetime datasets and sometimes is called J-shaped distribution. In this paper, we proposed a new lifetime distribution named transmuted Exponential- Topp Leon distribution in short (TE-TLD) which possessed different density shapes. Some properties of the distribution were presented in an explicit form and the parameters of the distribution are estimated by the method of maximum likelihood. The hazard function of the TE-TLD can be monotonic or non-monotonic failure rate which makes it more robust in terms of studying failure rates. The TE-TLD outperformed other distributions with the same underlying baseline distribution when applied to real datasets in the study. Furthermore, the likelihood ratio test (LRT) shows that the additional parameter(s) are significant which further proves the robustness of the TE-TLD over the nested distributions in the study.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-197-209

 

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S. Sunitha Devi, T. Satyanarayana, K. L. Sai Prasad

Curvature Tensors In SP-Kenmotsu Manifolds With Respect To Quarter-Symmetric Metric Connection

 

A conformal curvature tensor and con-circular curvature tensor in an SP-Kenmotsu manifold are derived in this article which admits a quarter-symmetric metric connection. Conclusively, we verified our results by considering a case of 3-D SP-Kenmotsu manifold.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-210-218

 

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Chanchal, Renu Singh, Deepika Garg, Ajay Kumar

Twin-Piston Pressure Balance For Measurement And Uncertainty Evaluation Of Differential Pressure Digital Transducer

 

Pressure measurement plays significant role in development of various instruments and in industry. Pressure measurement, its control and accuracy are always attraction of scientist. There are many devices for the pressure measurement like U-tube manometer, Bourdon tube/Dial gauge, Dead weight tester. The present study focused on the precise generation of differential pressures with static pressure range in 0 MPa to 50 MPa using twin pressure balance in hydraulic mode. The metrological characteristics of a differential pressure digital transducer were evaluated.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-219-225

 

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P. Vijaya Laxmi, Andwilile Abrahamu George and E. Girija Bhavani

Performance of a Single Server Batch Queueing Model with Second Optional Service under Transient and Steady State Domain

 

The aim of this paper is to investigate the performance of a single server batch queueing model with second optional service under transient and steady state domain. It is assumed that the customers arrive in groups as per compound Poisson process and the server gives two types of services, First Essential Service (FES), which is mandatory for all arriving customers and Second Optional Service (SOS), which is given to some customers those who request it. Both FES and SOS are provided in batches of maximum  capacity. The transient and steady state probabilities of the model are obtained by using probability generating function and Laplace transform techniques. Finally, some numerical examples are presented to study the effect of the parameters on the system performance measures.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-226-238

 

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Kamlesh Kumar Pandey, Diwakar Shukla

Stratified Remainder Linear Systematic Sampling Based Clustering Model For Loan Risk Detection In Big Data Mining

 

Nowadays, large volumes of data generate by numerous business organizations due to digital communications, web applications, social media, internet of things, cloud and mobile computing. Such has turned the nature of classical data into big data. Loan risk analysis is one of the most importance financial tasks, where financial organizations predict loan risk through customer financial history and behavioral data. Financial institutions face loan risk related issues when they make a loan to a bad customer. As a result, financial institutions divide loan applications into loan risk and non-risk clusters before making a loan for avoiding the loan risk challenges. Clustering approach is a data mining technique that uses data behavior and nature to discover the unexpected loan without any external information. Clustering algorithms face efficiency and effectiveness challenges as a result of the primary characteristics of big data. Sampling is of the data reduction technique that reduces computation time and improves cluster quality, scalability and speed of clustering algorithm. This study suggests a Stratified Remainder linear Systematic Sampling Extension (SRSE) approach for loan risk analysis in big data clustering using a single machine execution. The SRSE sampling plan enhances the effectiveness and efficiency of the clustering algorithm by employing maximum variance stratum formulation, remainder linear systematic sampling and extending sampling results into final result through centroid distance metric. The performance of the SRSE-based clustering algorithm has been compared to existing K-means and K-means++ algorithms using Davies Bouldin score, Silhouette coefficient, SD Validity, Ray-Turi index and CPU time validation metric on risk datasets.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-239-257

 

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Endalew Ayenew Hailez, Getachew Biru Worku, Asrat Mulatu Beyene, and Milkias Berhanu Tuka

Investigation of Effects of Uncertain Weather Conditions on the Power Generation Ability of Wind Turbines

 

Wind energy is one of the abundant and renewable energy sources that can be harvested using wind turbines. Many factors affect the energy-yielding ability of wind turbines. The goal of this paper is to investigate the effects of uncertain weather conditions on the power generation ability of wind turbines. Uniquely, it presented the influence of the uncertain weather conditions and uncertain aerodynamic parameters of wind turbine on wind energy harvesting. The mathematical model of these factors and statistical analysis of their effects on the performance of wind turbines are presented using real-time data. It is found that the impact of uncertain weather conditions on annual average air density, and hence on the performance of wind turbines, is 1.33%. Whereas, the impact of variations of yearly average wind speed on the performance of wind turbines is found to be substantial. In particular, the annual uncertainty output power of wind turbines is found to be 32%. This investigation helps to find the mitigation mechanism and improve power generation efficiency from wind.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-258-274

 

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Pulak Swain, Subarna Bhattacharjee, Satya Kr. Misra

A Case Study to Analyze Ageing Phenomenon in Reliability Theory

 

Hazard rate, and ageing intensity (AI) are measures or functions required for qualitative and quantitative analysis of ageing phenomena of a system with a well-defined statistical distribution respectively. In this paper, we reiterate upon the fact that in a few cases hazard rate and ageing intensity do not depict the same pattern as far as monotonicity is concerned. So, a question naturally arises which among hazard rate, and ageing intensity is a preferable measure for characterizing ageing phenomena of a system. As a consequence, an example involving two design systems are analyzed and is illustrated to answer the aforementioned question.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-275-285

 

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Chacko V M

On Joint Importance Measures For Multistate Reliability Systems

 

The use of importance and joint importance measures to identify the weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system, is explained by several researchers in system engineering. But a few research outputs are available in literature for finding joint importance measures for two or more components. This paper introduces, new Joint Reliability Achievement Worth (JRAW), Joint Reliability Reduction Worth (JRRW) and Joint Reliability Fussell-Vesely measure (JRFV) for two components, of a multistate system. This is a new approach to find out the joint effect of group of components in improving system reliability. A steady state performance level distribution with restriction to the component’s states is used to evaluate the proposed measures. Universal generating function (UGF) technique is applied for the evaluation of proposed joint importance measures. An illustrative example is provided.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-286-293

 

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Jeena Joseph, Asisha A P

Power - Exponential Geometric Quantile Function

 

In this article, we introduced a new quantile function which is the sum of quantile functions of Power and Exponential geometric distributions. Different distributional charactaristics and reliability properties are discussed and also simulation study is conducted by using R software. Finally the new model is applied to a real data set.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-294-307

 

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Vijayaraghavan R, Saranya C R, Sathya Narayana Sharma K

Reliability Single Sampling Plans Under The Assumption Of Burr Type Xii Distribution

 

Acceptance sampling or sampling inspection is an essential quality control technique which describes the rules and procedures for making decisions about the acceptance or rejection of a batch of commodities by the inspection of one or more samples. When quality of an item is evaluated based on the life time of the item, which can be adequately described by a continuous-type probability distribution, the plan is known as life test sampling plan. The application of Burr (XII) distribution in reliability sampling plans is considered in this article. A procedure for selection of the plan parameters to protect the both producer as well as the consumer indexed by the acceptable mean life and operating ratio is evolved. Application of proposed plan is discussed with the help of numerical illustrations. Evaluation of such plans is explained utilising a set of simulated observations from Burr (XII) distribution.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-308-322

 

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Indira Singuluri, N. Ravishankar

A Novel Transportation Approach To Solving Type - 2 Triangular Intuitionistic Fuzzy Transportation Problems

 

In this article we propose a new transportation strategy to achieve an ideal answer for triangular intuitionistic fuzzy transportation problem of type – 2 i.e., limits and requests are considered as real numbers and the transportation cost from cause to objective is considered as triangular intuitionistic fuzzy numbers as product cost per unit. The proposed method is solving by using ranking function. The appropriate response system is delineated with a numerical model.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-323-330

 

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N. W. Andure (Yawale), R. B. Ade

The New Length Biased Quasi Lindley Distribution And Its Applications

 

In this paper, Length biased Quasi Lindley (LBQL) distribution is proposed. The different properties of the proposed distribution are derived and discussed. The parameters of the proposed distribution are estimated by using method of maximum likelihood estimation and also the Fisher’s Information matrix is obtained. The performance of the proposed distribution is studied using real-life data sets.

 

 

DOI: https://doi.org/10.24412/1932-2321-2021-465-331-345

 

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Sridevi Ravada, Sudheer Gopinathan, D. Lalitha Bhaskari

Identification Of Spatial Relations In Mathematical Expressions