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Pradeep Chaudhary, Anika Sharma, Rakesh Gupta
The paper deals with the stochastic analysis of two non-identical units (unit-1 and unit-2). Initially, one unit is operative and other is kept into warm standby. Each unit of the system has two possible modes-Normal (N) and Total Failure (F). A single repairman is always available with the system to repair a failed unit. The operative unit is non-repairable, hence upon failure it goes for replacement. The system failure occurs when both the units are in total failure mode. Failure and repair times of a unit are taken as independent random variables of discrete nature having geometric distributions with different parameters.
DOI: https://doi.org/10.24412/1932-2321-2022-268-21-30
Irina Gadolina, Alexei Erpalov, Nelly Dinyaeva Random Processes Imitation in Fatigue Studies
Modelling random processes traditionally supposes working with the spectral density. Although many engineering problems require the knowledge of spectral density, the specific character of fatigue damage accumulation dictates the different approach – namely, the consideration of the distribution of random values of the local extremes, which is responsible for fatigue damage accumulation. There is a need in developing the methods of random loading imitation in the experimental and numerical study of fatigue. According to the up-to-date situation in science in fatigue, both opposing approaches should be considered - the time domain and the frequency domain. The proposed method, which consists of two stages, meets that requirement. The performed case study based on laboratory fatigue testing confirms its applicability.
DOI: https://doi.org/10.24412/1932-2321-2022-268-31-37
Ch. Ganapathi Swamy, K. Srinivasa Rao
Human Resource Management and other companies rely heavily on manpower models. Manpower planning was a prerequisite for effective organization administration. The construction and analysis of two graded manpower models with direct Duane recruiting processes in both graduates is the subject of this paper. Duane's recruitment procedure was capable of identifying time-dependent recruitments. Poisson and non-homogeneous Poisson processes are used in the Duane recruitment process as precise instances for specified parameter values. It is assumed that the organization has two grades and that the recruitment procedure is based on the Duane Process. The processes of leaving and promotion are Poisson processes. The model's transient behavior was investigated by deriving unambiguous expressions for system characteristics such as the mean number of employees in each grade, the mean durational stay of an employee in each grade, and the variance of number of employees in each grade using differential equations. The model's sensitivity analysis of parameters shows that the Duane recruiting process has a substantial impact on system performance indicators. It was also noted that this model incorporates rates of recruitment that are increasing, decreasing, or stable. This model proved helpful in analyzing organizational manpower issues.
DOI: https://doi.org/10.24412/1932-2321-2022-268-38-55
Neetu Dabas, Reetu Rathee Parallel System Analysis with Priority and Inspection Using Semi-Markov Approach
In this paper a parallel system has been discussed with the idea of priority to preventive maintenance over replacement. The system has two identical units and facility of inspection is given to the failed unit before repair/replacement. There is a single server who play four-in-one role of inspection, replacement, repair and preventive maintenance and comes immediately when required. Units are failed with constant rate whereas failure time is random. The distribution of time for repair activities is arbitrary and there rates follow exponential distribution. The random variable associate with different rates are stochastically independent. Mathematical expression for several reliability terms like MTSF, availability, busy period analysis for server , expected number of visits by the server and cost benefit are obtained by using semi-markov process and regenerative point technique. Graphs are drawn to find the effect of various parameters on MTSF, Availability and profit.
DOI: https://doi.org/10.24412/1932-2321-2022-268-56-66
Indira Singuluri, N. Ravishankar, CH. Uma Swetha AN UNIQUE OPTIMAL SOLUTION FOR TYPE – III TRIANGULAR INTUITIONSTIC FUZZY TRANSPORTATION ISSUE
In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which availability, demand and costs are mixed terms of real, triangular intuitionistic fuzzy numbers. In this paper, a simple method for solving type-3 intuitionistic fuzzy transportation is applied. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of numerical examples.
DOI: https://doi.org/10.24412/1932-2321-2022-268-67-73
Sunday Adeyeye, Ademola Adewara, Emmanuela Akarawak, Adeyinka Ogunsanya, Alabbasi Jamal ZECH DISTRIBUTION: DERIVATION, PROPERTIES AND APPLICATIONS TO REAL LIFE DATA
The roles of heavy – tailed distribution in modelling real life events, especially in financial and actuarial sciences, cannot be over – emphasized. In this paper, a new heavy right – tailed, three – parameter continuous distribution with increasing hazard rate called Zech distribution is developed. The proposed model is very suitable for modelling heavy right- tailed data. Zech distribution is the reciprocal of the random variable which follows Gompertz- Inverse – Exponential (GoIE) distribution and it does not involve addition of extra parameter, thereby removing the cumbersomeness in the estimation process posed by other methods involving additional extra parameters, especially where more than three parameters are involved. The statistical properties of the new distribution such as survival function, hazard function, cumulative hazard function, reversed hazard function, quantile function, order statistics, moments, mean, median, variance, skewness, and kurtosis were derived. The Linear representation of the pdf of the newly developed distribution revealed that its probability density function is a weighted exponential distribution. Also, method of maximum likelihood was used in estimating the model’s parameters. The simulation results revealed that as the sample sizes increased, the root mean squared errors decreased which showed that the parameters of Zech distribution are stable. The proposed distribution was applied to two real life data sets. The results showed that Zech distribution performs better than Gompertz Inverse Exponential distribution, Weibull Exponential distribution and Gompertz Exponential distribution.
DOI: https://doi.org/10.24412/1932-2321-2022-268-74-88
Kaushik A Joshi, Kirankumar L. Bondar, Pandit U. Chopade A New Effective Approach to Solve Fuzzy Transportation Problems
In this article, we will take a look at FTP, and then present a way to solve many such problems by using the affected method for FN level. Some of the numbers in FTP may be sharp or sharp numbers. In many decision-making problems, numbers are represented in terms of FN. FN can be normal or oblique, triangular or trapezoidal or any other FN LR. So, some FNs do not compare immediately. First, we convert QF such as price, quantity, supply and demand, into accurate quantities by using our system, and then using sophisticated algorithms, we solve and solve the problem. The new system is a configuration, easy to install and can be used for all types of TP, or to increase or decrease the target function. In the end, this process is illustrated by digital examples.
DOI: https://doi.org/10.24412/1932-2321-2022-268-89-97
N. W. Andure (Yawale), R. B. Ade THE LENGTH BIASED NEW QUASI LINDLEY DISTRIBUTION: STATISTICAL PROPERTIES AND APPLICATION
In this paper, a new distribution namely the length biased new quasi-Lindley distribution is proposed with the different weight function. The different mathematical and statistical properties of the proposed distribution are derived and discussed. The survival function, hazard rate function and mean residual life function for the length biased new quasi Lindley distribution is discussed. Also, concepts like stochastic ordering and entropy for proposed distribution are studied. The parameters of the proposed distribution are estimated by using the method of maximum likelihood estimation. The performance of the newly introduced distribution is studied using a real- life data set.
DOI: https://doi.org/10.24412/1932-2321-2022-268-98-110
Rama Shanker, Kamlesh Kumar Shukla POWER WEIGHTED AKASH DISTRIBUTION WITH PROPERTIES AND APPLICATIONS
In In this paper power weighted Akash distribution (PWAD) which includes weighted Akash distribution (WAD), power Akash distribution (PAD) and Akash distribution as particular cases has been proposed and investigated. Its moments, hazard rate function and mean residual life function have been discussed. Method of maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Applications of the proposed distribution to two real lifetime datasets have been presented and compared with other one parameter, two-parameter and three-parameter well-known lifetime distributions.
DOI: https://doi.org/10.24412/1932-2321-2022-268-111-126
Dr. K. Srinivasa Rao, Dr. U. V. Adinarayana Rao
Combined-numeral nonlinearity coding problem (CNNLCP) troubles concerning usual restrictions and empirical roles and constant then numeral variable quantity frequently appear in a production project, substance method business, and organization. Even though several optimize techniques need to be established for CNNLCP troubles, these techniques can hold signal relationships together with a particular variable quantity. Thus, this analysis intends a different approach used to explain a signal CNNLCP trouble and set free variable amount towards achieving an internationally optimum explanation. The signal CNNLCP trouble is initially converted into an individual with one certain variable quantity. However, the changed trouble is redeveloped as a curving combined-numeral system as the Convexness of the approaches and piecewise linearization systems. A comprehensive optimal signal CNNLCP trouble can ultimately be realized inside the acceptable inaccuracy. Algebraic models are also introduced to establish the effectiveness of the recommended approach.
DOI: https://doi.org/10.24412/1932-2321-2022-268-127-135
R. Vijayaraghavan, A. Pavithra SELECTION OF SINGLE SAMPLING PLANS BY VARIABLES BASED ON GENERALIZED BETA DISTRIBUTION
Statistical quality control (SQC) has wider applications in industries and production engineering. Product control, one of the two major categories of SQC, consists in procedures by which decisions are made on the disposition of one or more lots of finished items or materials produced by manufacturing industries. Sampling inspection by variables in product is the methodology that is employed for deciding about the disposition of a lot of individual units based on the observed measurements on a quality characteristic of randomly sampled units from the lot submitted for inspection. These procedures are defined under the assumption that the quality characteristic is measurable on a continuous scale and the functional form of the probability distribution must be known. Inspection procedures which have been developed based on the implicit assumption that the quality characteristic is distributed as normal with the related properties are found in the literature of sampling inspection procedures. The assumption of normality may not be realized often in practice and it becomes inevitable to investigate the properties of variable sampling plans based on non-normal distributions. In this paper a single sampling plan by variables is formulated and evaluated under the assumption that the quality characteristic is distributed according to a generalized beta distribution of first kind. Procedures are developed for determining the parameters of the proposed plan for specified requirements in terms of producer’s and consumer’s protection.
DOI: https://doi.org/10.24412/1932-2321-2022-268-136-150
Anas Sani Maihulla, Ibrahim Yusuf RELIABILITY ANALYSIS OF REVERSE OSMOSIS FILTRATION SYSTEM USING COPULA
In this study, the reliability metrics used to assess the strength of a three-subsystem reverse osmosis filtering system. The subsystems include sand filter, carbonated filter, and precision filter. Each subsystem is composed of active components that can operate in series parallel. The system of partial differential equations was built using the mnemonic rule and analytically solved. Other reliability variables that were investigated for determining system strength included availability, reliability, mean time to failure (MTTF), profit analysis, and sensitivity analysis. The Maple software was used to obtain numerical solutions. In addition, a graphical representation of the numerical results was provided to demonstrate the behaviors of reliability characteristics with regard to time and failure rate. The study could assist water treatment firms and their repairers in overcoming some of the challenges faced by repairers of specialized manufacturing and industrial systems working in harsh settings or contaminated environments unfit for human consumption.
DOI: https://doi.org/10.24412/1932-2321-2022-268-163-177
Deepika Garg, Arun Kumar, Vimal Kumar Joshi, Nahid Fatima SENSITIVITY ANALYSIS OF A UREA FERTILIZER PLANT
Purpose – This paper presents a sensitivity analysis of a urea fertilizer manufacturing system comprising several sub-systems of differing nature. Design/methodology/approach–A mathematical model is developed for the consistent general repair and disappointment rates for every subsystem. The framework is analyzed by utilizing regenerative point graphical technique; as a result, some recommendations are made for the optimized output. A state transition diagram of the system is developed to find mean time to busy period server, system failure and system availability. Findings – The present study suggests an approach to improve the system performance. The analysis and results outlined in this paper are useful to system managers, training supervisor, engineers and reliability analysts in the manufacturing industry. Originality/ value – The manufacturing system of Urea fertilizer consists of a complex structure with the high risk of machine failure. Machine/ Production failure leads to high risks of economic & environmental loss and worker’s safety. To address this challenge effectively, sensitivity analysis of the urea fertilizer plant is discussed for minimizing the risk of machine failure.
DOI: https://doi.org/10.24412/1932-2321-2022-268-178-189
Sheema Sadia, Qazi Mazhar Ali, Zainab Asim, Ahteshamul Haq Fractional Multi-objective Capacitated Transportation Problem with Different Membership Functions
This Fractional Transportation Problem arises when an enterprise has to face the issue of maintaining a good ratio of some critical parameters. These parameters are directly concerned with product(s) transportation from sources to destination. This paper considers a multi-objective Capacitated Transportation Problem with Fractional Objectives. A fuzzy goal programming approach with different membership functions is applied to generate a different set of solutions. We also use Chebyshev’s Goal Programming for obtaining the solutions. Finally, a numerical illustration is provided to validate our proposed model.
DOI: https://doi.org/10.24412/1932-2321-2022-268-190-198
Akanksha Mishra, G. V. Nagesh Kumar, D. Deepak Chowdary, B. Sravana Kumar
Gas Insulated Substation (GIS) is essential for the transmission and control of power both in AC and DC electrical systems. Functionally Graded Material (FGM) technology is widely used for the design of the spacer material in the GIS to reduce the electric stress in the system. Optimal designing of the material of the spacer gradings with a particular attention to the number of gradings may prove to be very useful in reduction of the stress in the GIS at an effective cost. This paper deals with the design and development of an optimal dielectric material for the functionally graded material (FGM) spacer in a GIS. A novel optimization method has been proposed which is used for the optimization of the conductor material and the FGM epoxy spacer. The optimal value for each grading of functionally graded material spacer is determined by the proposed method. A dual-objective function is chosen for the optimization problem. The objective of the problem is to minimize the maximum field stress in addition to the standard deviation in the electric field. A post type spacer has been considered for the study. Initially, the optimization of the dielectric material is done only for 4 gradings. Gradually, the number of gradings in the FGM-spacer is increased to determine the optimal number of gradings suitable for the design.
DOI: https://doi.org/10.24412/1932-2321-2022-268-199-216
Sarla More, Diwakar Shukla
Consider a multi-processors computer system consisting of a ready queue of different jobs to be executed/processed. Lottery scheduling is fair enough to schedule the resources for each and every job. The research idea assumes condition where one can observe some processes to be fully executed; some partially executed few blocked/suspended/ terminated, after sudden system breakdown. An estimation strategy has been designed for the estimation of the total time required to process all these types of processes (processed, partially processed and blocked processes). How much time is required to process the remaining in any hazardous situation? A regression type estimator of sampling theory is used to perform this task. This remaining time estimation technique deals with the backup cost and recovery management as well. Sampling techniques are used in proposed approach for the testing purpose and a simulation has been performed. Another tool adopted is the confidence intervals which are calculated and gives proper précised values in comparison to the true mean for the total remaining time. The linear, square root and square cost function model are adopted for the calculation of backup cost and recovery management. In addition some auxiliary information is also incorporated in the form of size measure of the processes which is an effective approach to calculate the complete remaining time of the processes in multiprocessor environment. The purpose of the proposed research has been served effectively as one can observe the results of disaster and recovery management of the computer system.
DOI: https://doi.org/10.24412/1932-2321-2022-268-217-234
Farhadzadeh E.M., Muradaliyev A.Z., Abdullayeva S.A. IMPROVEMENT OF MANAGEMENT METHODS FOR THE OPERATIONAL RELIABILITY OF DISTRIBUTED ENERGY FACILITIES
Improving the management of the technical condition of equipment, devices and installations, the service life of which exceeds the standard value, is one of the most important problems of state security. Today, the relative number of such equipment already exceeds 60%. The results of the analysis of literature data on this problem presented, which confirm its relevance and significance. It is important to note that these findings apply to not only electrical power systems, but many other production systems as well. The main difficulties in solving the analyzed problem, first of all, the paucity of statistical data characterizing the reliability of work, their multidimensional and random nature. The authors propose to solve this problem by moving from average annual reliability indicators to average monthly indicators of operational reliability. A brief description of the solution of individual tasks of this problem for overhead power lines is given, which together represent a new methodology for managing the technical condition of distributed type objects. Science-intensive, cumbersome and labor-intensive calculation algorithms determine the expediency of the transition to intelligent systems. At the same time, the management of the electric power system and its individual production enterprises will monthly receive specialized forms indicating recommendations that optimize the increase in the reliability of overhead power transmission lines by restoring wear and tear.
DOI: https://doi.org/10.24412/1932-2321-2022-268-235-244
R. Vijayaraghavan, A. Pavithra RELIABILITY CRITERIA FOR DESIGNING LIFE TEST SAMPLING INSPECTION PLANS BASED ON LOMAX DISTRIBUTION
Acceptance sampling plays an important role in ensuring the quality of the products manufactured by the industrial production processes. Sampling inspection plans by attributes are adopted for taking decisions about the lots submitted for inspection. Such procedures are employed for sentencing individual lots or batches or lots in continuous stream. Reliability sampling is s specific inspection procedure which is used to decide whether the submitted lot or batch is acceptable or non-acceptable based on life tests. In reliability sampling, the lifetime of the items randomly drawn from the lot is considered as a random variable which follows a continuous probability distribution. In this paper, designing of single sampling plans for life tests is considered under the assumption that the lifetime random variable follows a Lomax distribution. Reliability criteria for designing life test plans when lot quality is evaluated in terms of mean life, median life, hazard rate and reliability life are proposed. Conversion factors for adapting acceptable quality levels to life and reliability testing under the assumption of Lomax distribution are determined and suitable illustrations are provided.
DOI: https://doi.org/10.24412/1932-2321-2022-268-245-258
Adilakshmi Siripurapu, Ravi Shankar Nowpada A NEW RANKING IN HEPTAGONAL FUZZY NUMBER AND ITS APPLICATION IN PROJECT SCHEDULING
Ranking fuzzy numbers is significant in optimization approaches such as assignment challenges, transportation problems, project schedules, artificial intelligence, data analysis, network flow analysis, an uncertain environment in organizational economics etc. This paper introduces a new fuzzy ranking in Heptagonal fuzzy numbers and arithmetic operations of Heptagonal fuzzy numbers defined. In the network, every activity duration is viewed by a Heptagonal fuzzy number. Every Heptagonal fuzzy number is transformed into a crisp number using the ranking function. By applying the traditional method, we calculate the fuzzy critical path. These procedures are illustrated with numerical examples and compared with existing ranking functions.
DOI: https://doi.org/10.24412/1932-2321-2022-268-259-271
Muzamil Jallal, Aijaz Ahmad, Rajnee Tripathi Weibull Inverse Power Rayleigh Distribution with Applications Related to Distinct Fields of Science
In this paper an extension of Weibull Power Rayleigh Distribution has been introduced, and named it is as Weibull Inverse Power Rayleigh Distribution. This distribution is obtained by adopting T-X family technique. Various Structural properties, Reliability measures and Characteristics have been calculated and discussed. The behaviour of Probability density function, Cumulative distribution function, Survival function, Hazard rate function and mean residual function are illustrated through different graphs. Various parameters are estimated through the technique of MLE. The versatility and flexibility of the new distribution is done by using real life data sets. To evaluate and compare the out effectiveness of estimators, a simulation analysis has also been carried out.
DOI: https://doi.org/10.24412/1932-2321-2022-268-272-290
Aakriti Pandey, A. Kaushik, S. K. Singh
In this article, we propose the estimators for the parameters of exponentiated exponential distribution under generalized progressive hybrid censoring scheme obtained through different methods of estimations like maximum likelihood, Maximum product spacing, Bootstrap and Bayesian. Asymptotic confidence, Bootstrap and HPD intervals have also been computed. Moreover, Stress Strength reliability estimation is also discussed. The performance of the estimators have been studied in terms of their MSEs. Bayesian prediction of future observations has also been attempted. For illustrating the proposed methodology, a real data set is taken into account.
DOI: https://doi.org/10.24412/1932-2321-2022-268-291-306
Vishal Pradhan, Gunjan Tripathi, Ajay Kumar, Joydip Dhar RELEASE TIME ANALYSIS OF OPEN SOURCE SOFTWARE USING ENTROPY AND RELIABILITY
Any software system, however securely written or precise the code is, is always susceptible to failure. These factors, such as the number of errors in the program or the mean-time for software failure, measure the program’s reliability. In order to meet more customer needs, current OSS products must be reliable. To measure these parameters, like the reliability of the software, we use different growth models called Software Reliability Growth Models. These models help us in determining the different reliability measures. Faults occur due to several reasons in software- sometimes, it is the environmental factors. It can also be because of casual human behavior. Faults may also occur during the process of removal of previous faults. Whenever the code is changed, randomness in the software increases. We can calculate the optimal release time of a software product based on the calculated reliability measures, which have entropy also been considered. Finally, the user’s satisfaction level can also be considered.
DOI: https://doi.org/10.24412/1932-2321-2022-268-307-316
Upasana Sharma, Rajveer Kaur Performance Analysis of System where Service Type for Boiler Depends Upon Major or Minor Failures
In industries, the type of failure sensitively affects the system. So, it is essential to Categorize these failures into different categories to enhance the system performance. In this research, concentration made in differentiating the failure type into major/minor categories with repair/replacement facility for the service by single repairman. Currently, we studied the boiler system of the steam generation plant to perform the task of repair/replacement with a single repairman. A reliability model constructs to compute MTSF(mean time to system failure), availability, Busy period for repair/replacement, and profit evaluation. The above measures were estimated numerically and plotted graphically using semi-Markov processes and regenerative point technique. Various effectiveness measures show how system performance gets affected by major/minor failures & the type of service provided.
DOI: https://doi.org/10.24412/1932-2321-2022-268-317-325
Vivek Kumar Gupta, Diwakar Shukla
In recent past, Online Social Networks (OSN) has emerged as a platform for sharing information, thoughts, and activities. In the real-world network, method of considering the appropriate samples is most frequently used for network analysis. Graph sampling is a procedure used for computing unknown parameters. Many sampling algorithms exist in literature such as Random node, Random edge sampling, Rank degree, etc. can be used for estimation. This paper presents a comparison of clique based procedure (CBP) and shortest path based procedure (SPP) to estimate the average degree of a vertex in a social network using an overlapping cluster sampling. A comparative procedure is used to obtain the lower and upper limit of confidence intervals with the help of multiple samples. Ogive based simulation is also used for single value computation of limits of CI. The results, obtained from simulation, show that clique based sampling algorithm (CBP) is more efficient than the shortest path based sampling algorithm (SPP). The estimated confidence intervals can be used for monitoring the reliability of a social network in terms of control over average network degree.
DOI: https://doi.org/10.24412/1932-2321-2022-268-326-339
Aijaz Ahmad, Mujamil Jallal, I. H. Dar, Rajnee Tripathi
The objective of this study is to develop an extension of the Burr-III distribution which is achieved by adopting the inverse Weibull-G family of distribution and is referred as inverse Weibull-Burr III distribution (IWB-III) to evaluate complicated data. Different structural characteristics of the suggested distribution have been determined and analysed. Distinct plots depict the behaviour of the probability density function (pdf) and the cumulative distribution function (cdf). The maximum likelihood estimation method is applied to estimate the stated distribution parameters. To assess and investigate the efficacy of estimators in terms of bias, variance, and mean square error (MSE), a simulation study was conducted. Lastly, the effectiveness of the stated distribution is proven by an actual data set relevant to survival rates in animals.
DOI: https://doi.org/10.24412/1932-2321-2022-268-340-355
Upasana Sharma, Avtar Singh Reliability and Economic Analysis of Captive Power Plant With Reduced Capacity
This paper reported the performance evaluation of Captive Power plant working in the fertilizer industry with possible production capacities. The idea of reduced capacity and load sharing to use the available system optimally is analyzed. The system works on two STG’s (steam turbine generators) and one gridline. Gridline can bear the load of one or both STG’s on failures. At the breakdown in gridline and STG, the system work at reduced capacity. Gridline repaired on a priority basis. The semi-Markov processses and regenerative point technique are used to evaluate the reliability and economic measures such as availability, busy period of repairman, and expected no. of repairs. The graphical study shows the relationships between these measures with the failure rates of STG and gridline.
DOI: https://doi.org/10.24412/1932-2321-2022-268-356-366
G. Ayyappan, S. Sankeetha
The paper considers a single server that provides consumers with both regular and optional services. The system’s inter-arrival time is determined by a Markovian Arrival Process (MAP), the service time is determined by a phase type distribution, and the remaining random variables are distributed exponentially. This system was represented as a QBD process, with the block elements of the generated matrix having finite dimensions, to investigate steady state. Additionally, we addressed the busy period and waiting time distribution for our concept. The system’s performance parameters are calculated and graphically shown.
DOI: https://doi.org/10.24412/1932-2321-2022-268-367-386
C. Satheesh Kumar, G. V. Anila On a Wide Plurimodal Class of Distributions Suitable for Asymmetric Data Sets
Asymmetric normal distributions have received much attention in the literature during the last three decades. But, plurimodal asymmetric normal distributions are not much studied in the literature even though it has much relevance in practical situations. Here we propose a new class of plurimodal, asymmetric normal distribution and investigate its several statistical properties, including certain reliability aspects. A location-scale extension of the proposed model is developed and studied their properties. The maximum likelihood estimation method is employed for estimating the parameters of the proposed extended class of distributions and conducted generalized likelihood ratio test procedure for testing the parameters of the distribution. Three real-life data sets are considered for illustrating the usefulness of the model and a brief simulation study is carried out for examining the performance of maximum likelihood estimators of the proposed model.
DOI: https://doi.org/10.24412/1932-2321-2022-268-387-402
Shanti Parkash, P.C. Tewari PERFORMANCE MODELING AND DSS FOR ASSEMBLY LINE SYSTEM OF LEAF SPRING MANUFACTURING PLANT
This work deals with the Performance Modelling and purposed the Decision Support System (DSS) for maintenance priorities of an assembly line system using a probabilistic approach. This system consists of four subsystems i.e. Shot Peening, Painting Machine, Assembly Platform and Riveting Machine. Performance modelling among various subsystems has been done by Markovian approach. Steady state probabilities are determined by drawing transition diagram and solving the differential equations. Decision matrices are formed with the help of different combinations of failure and repair rates of all the subsystems. The key finding of this work is that painting machine is the most critical subsystem.
DOI: https://doi.org/10.24412/1932-2321-2022-268-403-412
S. Sunitha Devi, K. L. Sai Prasad, T. Satyanarayana CERTAIN CURVATURE CONDITIONS ON LORENTZIAN PARA-KENMOTSU MANIFOLDS
We classify Lorentzian para-Kenmotsu manifolds which satisfy the curvature conditions W2.C = 0, Z.C = LCQ(g, C), W2.Z − Z.W2 = 0 and W2.Z + Z.W2 = 0, where W2 is the Weyl- projective tensor, Z is the concircular tensor, and C is the Weyl conformal curvature tensor. We study and have shown that the manifold M is η-Einstein provided that the Weyl-projective curvature tensor W2 meets the condition W2.Z − Z.W2 = 0, and it is an Einstein manifold if W2.Z + Z.W2 = 0. Finally, in this article, we derive the conditions in relation to conformally flatness of the manifold, whenever the LP-Kenmotsu manifold satisfies the condition Z.C = LCQ(g, C).
DOI: https://doi.org/10.24412/1932-2321-2022-268-413-421
Shazia Farhin, Firdoos Yousuf and Athar Ali Khan
The purpose of this paper is to fit the Marshall-Olkin generalized-G(MOG-G) family to censored survival data with random effect in the Bayesian environment. Three special distrbution based on MOG-G family are obtained, namely Marshall-Olkin generalized-exponential, Marshall-Olkin generalized-Weibull, and Marshall-Olkin generalized-Lomax. The probabilistic programming language STAN is used for the fitting of these three distrbution to the survival data. STAN offers full Bayesian inference and implements via Hamiltonian Monte Carlo algorithm and No-U-Turn Sampler(NUTS) algorithm of MCMC. We compared the models with the help of leave one out cross-validation information criteria and Watanabe Akaike information criteria. Stan codes for the analysis are provided.
DOI: https://doi.org/10.24412/1932-2321-2022-268-422-440
Valentin Vankov Iliev On the Use of Entropy as a Measure of Dependence of Two Events. Part 2
The joint experiment J(A,B) of two binary trials A [ Ac and B [ Bc in a probability space can be produced not only by the ordered pair (A, B) but by a set consisting, in general, of 24 ordered pairs of events (named Yule’s pairs). The probabilities x1, x2, x3, x4 of the four results of J(A,B) are linear functions in three variables a = Pr(A), b = Pr(B), q = Pr(A \ B), and constitute a probability distribution. The symmetric group S4 of degree four has an exact representation in the affine group Aff(3,R), which is constructed by using the types of the form [a, b, q] of those 24 Yule’s pairs. The corresponding action of S4 permutes the components of the probability distribution (x1, x2, x3, x4), and, in particular, its entropy function is S4-invariant. The function of degree of dependence of two events, defined in the first part of this paper via modifying the entropy function, turns out to be a relative invariant of the dihedral group of order 8.
DOI: https://doi.org/10.24412/1932-2321-2022-268-441-446
G. Ayyappan, G. Archana Gurulakshmi, B. Somasundaram
The purpose of this paper is to analyse a single server queueing model with multiple vacations, optional service, close-down, setup, balking, breakdown and repair under the assumption that the customers arrive according to a Markovian Arrival Process (MAP). The service and repair times follow the phase-type distributions. At the completion of service, in case there are no customers in the system, the server closes down the system and goes for vacation. After completion of the vacation, the server has to start the setup process if a minimum of one customer is present in the system or else the server goes for another vacation. The server provides optional service to the customers those who are in need of additional services. By employing the matrix analytic method, the stationary probability vector has been evaluated. The stability condition, busy period analysis, distribution function for waiting time and some of the system performance measures concerning this model are derived. The outcome arising out of numerical values and graphical representations are also presented for this model.
DOI: https://doi.org/10.24412/1932-2321-2022-268-447-468
Amit Manocha, Anil Kumar Taneja, Gulshan Lal Taneja
This paper examines the stochastic behavior of standby redundant system having two non-identical units. The system comprised of main unit and non-identical cold standby unit. When the main unit collapses, standby unit is exposed to operable conditions. Due to long-time and non-use of standby unit, though with small chances, it is observed that standby unit gets corrupt and becomes inoperable even in standby mode. Further, it demands repair/maintenance to make it worth-operating. Henceforth, it is considered to perform random inspection of standby unit to ensure that whether it is in operable condition or not. Inspection as well as repair both the tasks are performed by single repair facility. semi-Markov and regenerative processes are applied to derive expressions for the system performance indices. Profit function and bounds (upper/lower) for various costs involved are evaluated. Numerical study has been performed to illustrate the behavior of model developed. Sensitivity and relative sensitivity analysis has also been done for MTSF and steady-state availability.
DOI: https://doi.org/10.24412/1932-2321-2022-268-469-481
Rajitha C.S., Ashly Regi THE NEGATIVE BINOMIAL-AKASH DISTRIBUTION AND ITS APPLICATIONS
A new two-parameter negative binomial mixture distribution named as negative binomial-Akash distribution is introduced in this paper. The proposed distribution is attained by compounding the negative binomial distribution with the Akash distribution. Some of its special characteristics are also derived, including factorial moments, mean, variance, index of dispersion etc. Furthermore, the behaviour of mean, variance and index of dispersion are discussed. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method. This distribution can be used for modeling overdispersed count data. The usefulness and application of the proposed distribution are illustrated using two actual count data sets.
DOI: https://doi.org/10.24412/1932-2321-2022-268-482-491
A. S. Mohammed, F. I. Ugwuowo, T. S. Patrice, H. Muhammad Generalized Transmuted Exponential-Exponential Distribution and its Applications
Modeling of datasets requires knowledge of their appropriate distributional assumptions. In this research, we generalized the transmuted exponential-exponential distribution, and it was observed that the addition of the shape parameter to the model proved to be helpful in improving the flexibility of the model. Different characteristics, as well as structural properties of the model, were investigated and presented in an explicit form. The probability density function of the order statistics and numerical results for some descriptive statistics were obtained. A 95% confidence interval and interval widths, together with biases and mean square errors (MSEs) of the mean estimates, were equally evaluated using the Monte-Carlo simulation approach. To validate the flexibility of the model, we used real datasets and the generalized transmuted exponential-exponential distribution (GTE-ED) outperformed the competing distributions.
DOI: https://doi.org/10.24412/1932-2321-2022-268-492-506
P. Vijaya Laxmi, Hasan A.B.D. Qrewi, Andwilile A. George WITH FEEDBACK AND SECOND OPTIONAL SERVICE
The aim of this paper is to analyze a single server batch service queue model with feedback and second optional service under a transient and steady state environment. The server provides the first essential service (FES) to all customers who arrive at the system and the second optional service (SOS) to those who need it. After completion of FES, if the customer is not satisfied with the service, he may rejoin the queue or may opt for SOS or exit the system with a particular probability. The service times of both FES and SOS follow exponential distribution. We use the probability generating function and the Laplace transform expression to obtain probabilities in the transient state after inverting Laplace transforms into the time domain. Also, we apply the Tauberian property in the Laplace transform expression to get the steady state probabilities. Finally, some performance measures and numerical results are provided.
DOI: https://doi.org/10.24412/1932-2321-2022-268-507-518
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Safety Research :
Safety, Risk, Reliability and Quality:
Statistic, Probability and Uncertainty :
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