This document summarizes a research article that analyzes the performance of a sugar mill feeding system using Markov process modeling. The feeding system has four subsystems: a cutting system, crushing system, bagasse carrying system, and heat generating system. The researchers model the system's states using a time-homogeneous Markov process to determine the reliability function and steady-state availability. They then use genetic algorithm optimization to determine optimal system design parameters that maximize availability. The methodology section outlines the assumptions made and describes how Markov modeling and genetic algorithms are applied to analyze the system and optimize its performance.
Applying the big bang-big crunch metaheuristic to large-sized operational pro...IJECEIAES
In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Neurocomputing is widely implemented in time series area, however the nearness of exceptions that for the most part happen in information time arrangement might be hurtful to the information organize preparing. This is on the grounds that the capacity to consequently discover any examples without earlier suppositions and loss of all-inclusive statement. In principle, the most well-known preparing calculation for Backpropagation calculations inclines toward lessening ordinary least squares estimator (OLS) or all the more particularly, the mean squared error (MSE). In any case, this calculation is not completely hearty when exceptions exist in preparing information, and it will prompt false estimate future esteem. Along these lines, in this paper, we show another calculation that control calculations firefly on slightest middle squares estimator (FFA-LMedS) for BFGS quasi-newton backpropagation neural network nonlinear autoregressive moving (BPNN-NARMA) model to lessen the effect of exceptions in time arrangement information. In the in the mean time, the monthly data of Malaysian Roof Materials cost index from January 1980 to December 2012 (base year 1980=100) with various level of exceptions issue is adjusted in this examination. Toward the finish of this paper, it was found that the upgraded BPNN-NARMA models utilizing FFA-LMedS performed extremely well with RMSE values just about zero errors. It is expected that the finding would help the specialists in Malaysian development activities to handle cost indices data accordingly.
Optimal control in microgrid using multi agent reinforcement learningISA Interchange
This paper presents an improved reinforcement learning method to minimize electricity costs on the premise of satisfying the power balance and generation limit of units in a microgrid with grid- connected mode. Firstly, the microgrid control requirements are analyzed and the objective function of optimal control for microgrid is proposed. Then, a state variable ‘‘Average Electricity Price Trend’’ which is used to express the most possible transitions of the system is developed so as to reduce the complexity and randomicity of the microgrid, and a multi-agent architecture including agents, state variables, action variables and reward function is formulated. Furthermore, dynamic hierarchical reinforcement learning, based on change rate of key state variable, is established to carry out optimal policy exploration. The analysis shows that the proposed method is beneficial to handle the problem of ‘‘curse of dimensionality’’ and speed up learning in the unknown large-scale world. Finally, the simulation results under JADE (Java Agent Development Framework) demonstrate the validity of the presented method in optimal control for a microgrid with grid-connected mode.
Risk Prediction for Production of an EnterpriseEditor IJCATR
Despite all preventive measures, there is so much possibility of risks in any project development as well as in enterprise management. There is no any standard mechanism or methodology available to assess the risks in any project or production management. Using some precautionary steps, the manager can only avoid the risks as much as he can. To address this issue, this paper presents a probabilistic risk assessment model for the production of an enterprise. For this, Multi-Entity Bayesian Network (MEBN) has been used to represent the requirements for production management as well as to assess the risks adherence in production management, where MEBN combines expressivity of first-order logic and probabilistic feature of Bayesian network. Bayesian network provides the feature to represent the probabilistic uncertainty and reasoning about probabilistic knowledge base, which is used here to represent the probable risks behind each causes of a risk. The proposed probabilistic model is discussed with the help of a case study, which is used to predict risks inherent in the production of an enterprise, which depends upon various measures like labour availability, power backup, transport availability etc.
Power System Reliability Assessment in a Complex Restructured Power SystemIJECEIAES
The basic purpose of an electric power system is to supply its consumers with electric energy as parsimoniously as possible and with a sensible degree of continuity and quality. It is expected that the solicitation of power system reliability assessment in bulk power systems will continue to increase in the future especially in the newly deregulated power diligence. This paper presents the research conducted on the three areas of incorporating multi-state generating unit models, evaluating system performance indices and identifying transmission paucities in complex system adequacy assessment. The incentives for electricity market participants to endow in new generation and transmission facilities are highly influenced by the market risk in a complex restructured environment. This paper also presents a procedure to identify transmission deficiencies and remedial modification in the composite generation and transmission system and focused on the application of probabilistic techniques in composite system adequacy assessment
Q-learning vertical handover scheme in two-tier LTE-A networks IJECEIAES
Global mobile communication necessitates improved capacity and proper quality assurance for services. To achieve these requirements, small cells have been deployed intensively by long term evolution (LTE) networks operators beside conventional base station structure to provide customers with better service and capacity coverage. Accomplishment of seamless handover between Macrocell layer (first tier) and Femtocell layer (second tier) is one of the key challenges to attain the QoS requirements. Handover related information gathering becomes very hard in high dense femtocell networks, effective handover decision techniques are important to minimize unnecessary handovers occurred and avoid Ping-Pong effect. In this work, we proposed and implemented an efficient handover decision procedure based on users’ profiles using Q-learning technique in an LTE-A macrocellfemtocell networks. New multi-criterion handover decision parameters are proposed in typical/dense femtocells in microcells environment to estimate the target cell for handover. The proposed handover algorithms are validated using the LTE-Sim simulator under an urban environment. The simulation results showed noteworthy reduction in the average number of handovers.
For years, the Machine Learning community has focused on developing efficient
algorithms that can produce very accurate classifiers. However, it is often much easier
to find several good classifiers based on dataset combination, instead of single classifier
applied on deferent datasets. The advantages of using classifier dataset combinations
instead of a single one are twofold: it helps lowering the computational complexity by
using simpler models, and it can improve the classification accuracy and performance.
Most Data mining applications are based on pattern matching algorithms, thus improving
the performance of the classification has a positive impact on the quality of the overall
data mining task. Since combination strategies proved very useful in improving the
performance, these techniques have become very important in applications such as
Cancer detection, Speech Technology and Natural Language Processing .The aim of this
paper is basically to propose proprietary metric, Normalized Geometric Index (NGI)
based on the latent properties of datasets for improving the accuracy of data mining tasks.
Stochastic behavior analysis of complex repairable industrial systemsISA Interchange
The purpose of this paper is to present a novel technique for analyzing the behavior of an industrial system stochastically by utilizing vague, imprecise, and uncertain data. In the present study two important tools namely Lambda-Tau methodology and particle swarm optimization are combinedly used to present a novel technique named as particle swarm optimization based Lambda-Tau (PSOBLT) for analyzing the behavior of a complex repairable system stochastically up to a desired degree of accuracy. Expressions of reliability indices like failure rate, repair time, mean time between failures (MTBF), expected number of failures (ENOF), reliability and availability for the system are obtained by using Lambda-Tau methodology and particle swarm optimization is used to construct their member- ship function. The interaction among the working units of the system is modeled with the help of Petri nets. The feeding unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. Sensitivity analysis of system’s behavior has also been done. The behavior analysis results computed by PSOBLT technique have a reduced region of prediction in comparison of existing technique region,
i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties.
Reliability, availability, maintainability (RAM) study, on reciprocating comp...John Kingsley
What is needed to perform a RAM Study and more details #RAM #Training #iFluids #RAMstudy
.
To know more, on How iFluids can help you operate & maintain Safe and Reliable plant Contact us Today --> info@ifluids.com
For any training enquiries, contact us today --> training@ifluids.com
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Applying the big bang-big crunch metaheuristic to large-sized operational pro...IJECEIAES
In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Neurocomputing is widely implemented in time series area, however the nearness of exceptions that for the most part happen in information time arrangement might be hurtful to the information organize preparing. This is on the grounds that the capacity to consequently discover any examples without earlier suppositions and loss of all-inclusive statement. In principle, the most well-known preparing calculation for Backpropagation calculations inclines toward lessening ordinary least squares estimator (OLS) or all the more particularly, the mean squared error (MSE). In any case, this calculation is not completely hearty when exceptions exist in preparing information, and it will prompt false estimate future esteem. Along these lines, in this paper, we show another calculation that control calculations firefly on slightest middle squares estimator (FFA-LMedS) for BFGS quasi-newton backpropagation neural network nonlinear autoregressive moving (BPNN-NARMA) model to lessen the effect of exceptions in time arrangement information. In the in the mean time, the monthly data of Malaysian Roof Materials cost index from January 1980 to December 2012 (base year 1980=100) with various level of exceptions issue is adjusted in this examination. Toward the finish of this paper, it was found that the upgraded BPNN-NARMA models utilizing FFA-LMedS performed extremely well with RMSE values just about zero errors. It is expected that the finding would help the specialists in Malaysian development activities to handle cost indices data accordingly.
Optimal control in microgrid using multi agent reinforcement learningISA Interchange
This paper presents an improved reinforcement learning method to minimize electricity costs on the premise of satisfying the power balance and generation limit of units in a microgrid with grid- connected mode. Firstly, the microgrid control requirements are analyzed and the objective function of optimal control for microgrid is proposed. Then, a state variable ‘‘Average Electricity Price Trend’’ which is used to express the most possible transitions of the system is developed so as to reduce the complexity and randomicity of the microgrid, and a multi-agent architecture including agents, state variables, action variables and reward function is formulated. Furthermore, dynamic hierarchical reinforcement learning, based on change rate of key state variable, is established to carry out optimal policy exploration. The analysis shows that the proposed method is beneficial to handle the problem of ‘‘curse of dimensionality’’ and speed up learning in the unknown large-scale world. Finally, the simulation results under JADE (Java Agent Development Framework) demonstrate the validity of the presented method in optimal control for a microgrid with grid-connected mode.
Risk Prediction for Production of an EnterpriseEditor IJCATR
Despite all preventive measures, there is so much possibility of risks in any project development as well as in enterprise management. There is no any standard mechanism or methodology available to assess the risks in any project or production management. Using some precautionary steps, the manager can only avoid the risks as much as he can. To address this issue, this paper presents a probabilistic risk assessment model for the production of an enterprise. For this, Multi-Entity Bayesian Network (MEBN) has been used to represent the requirements for production management as well as to assess the risks adherence in production management, where MEBN combines expressivity of first-order logic and probabilistic feature of Bayesian network. Bayesian network provides the feature to represent the probabilistic uncertainty and reasoning about probabilistic knowledge base, which is used here to represent the probable risks behind each causes of a risk. The proposed probabilistic model is discussed with the help of a case study, which is used to predict risks inherent in the production of an enterprise, which depends upon various measures like labour availability, power backup, transport availability etc.
Power System Reliability Assessment in a Complex Restructured Power SystemIJECEIAES
The basic purpose of an electric power system is to supply its consumers with electric energy as parsimoniously as possible and with a sensible degree of continuity and quality. It is expected that the solicitation of power system reliability assessment in bulk power systems will continue to increase in the future especially in the newly deregulated power diligence. This paper presents the research conducted on the three areas of incorporating multi-state generating unit models, evaluating system performance indices and identifying transmission paucities in complex system adequacy assessment. The incentives for electricity market participants to endow in new generation and transmission facilities are highly influenced by the market risk in a complex restructured environment. This paper also presents a procedure to identify transmission deficiencies and remedial modification in the composite generation and transmission system and focused on the application of probabilistic techniques in composite system adequacy assessment
Q-learning vertical handover scheme in two-tier LTE-A networks IJECEIAES
Global mobile communication necessitates improved capacity and proper quality assurance for services. To achieve these requirements, small cells have been deployed intensively by long term evolution (LTE) networks operators beside conventional base station structure to provide customers with better service and capacity coverage. Accomplishment of seamless handover between Macrocell layer (first tier) and Femtocell layer (second tier) is one of the key challenges to attain the QoS requirements. Handover related information gathering becomes very hard in high dense femtocell networks, effective handover decision techniques are important to minimize unnecessary handovers occurred and avoid Ping-Pong effect. In this work, we proposed and implemented an efficient handover decision procedure based on users’ profiles using Q-learning technique in an LTE-A macrocellfemtocell networks. New multi-criterion handover decision parameters are proposed in typical/dense femtocells in microcells environment to estimate the target cell for handover. The proposed handover algorithms are validated using the LTE-Sim simulator under an urban environment. The simulation results showed noteworthy reduction in the average number of handovers.
For years, the Machine Learning community has focused on developing efficient
algorithms that can produce very accurate classifiers. However, it is often much easier
to find several good classifiers based on dataset combination, instead of single classifier
applied on deferent datasets. The advantages of using classifier dataset combinations
instead of a single one are twofold: it helps lowering the computational complexity by
using simpler models, and it can improve the classification accuracy and performance.
Most Data mining applications are based on pattern matching algorithms, thus improving
the performance of the classification has a positive impact on the quality of the overall
data mining task. Since combination strategies proved very useful in improving the
performance, these techniques have become very important in applications such as
Cancer detection, Speech Technology and Natural Language Processing .The aim of this
paper is basically to propose proprietary metric, Normalized Geometric Index (NGI)
based on the latent properties of datasets for improving the accuracy of data mining tasks.
Stochastic behavior analysis of complex repairable industrial systemsISA Interchange
The purpose of this paper is to present a novel technique for analyzing the behavior of an industrial system stochastically by utilizing vague, imprecise, and uncertain data. In the present study two important tools namely Lambda-Tau methodology and particle swarm optimization are combinedly used to present a novel technique named as particle swarm optimization based Lambda-Tau (PSOBLT) for analyzing the behavior of a complex repairable system stochastically up to a desired degree of accuracy. Expressions of reliability indices like failure rate, repair time, mean time between failures (MTBF), expected number of failures (ENOF), reliability and availability for the system are obtained by using Lambda-Tau methodology and particle swarm optimization is used to construct their member- ship function. The interaction among the working units of the system is modeled with the help of Petri nets. The feeding unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. Sensitivity analysis of system’s behavior has also been done. The behavior analysis results computed by PSOBLT technique have a reduced region of prediction in comparison of existing technique region,
i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties.
Reliability, availability, maintainability (RAM) study, on reciprocating comp...John Kingsley
What is needed to perform a RAM Study and more details #RAM #Training #iFluids #RAMstudy
.
To know more, on How iFluids can help you operate & maintain Safe and Reliable plant Contact us Today --> info@ifluids.com
For any training enquiries, contact us today --> training@ifluids.com
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Gage Repeatability and Reproducibility in Semiconductor Manufacturing.pptxyieldWerx Semiconductor
In the semiconductor manufacturing industry, precision, reliability, and consistency are of utmost importance. Every aspect of production and quality control relies on accurate and repeatable measurements.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
System identification of a steam distillation pilot scale using arx and narx ...eSAT Journals
Abstract This paper presents steam temperature models for steam distillation pilot-scale (SDPS) by comparing Pseudo Random Binary Sequence (PRBS) versus Multi-Sine (M-Sine) perturbation signal Both perturbation signals were applied to nonlinear steam distillation system to study the capability of these input signals in exciting nonlinearity of system dynamics. In this work, both linear and nonlinear ARX model structures have been investigated. Five statistical approaches have been observed to evaluate the developed steam temperature models, namely, coefficient of determination, R2; auto-correlation function, ACF; cross-correlation function, CCF; root mean square error, RMSE; and residual histogram. The results showed that the nonlinear ARX models are superior as compared to the linear models when M-Sine perturbation applied to the steam distillation system. While, PRBS perturbation exhibit insufficient to model nonlinear system dynamic Keywords: SDPS, PRBS, M-Sine, ARX, R2, ACF, CCF, RMSE
Failure analysis of polymer and rubber materialsKartik Srinivas
Rubber products are designed using engineering principles of loads and deflections applied to a certain volume of material. The use of engineering principles in the development of rubber products provide an application envelope in which the products are expected to perform. Most of the products do provide the required services for satisfactory lifetimes, however failures do occur. Failures occurring under field services conditions are expensive and it becomes imperative to identify the cause and rectify it as soon as possible. The failure mode of polymers sets limits to the process of engineering design.
Optimal Maintainability of Hydraulic Excavator Through Fmea/FmecaIJRESJOURNAL
ABSTRACT: The concept of advanced maintenance management technique in the field of heavy earthmoving mining machinery is recently developed in India, and has taken pace with the demand of the same, rising continuously over the years. This paper indulges into considering of hydraulic excavators, which is a large machinery that is designed for excavation and demolitions purposes. It spreads to various sizes and functions. The development of the mining industry has been escalated largely due to the introduction of different types of excavators. These excavators are used to satisfy various mining, industrial and construction needs. The mining excavators are mainly of two types that are used in modern era namely backhoe and dragline, other being suction excavator, long reach/long arm, crawlers and compact excavators, power shovel etc. The data collected and analysis has been done keeping in mind the vicinity of the coal capital of India, where hydraulic excavator is mainly used. It is so, that the same gets prime focus in the paper. The increased penetration of service of the high yield machines in the above-mentioned sectors have made them really important. Halting or stoppages are seen as the bottlenecks, which disturbs the productivity. Seeing the large benefits, and associated productivity and profit loss, the maintenance engineer felt the need to have advanced maintenance of the same. The paper deals with different faults of the excavator, and based on the data acquired, takes on further steps towards carrying out the FMEA analysis which incorporates into it by estimating Severity, Occurrence and Detection of the considered parts respectively, and then Risk Priority Number (RPN) is calculated, ranging from 1 to 1000. The quantitative approach helps in deciding the various maintenance strategies for the different parts and subparts. It is based on the above factors that maintenance plans are initiated, designed and implemented.
Abstract The deployment of statistical process control (SPC) in manufacturing environments is a prominent global phenomenon. Statistical Process Control is largely used in industries for monitoring the process parameters. It is a standard method for visualizing and controlling processes on the basis of measurements of randomly selected samples. The decisions about what needs to be improved, the possible methods to improve it, and the steps to take after getting results from the charts are all made by humans and based on wisdom and experience. The statistical process control described in this paper gives the details about the SPC, its advantages and limitation, applications and information regarding the control charts. Keywords: Statistical Process Control, Control chart, 5M’s, Capability Indices.
Harnessing deep learning algorithms to predict software refactoringTELKOMNIKA JOURNAL
During software maintenance, software systems need to be modified by adding or modifying source code. These changes are required to fix errors or adopt new requirements raised by stakeholders or market place. Identifying thetargeted piece of code for refactoring purposes is considered a real challenge for software developers. The whole process of refactoring mainly relies on software developers’ skills and intuition. In this paper, a deep learning algorithm is used to develop a refactoring prediction model for highlighting the classes that require refactoring. More specifically, the gated recurrent unit algorithm is used with proposed pre-processing steps for refactoring predictionat the class level. The effectiveness of the proposed model is evaluated usinga very common dataset of 7 open source java projects. The experiments are conducted before and after balancing the dataset to investigate the influence of data sampling on the performance of the prediction model. The experimental analysis reveals a promising result in the field of code refactoring prediction
Tom Selleck Net Worth: A Comprehensive Analysisgreendigital
Over several decades, Tom Selleck, a name synonymous with charisma. From his iconic role as Thomas Magnum in the television series "Magnum, P.I." to his enduring presence in "Blue Bloods," Selleck has captivated audiences with his versatility and charm. As a result, "Tom Selleck net worth" has become a topic of great interest among fans. and financial enthusiasts alike. This article delves deep into Tom Selleck's wealth, exploring his career, assets, endorsements. and business ventures that contribute to his impressive economic standing.
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Early Life and Career Beginnings
The Foundation of Tom Selleck's Wealth
Born on January 29, 1945, in Detroit, Michigan, Tom Selleck grew up in Sherman Oaks, California. His journey towards building a large net worth began with humble origins. , Selleck pursued a business administration degree at the University of Southern California (USC) on a basketball scholarship. But, his interest shifted towards acting. leading him to study at the Hills Playhouse under Milton Katselas.
Minor roles in television and films marked Selleck's early career. He appeared in commercials and took on small parts in T.V. series such as "The Dating Game" and "Lancer." These initial steps, although modest. laid the groundwork for his future success and the growth of Tom Selleck net worth. Breakthrough with "Magnum, P.I."
The Role that Defined Tom Selleck's Career
Tom Selleck's breakthrough came with the role of Thomas Magnum in the CBS television series "Magnum, P.I." (1980-1988). This role made him a household name and boosted his net worth. The series' popularity resulted in Selleck earning large salaries. leading to financial stability and increased recognition in Hollywood.
"Magnum P.I." garnered high ratings and critical acclaim during its run. Selleck's portrayal of the charming and resourceful private investigator resonated with audiences. making him one of the most beloved television actors of the 1980s. The success of "Magnum P.I." played a pivotal role in shaping Tom Selleck net worth, establishing him as a major star.
Film Career and Diversification
Expanding Tom Selleck's Financial Portfolio
While "Magnum, P.I." was a cornerstone of Selleck's career, he did not limit himself to television. He ventured into films, further enhancing Tom Selleck net worth. His filmography includes notable movies such as "Three Men and a Baby" (1987). which became the highest-grossing film of the year, and its sequel, "Three Men and a Little Lady" (1990). These box office successes contributed to his wealth.
Selleck's versatility allowed him to transition between genres. from comedies like "Mr. Baseball" (1992) to westerns such as "Quigley Down Under" (1990). This diversification showcased his acting range. and provided many income streams, reinforcing Tom Selleck net worth.
Television Resurgence with "Blue Bloods"
Sustaining Wealth through Consistent Success
In 2010, Tom Selleck began starring as Frank Reagan i
Skeem Saam in June 2024 available on ForumIsaac More
Monday, June 3, 2024 - Episode 241: Sergeant Rathebe nabs a top scammer in Turfloop. Meikie is furious at her uncle's reaction to the truth about Ntswaki.
Tuesday, June 4, 2024 - Episode 242: Babeile uncovers the truth behind Rathebe’s latest actions. Leeto's announcement shocks his employees, and Ntswaki’s ordeal haunts her family.
Wednesday, June 5, 2024 - Episode 243: Rathebe blocks Babeile from investigating further. Melita warns Eunice to stay clear of Mr. Kgomo.
Thursday, June 6, 2024 - Episode 244: Tbose surrenders to the police while an intruder meddles in his affairs. Rathebe's secret mission faces a setback.
Friday, June 7, 2024 - Episode 245: Rathebe’s antics reach Kganyago. Tbose dodges a bullet, but a nightmare looms. Mr. Kgomo accuses Melita of witchcraft.
Monday, June 10, 2024 - Episode 246: Ntswaki struggles on her first day back at school. Babeile is stunned by Rathebe’s romance with Bullet Mabuza.
Tuesday, June 11, 2024 - Episode 247: An unexpected turn halts Rathebe’s investigation. The press discovers Mr. Kgomo’s affair with a young employee.
Wednesday, June 12, 2024 - Episode 248: Rathebe chases a criminal, resorting to gunfire. Turf High is rife with tension and transfer threats.
Thursday, June 13, 2024 - Episode 249: Rathebe traps Kganyago. John warns Toby to stop harassing Ntswaki.
Friday, June 14, 2024 - Episode 250: Babeile is cleared to investigate Rathebe. Melita gains Mr. Kgomo’s trust, and Jacobeth devises a financial solution.
Monday, June 17, 2024 - Episode 251: Rathebe feels the pressure as Babeile closes in. Mr. Kgomo and Eunice clash. Jacobeth risks her safety in pursuit of Kganyago.
Tuesday, June 18, 2024 - Episode 252: Bullet Mabuza retaliates against Jacobeth. Pitsi inadvertently reveals his parents’ plans. Nkosi is shocked by Khwezi’s decision on LJ’s future.
Wednesday, June 19, 2024 - Episode 253: Jacobeth is ensnared in deceit. Evelyn is stressed over Toby’s case, and Letetswe reveals shocking academic results.
Thursday, June 20, 2024 - Episode 254: Elizabeth learns Jacobeth is in Mpumalanga. Kganyago's past is exposed, and Lehasa discovers his son is in KZN.
Friday, June 21, 2024 - Episode 255: Elizabeth confirms Jacobeth’s dubious activities in Mpumalanga. Rathebe lies about her relationship with Bullet, and Jacobeth faces theft accusations.
Monday, June 24, 2024 - Episode 256: Rathebe spies on Kganyago. Lehasa plans to retrieve his son from KZN, fearing what awaits.
Tuesday, June 25, 2024 - Episode 257: MaNtuli fears for Kwaito’s safety in Mpumalanga. Mr. Kgomo and Melita reconcile.
Wednesday, June 26, 2024 - Episode 258: Kganyago makes a bold escape. Elizabeth receives a shocking message from Kwaito. Mrs. Khoza defends her husband against scam accusations.
Thursday, June 27, 2024 - Episode 259: Babeile's skillful arrest changes the game. Tbose and Kwaito face a hostage crisis.
Friday, June 28, 2024 - Episode 260: Two women face the reality of being scammed. Turf is rocked by breaking
Modern Radio Frequency Access Control Systems: The Key to Efficiency and SafetyAITIX LLC
Today's fast-paced environment worries companies of all sizes about efficiency and security. Businesses are constantly looking for new and better solutions to solve their problems, whether it's data security or facility access. RFID for access control technologies have revolutionized this.
Meet Dinah Mattingly – Larry Bird’s Partner in Life and Loveget joys
Get an intimate look at Dinah Mattingly’s life alongside NBA icon Larry Bird. From their humble beginnings to their life today, discover the love and partnership that have defined their relationship.
Young Tom Selleck: A Journey Through His Early Years and Rise to Stardomgreendigital
Introduction
When one thinks of Hollywood legends, Tom Selleck is a name that comes to mind. Known for his charming smile, rugged good looks. and the iconic mustache that has become synonymous with his persona. Tom Selleck has had a prolific career spanning decades. But, the journey of young Tom Selleck, from his early years to becoming a household name. is a story filled with determination, talent, and a touch of luck. This article delves into young Tom Selleck's life, background, early struggles. and pivotal moments that led to his rise in Hollywood.
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Early Life and Background
Family Roots and Childhood
Thomas William Selleck was born in Detroit, Michigan, on January 29, 1945. He was the second of four children in a close-knit family. His father, Robert Dean Selleck, was a real estate investor and executive. while his mother, Martha Selleck, was a homemaker. The Selleck family relocated to Sherman Oaks, California. when Tom was a child, setting the stage for his future in the entertainment industry.
Education and Early Interests
Growing up, young Tom Selleck was an active and athletic child. He attended Grant High School in Van Nuys, California. where he excelled in sports, particularly basketball. His tall and athletic build made him a standout player, and he earned a basketball scholarship to the University of Southern California (U.S.C.). While at U.S.C., Selleck studied business administration. but his interests shifted toward acting.
Discovery of Acting Passion
Tom Selleck's journey into acting was serendipitous. During his time at U.S.C., a drama coach encouraged him to try acting. This nudge led him to join the Hills Playhouse, where he began honing his craft. Transitioning from an aspiring athlete to an actor took time. but young Tom Selleck became drawn to the performance world.
Early Career Struggles
Breaking Into the Industry
The path to stardom was a challenging one for young Tom Selleck. Like many aspiring actors, he faced many rejections and struggled to find steady work. A series of minor roles and guest appearances on television shows marked his early career. In 1965, he debuted on the syndicated show "The Dating Game." which gave him some exposure but did not lead to immediate success.
The Commercial Breakthrough
During the late 1960s and early 1970s, Selleck began appearing in television commercials. His rugged good looks and charismatic presence made him a popular brand choice. He starred in advertisements for Pepsi-Cola, Revlon, and Close-Up toothpaste. These commercials provided financial stability and helped him gain visibility in the industry.
Struggling Actor in Hollywood
Despite his success in commercials. breaking into large acting roles remained a challenge for young Tom Selleck. He auditioned and took on small parts in T.V. shows and movies. Some of his early television appearances included roles in popular series like Lancer, The F.B.I., and Bracken's World. But, it would take a
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Matt Rife Cancels Shows Due to Health Concerns, Reschedules Tour Dates.pdfAzura Everhart
Matt Rife's comedy tour took an unexpected turn. He had to cancel his Bloomington show due to a last-minute medical emergency. Fans in Chicago will also have to wait a bit longer for their laughs, as his shows there are postponed. Rife apologized and assured fans he'd be back on stage soon.
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Monday, 3 June 2024
Episode 47
A friend is compelled to expose a manipulative scheme to prevent another from making a grave mistake. In a frantic bid to save Jojo, Phakamile agrees to a meeting that unbeknownst to her, will seal her fate.
Tuesday, 4 June 2024
Episode 48
A mother, with her son's best interests at heart, finds him unready to heed her advice. Motshabi finds herself in an unmanageable situation, sinking fast like in quicksand.
Wednesday, 5 June 2024
Episode 49
A woman fabricates a diabolical lie to cover up an indiscretion. Overwhelmed by guilt, she makes a spontaneous confession that could be devastating to another heart.
Thursday, 6 June 2024
Episode 50
Linda unwittingly discloses damning information. Nhlamulo and Vuvu try to guide their friend towards the right decision.
Friday, 7 June 2024
Episode 51
Jojo's life continues to spiral out of control. Dintle weaves a web of lies to conceal that she is not as successful as everyone believes.
Monday, 10 June 2024
Episode 52
A heated confrontation between lovers leads to a devastating admission of guilt. Dintle's desperation takes a new turn, leaving her with dwindling options.
Tuesday, 11 June 2024
Episode 53
Unable to resort to violence, Taps issues a verbal threat, leaving Mdala unsettled. A sister must explain her life choices to regain her brother's trust.
Wednesday, 12 June 2024
Episode 54
Winnie makes a very troubling discovery. Taps follows through on his threat, leaving a woman reeling. Layla, oblivious to the truth, offers an incentive.
Thursday, 13 June 2024
Episode 55
A nosy relative arrives just in time to thwart a man's fatal decision. Dintle manipulates Khanyi to tug at Mo's heartstrings and get what she wants.
Friday, 14 June 2024
Episode 56
Tlhogi is shocked by Mdala's reaction following the revelation of their indiscretion. Jojo is in disbelief when the punishment for his crime is revealed.
Monday, 17 June 2024
Episode 57
A woman reprimands another to stay in her lane, leading to a damning revelation. A man decides to leave his broken life behind.
Tuesday, 18 June 2024
Episode 58
Nhlamulo learns that due to his actions, his worst fears have come true. Caiphus' extravagant promises to suppliers get him into trouble with Ndu.
Wednesday, 19 June 2024
Episode 59
A woman manages to kill two birds with one stone. Business doom looms over Chillax. A sobering incident makes a woman realize how far she's fallen.
Thursday, 20 June 2024
Episode 60
Taps' offer to help Nhlamulo comes with hidden motives. Caiphus' new ideas for Chillax have MaHilda excited. A blast from the past recognizes Dintle, not for her newfound fame.
Friday, 21 June 2024
Episode 61
Taps is hungry for revenge and finds a rope to hang Mdala with. Chillax's new job opportunity elicits mixed reactions from the public. Roommates' initial meeting starts off on the wrong foot.
Monday, 24 June 2024
Episode 62
Taps seizes new information and recruits someone on the inside. Mary's new job
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240529_Teleprotection Global Market Report 2024.pdfMadhura TBRC
The teleprotection market size has grown
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growth rate (CAGR) of 26.0%.
2. 2 Journal of Industrial Mathematics
plant, respectively. Kumar et al. [11, 12] have analysed the
reliability and availability behaviour of subsystems of paper
industry and sugar industry by modelling their states and
using probabilistic approach. The availability analysis of
steam and power generation systems in thermal power plant
has been done by Arora and Kumar [13] by using Chapman-
Kolmogorov birth-death process. Gupta [14] has analysed the
operational behaviour of a chemical production system by
using a methodology based on Markov modelling. Kumar
and Tewari [15] have modelled the CO2 cooling system of
a fertilizer plant by Markov birth-death process and then
optimized the system performance by genetic algorithm.
Gupta et al. [16] have dealt with the system reliability and
availability in butter oil processing plant by using Markov
process and Runge-kutta method. Kumar et al. [17] have
proposed a method based on Markov approach to evaluate
an availability simulation model in a thermal power plant.
Recently Manglik and Ram [18] have analysed the reliability
of a two-unit cold standby system using Markov process
and Kumar [19] has done the availability analysis of thermal
power plant boiler air circulation system by using Markov
approach. Therefore, it is found from the literature that the
Markov approach has become a popular technique among
other methods for the behavioural analysis and modelling of
systems. In order to enhance the performance measures by
selecting suitable choices of units, it is necessary to consider
an efficient optimization technique. There is a variety of
methods available in the literature [20–22]. The reliability of
industrial systems using soft-computing based technique has
been analysed by Garg et al. [23]. One of the optimization
techniques, genetic algorithm (GA) which resembles the
phenomenon of natural selection and reproduction, is a
random search technique and it has been used for various
reliability optimization problems. Khanduja et al. [24] have
used GA with Markovian approach for paper making system
of paper industry. The series parallel system was studied by
Sharma et al. [25] and best design policy is obtained using
GA. Thus GA is found to be a powerful technique as it
provides a robust search and is not limited to the restricted
search spaces.
In the present paper the importance of Markov process
is shown by analysing the reliability function and availability
of feeding system of sugar industry. The Markov transition
diagram indicating the system states is presented as it
gives availability function and the updated diagram leads
to the expression for reliability function. While applying
the normalizing condition, the expression for steady state
availability is obtained and optimized by using genetic algo-
rithm. Software package MATLAB with genetic algorithm
toolbox is used for the execution of GA to the optimization
problem. Thus the optimum design parameters obtained can
give system analyst the best policy for high availability and
productivity of the system. The purpose of this study is to
obtain (1) reliability function and availability function both
from Markov diagram of feeding system of sugar industry, (2)
an expression of steady state availability optimization model
with components’ constant failure and repair rates, and (3)
optimal system parameters by employing GA and a decision
of system design policy.
Phase I Phase II Phase III
0 t
𝜆(t)
Figure 1
2. Some Terminologies
Some terms and their importance in this study are described
below.
2.1. Reliability. It is a measure that the item/system will
perform its required function under given conditions for
stated time interval [1, 26, 27] and it is denoted by 𝑅(𝑡).
Mathematically
𝑅 (𝑡) = Pr {no failure in (0, 𝑡]}
with 𝑅 (0) = 1, lim
𝑡 → ∞
𝑅 (𝑡) = 0.
(1)
If the failure rate 𝜆(𝑡) is constant, then 𝜆(𝑡) = 𝜆 and
𝑅(𝑡) = exp(−𝜆𝑡). In many practical applications, failure rate
of item/system is considered as constant by assuming the
condition of as-good-as-new for every repaired item/system.
It is well explained in [1] that the resultant bathtub curve
as shown in Figure 1 of failure rate of large population
of statistically identical and independent items gives three
phases: (i) early failures, (ii) failures with constant failure rate,
and (iii) wearout failures, in all the phases the period of the
second one is very much useful for many real life situations.
2.2. Availability. It is the probability that a system will
perform its required function at a given instant of time or
over a stated period of time when operated and maintained
in a prescribed manner [1, 26, 27]. The three classifications of
availability over operational time are given as follows.
(i) Point availability: the probability of satisfactorily
functioning of the system at a given instant of time
𝑡 is termed as point availability and denoted as 𝐴(𝑡).
(ii) Mission availability: it is the average availability over
the interval (0, 𝑇] and is expressed as
𝐴 (𝑇) = (
1
𝑇
) ∫
𝑇
0
𝐴 (𝑡) 𝑑𝑡. (2)
(iii) Steady state availability: it is defined as the probability
that the system is performing its intended function
with maintenance strategy for long run time; that is,
the point availability for steady state and is given as
𝐴 = lim
𝑡 → ∞
𝐴 (𝑡) . (3)
3. Journal of Industrial Mathematics 3
0 t
1
A(t)
𝜇/𝜆 + 𝜇
Figure 2
For single element system with constant failure and repair
rates, availability is 𝐴 = 𝜇/(𝜆+𝜇). Numerically, the difference
between reliability and availability of the system is that for
long run time reliability becomes zero, while availability goes
to some fixed value as shown graphically in Figure 2.
2.3. Markov Process. Reliability and availability can easily
be investigated in many industrial systems having structures
convertible to reliability block diagram (RBD) but a tough sit-
uation arises when RBD of systems does not exist or cannot be
easily found, as each component in RBD has only two states.
To investigate these complex repairable systems various
tools such as Markov process, semi-Markov, Petri nets, and
dynamic FTA are developed. It is found from bathtub curve
that failure and repair rates of components must be constant
in real life situations and thus simplifying the system analysis.
Hence system involving Markov process is considered in
this discussion with certain assumptions. Markov process, a
stochastic process exhibiting the memoryless property [1, 26,
28] is a very powerful technique in the analysis of reliability
and availability of complex repairable systems where the stay
time in the system states follows an exponential distribution;
that is, failure and repair rates are constant for all units during
this process and the probability that the system changes its
state depends only on the previous state. Finite state space and
time-homogeneous Markov process is considered here and
the diagram indicating the process is presented to develop
differential equations.
2.4. Genetic Algorithm. A very powerful search technique in
the field of optimization problems is genetic algorithm (GA)
which has been initially introduced by Holland [29] and after
that many researchers have carried their research with this
technique [30–32]. Genetic algorithms are the combination
of search algorithms which are based on the well-known
biological fact of natural selection and natural genetics. These
algorithms are very powerful for grasping improvement in
their search and also computationally simple and thus they
have wider area of applications such as business, scientific,
and engineering. The main advantage of GA over other
techniques is that it is not restricted by the condition on
search spaces such as existence of continuity, differentiability,
and unimodality. The flow chart depicting the process of GA
is shown in Figure 3 and here the technique is executed by
software MATLAB version 2008 with genetic algorithm and
direct search toolbox.
3. System Description
Sugar mill, a very popular process industry that fulfils our
various daily needs and other requirements, is considered
here. Feeding, evaporation, and crystallization systems are
the main constituents of sugar mill and their function-
ing/nonfunctioning affects the process of producing sugar
from sugarcanes. Every subsystem of sugar industry has
importance in its performance and hence each one plays a
distinguished role in the overall system operation. In this
section a subsystem of sugar industry, namely, feeding system
for which the functioning or failure of any of its component
affects the working process of the system in a certain manner,
is described.
3.1. Feeding System Description. The feeding system of sugar
industry has mainly four subsystems, namely, cutting system,
crushing system, bagasse carrying system, and heat generat-
ing system [12] which are described as follows.
(1) Cutting system (𝐴): a cutting system (𝐴) consists
of units connected in series each one of which is a
combination of a conveyor and a cutter; failure of any
unit leads to the failure of the system. Sugarcane is cut
into small pieces by the cutter for their use in the next
stage.
(2) Crushing system (𝐵): after cutting, sugarcane pieces
are sent to crushing system where a combination of
conveyor and crusher are connected in series to crush
the pieces for the extraction of raw juice and failure of
any one leads to the system failure.
(3) Bagasse carrying system (𝐶): to use the crushed cane
as a part of fuel for the boilers, there is a combination
of carrier to carry the bagasse from crushing system
to the heat generating system. The usage of bagasse
may increase the efficiency of generating heat which
is used for multiple purposes in the sugar system as for
evaporation, crystallization, and so forth. The system
𝐶 has carriers connected in series and failure of
anyone unit in 𝐶 reduces the efficiency of the system
and also it affects the fuel supply to the next connected
subsystem known as heat generating system (𝐷).
(4) Heat generating system (𝐷): heat is very much
required in the entire process of sugar mill and it is
generated in the sugar mill itself by burning fuel such
as coal, wood, and crushed cane (bagasse). Subsystem
𝐷 consists of parallel connected boilers in a way such
that failure of any one component in 𝐷 reduces only
the efficiency of the entire system.
4. Assumptions and Notations
(i) Failure-free time and repair time are stochastically
independent and continuous random variables.
(ii) Failures are not considered during repair at system
down state.
(iii) Repair is done according to first-in/first-out strategy
and a repaired unit is assumed as-good-as-new.
4. 4 Journal of Industrial Mathematics
Start
Randomly
generate initial
population, set
generation
Compute
fitness value
Is termination criteria
satisfied?
Stop
Reproduction
Crossover
Mutation
Generate new
population, generation
Yes
No
counter = 0
counter = generation
counter + 1
Figure 3
𝐴, 𝐵, 𝐶, 𝐷 operative states of all four subsys-
tems of feeding system.
𝑎, 𝑏, 𝐶, 𝐷 failed states of systems 𝐴, 𝐵 and
reduced state of 𝐶, 𝐷, respectively.
𝜆𝐴, 𝜆𝐵 failure rates for complete failure of sys-
tems 𝐴, 𝐵.
𝜇𝐴, 𝜇𝐵 repair rates of systems 𝐴, 𝐵.
𝛼𝐶, 𝛼𝐷, 𝛽𝐶, 𝛽𝐷 transition rate of 𝐶, 𝐷 into 𝐶, 𝐷
and 𝐶, 𝐷 into 𝐶, 𝐷, respectively.
0 represents operative state.
3, 6, 9 represent reduced states, while 1, 2, 4, 5,
7, 8, 10, and 11 represent failed states.
𝑝𝑗(𝑡) represents the probability that the system
is in state 𝑗 at time
⃝, ◊, ◻ represent good, reduced, and failed
states, respectively.
5. Methodology
It is clear from Section 2 and the literature that complex
repairable systems must possess constant failure and repair
rates for every unit in general. Thus the performance of a
repairable system can be easily analysed by exhibiting time-
homogeneous Markov process and modelling its finite states.
By updating the Markov model, other useful measures are
also easily obtained. The good decision of system parameters
is always required for maximum performance and therefore
for that an optimization technique is applied on the system
availability model over a range of unknown variables. The
main steps of the analysis done in this paper are pointed as
follows:
(i) modelling the system states by Markov process, that
is, taking constant failure and repair rates of each
individual. Update the model by considering all failed
states as absorbing states; that is, once entered in then
it is impossible to leave that state;
(ii) obtain reliability function, steady state availability,
and also state the optimization model;
(iii) optimize the model by GA to obtain optimal design
parameters and finally state all the values appropriate
for system survivability by using an example.
5.1. Modelling by Markov Process. The system is modelled as
in [12] but here we have considered that failure-free time as
well as time involved in repair of failed components must
be exponentially distributed. The corresponding transition
diagram of involved states is shown in Figure 4.
To investigate Markov process, differential equations are
easily derived from the transition diagram as
𝑑𝑝0 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛼𝐷) 𝑝0 (𝑡)
= 𝜇𝐴𝑝1 (𝑡) + 𝜇𝐵𝑝2 (𝑡) + 𝛽𝐶𝑝3 (𝑡) + 𝛽𝐷𝑝6 (𝑡) ,
𝑑𝑝3 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛽𝐶) 𝑝3 (𝑡)
= 𝜇𝐴𝑝4 (𝑡) + 𝜇𝐵𝑝5 (𝑡) + 𝛼𝐶𝑝0 (𝑡) + 𝛽𝐷𝑝9 (𝑡) ,
𝑑𝑝6 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛽𝐷) 𝑝6 (𝑡)
= 𝜇𝐴𝑝7 (𝑡) + 𝜇𝐵𝑝8 (𝑡) + 𝛼𝐷𝑝0 (𝑡) ,
𝑑𝑝9 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛽𝐷) 𝑝9 (𝑡)
= 𝜇𝐴𝑝10 (𝑡) + 𝜇𝐵𝑝11 (𝑡) + 𝛼𝐶𝑝6 (𝑡) ,
𝑑𝑝𝑗 (𝑡)
𝑑𝑡
+ 𝜇𝑖𝑝𝑗 (𝑡) = 𝜆𝑖𝑝0 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 1) (𝐵, 2)} ,
𝑑𝑝𝑗 (𝑡)
𝑑𝑡
+ 𝜇𝑖𝑝𝑗 (𝑡) = 𝜆𝑖𝑝3 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 4) (𝐵, 5)} ,
𝑑𝑝𝑗 (𝑡)
𝑑𝑡
+ 𝜇𝑖𝑝𝑗 (𝑡) = 𝜆𝑖𝑝6 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 7) (𝐵, 8)} ,
5. Journal of Industrial Mathematics 5
aBCD AbCD
ABCD
aBCD
ABCD
AbCD
ABCD
aBCD AbCD
AbCD
ABCD
aBCD
1 2
3
4
5
6
7
8
9
0
10 11
𝜆A
𝜆A
𝜆A
𝜆A
𝜆B
𝜆B
𝜆B
𝜆B
𝜇A
𝜇B
𝜇A
𝜇A
𝜇A
𝜇B
𝜇B
𝜇B
𝛽D
𝛽D
𝛽C
𝛼C
𝛼C
𝛼D
Figure 4
𝑑𝑝𝑗 (𝑡)
𝑑𝑡
+ 𝜇𝑖𝑝𝑗 (𝑡) = 𝜆𝑖𝑝9 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 10) (𝐵, 11)} .
(4)
A time-homogeneous Markov process is stationary if the state
probabilities do not depend on time 𝑡 [1]. Therefore the steady
state availability can be obtained by using the condition: as
𝑡 → ∞, 𝑝𝑗(𝑡) → 𝑝𝑗 and 𝑑𝑝𝑗(𝑡)/𝑑𝑡 → 0 ∀𝑗.
The above set of equations are then transformed into
(𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛼𝐷) 𝑝0
= 𝜇𝐴𝑝1 + 𝜇𝐵𝑝2 + 𝛽𝐶𝑝3 + 𝛽𝐷𝑝6,
(𝜆𝐴 + 𝜆𝐵 + 𝛽𝐶) 𝑝3
= 𝜇𝐴𝑝4 + 𝜇𝐵𝑝5 + 𝛼𝐶𝑝0 + 𝛽𝐷𝑝9,
(𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛽𝐷) 𝑝6 = 𝜇𝐴𝑝7 + 𝜇𝐵𝑝8 + 𝛼𝐷𝑝0,
(𝜆𝐴 + 𝜆𝐵 + 𝛽𝐷) 𝑝9 = 𝜇𝐴𝑝10 + 𝜇𝐵𝑝11 + 𝛼𝐶𝑝6,
𝜇𝑖𝑝𝑗 = 𝜆𝑖𝑝0 where (𝑖, 𝑗) belongs to {(𝐴, 1) (𝐵, 2)} ,
𝜇𝑖𝑝𝑗 = 𝜆𝑖𝑝3 where (𝑖, 𝑗) belongs to {(𝐴, 4) (𝐵, 5)} ,
𝜇𝑖𝑝𝑗 = 𝜆𝑖𝑝6 where (𝑖, 𝑗) belongs to {(𝐴, 7) (𝐵, 8)} ,
𝜇𝑖𝑝𝑗 = 𝜆𝑖𝑝9 where (𝑖, 𝑗) belongs to {(𝐴, 10) (𝐵, 11)} .
(5)
Solving the system of equations recursively in terms of 𝑝0, we
get the equations as follows:
𝑝1 =
𝜆𝐴
𝜇𝐴
𝑝0, 𝑝2 =
𝜆𝐵
𝜇𝐵
𝑝0, 𝑝3 =
𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
𝑝0,
𝑝4 =
𝜆𝐴𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝜇𝐴𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
𝑝0,
𝑝5 =
𝜆𝐵𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝜇𝐵𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
𝑝0,
𝑝6 =
𝛼𝐷
(𝛼𝐶 + 𝛽𝐷)
𝑝0, 𝑝7 =
𝜆𝐴𝛼𝐷
𝜇𝐴 (𝛼𝐶 + 𝛽𝐷)
𝑝0,
𝑝8 =
𝜆𝐵𝛼𝐷
𝜇𝐵 (𝛼𝐶 + 𝛽𝐷)
𝑝0, 𝑝9 =
𝛼𝐶𝛼𝐷
𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
𝑝0,
𝑝10 =
𝜆𝐴𝛼𝐶𝛼𝐷
𝜇𝐴𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
𝑝0, 𝑝11 =
𝜆𝐵𝛼𝐶𝛼𝐷
𝜇𝐵𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
𝑝0.
(6)
Now, using the normalizing condition
11
∑
𝑗=0
𝑝𝑗 = 1 (7)
in (6) we get,
𝑝0
= [1 +
𝜆𝐴
𝜇𝐴
+
𝜆𝐵
𝜇𝐵
+
𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐴𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝜇𝐴𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐵𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝜇𝐵𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
+
𝛼𝐷
(𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐴𝛼𝐷
𝜇𝐴 (𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐵𝛼𝐷
𝜇𝐵 (𝛼𝐶 + 𝛽𝐷)
+
𝛼𝐶𝛼𝐷
𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐴𝛼𝐶𝛼𝐷
𝜇𝐴𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
+
𝜆𝐵𝛼𝐶𝛼𝐷
𝜇𝐵𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
]
−1
.
(8)
6. 6 Journal of Industrial Mathematics
aBCD AbCD
ABCD
aBCD
ABCD
AbCD
ABCD
aBCD AbCD
AbCD
ABCD
aBCD
1 2
3
4
5
6
7
8
9
0
10 11
𝜆A
𝜆A
𝜆A
𝜆A
𝜆B
𝜆B
𝜆B
𝜆B
𝛽D
𝛽D
𝛽C
𝛼C
𝛼C
𝛼D
Figure 5
As the sum of state probabilities of all working states of the
system leads to the system availability [26, 27], the steady state
availability 𝐴V𝑆 is given by the equation as follows:
𝐴V𝑆
= 𝑝0 + 𝑝3 + 𝑝6 + 𝑝9
= [1 +
𝛼𝐶 (𝛼𝐶 + 𝛼𝐷 + 𝛽𝐷)
𝛽𝐶 (𝛼𝐶 + 𝛽𝐷)
+
𝛼𝐷
(𝛼𝐶 + 𝛽𝐷)
+
𝛼𝐶𝛼𝐷
𝛽𝐷 (𝛼𝐶 + 𝛽𝐷)
]𝑝0.
(9)
In view of the value of 𝑝0 as given by (8) the expression for
steady state availability reduces to
𝐴V𝑆 =
1
(1 + (𝜆𝐴/𝜇𝐴 ) + (𝜆𝐵/𝜇𝐵))
≈ 1 − (
𝜆𝐴
𝜇 𝐴
+
𝜆𝐵
𝜇𝐵
) .
(10)
This expression is the same as for a two-element series system.
Therefore cutting system 𝐴 and crushing system 𝐵 of sugar
mill behave like a 2-series system and hence the parameters
related to 𝐴 and 𝐵 affect directly the productivity of the
system.
To measure the reliability function associated with this
Markov process, all the failed states in the transition diagram
are considered as absorbing states [1] as shown in Figure 5.
The differential equations related to the transition dia-
gram (Figure 5) are given as
𝑑𝑝0 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛼𝐷) 𝑝0 (𝑡)
= 𝛽𝐶𝑝3 (𝑡) + 𝛽𝐷𝑝6 (𝑡) ,
𝑑𝑝3 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛽𝐶) 𝑝3 (𝑡)
= 𝛼𝐶𝑝0 (𝑡) + 𝛽𝐷𝑝9 (𝑡) ,
𝑑𝑝6 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛼𝐶 + 𝛽𝐷) 𝑝6 (𝑡) = 𝛼𝐷𝑝0 (𝑡) ,
𝑑𝑝9 (𝑡)
𝑑𝑡
+ (𝜆𝐴 + 𝜆𝐵 + 𝛽𝐷) 𝑝9 (𝑡) = 𝛼𝐶𝑝6 (𝑡) ,
𝑑𝑝𝑗 (𝑡)
𝑑𝑡
= 𝜆𝑖𝑝0 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 1) (𝐵, 2)} ,
𝑑𝑝𝑗 (𝑡) /𝑑𝑡 = 𝜆𝑖𝑝3 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 4) (𝐵, 5)} ,
𝑑𝑝𝑗 (𝑡) /𝑑𝑡 = 𝜆𝑖𝑝6 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 7) (𝐵, 8)} ,
𝑑𝑝𝑗 (𝑡) /𝑑𝑡 = 𝜆𝑖𝑝9 (𝑡) where
(𝑖, 𝑗) belongs to {(𝐴, 10) (𝐵, 11)} .
(11)
The above set of equations is a well-known system of linear
differential equations with constant coefficients which is
solved by various numerical methods. In this discussion, the
system of equations is solved by eigenvalue method with 𝑒𝑖
as the eigenvalues and V𝑖 as their corresponding eigenvectors
and the solution is expressed as
𝑋 (𝑡) =
11
∑
𝑖=0
𝑐𝑖 exp (𝑒𝑖 ∗ 𝑡) V𝑖 with 𝑋 (0) = [1 0 ⋅ ⋅ ⋅ 0]
𝑇
,
𝑋 (𝑡) = [𝑝0 (𝑡) 𝑝1 (𝑡) ⋅ ⋅ ⋅ 𝑝11 (𝑡)]
𝑇
.
(12)
The reliability of system at any time 𝑡 is given as 𝑅(𝑡) = 𝑝0(𝑡)+
𝑝3(𝑡) + 𝑝6(𝑡) + 𝑝9(𝑡) and mean time to failure of the whole
7. Journal of Industrial Mathematics 7
system is MTTF = ∫
∞
𝑡=0
𝑅(𝑡)𝑑𝑡. Thus system involving Markov
process is easily handled to find its reliability and availability
by only modelling its corresponding transition diagrams for
reliability function and availability function.
6. Optimization Analysis
In real life situations, system personnel is concerned about
how to increase profit and productivity of the system and
make the system highly reliable for long duration of time.
Therefore, it is necessary while designing the system to know
the information about its units which effect system’s working
capacity and also choose the best components which increase
the overall functioning of the system for long run time with
regard to their failures. Therefore our main purpose is to find
the best system design units by selecting appropriate values
of failure and repair rates within the specified ranges such
that the system long run availability maximizes. The ranges
or crisp values of failure and repair rates of the system can be
found by reviewing the previous records of that system or by
experimental process or by concerning that particular system
analyst.
In this study, to analyse and measure the performance
factors, we consider a physical situation where each subsys-
tem of feeding system has a mean failure rate of 0.001 to
0.002 per operating hour and mean repair rate of 0.2 to 0.4
per operating hour and the system is configured as 𝐴 and 𝐵
having four components each, 𝐶 having three components,
and 𝐷 having six components. Now for each macrostructure,
their individual failure rate and repair rate are calculated by
the formula given as follows:
𝜆𝐴 =
4
∑
𝑖=1
𝜆𝑖, 𝜇𝐴 ≈
𝜆1 + 𝜆2 + ⋅ ⋅ ⋅ + 𝜆4
(𝜆1/𝜇1) + (𝜆2/𝜇2) + ⋅ ⋅ ⋅ + (𝜆4/𝜇4)
,
𝜆𝐵 =
4
∑
𝑖=1
𝜆𝑖, 𝜇𝐵 ≈
𝜆1 + 𝜆2 + ⋅ ⋅ ⋅ + 𝜆4
(𝜆1/𝜇1) + (𝜆2/𝜇2) + ⋅ ⋅ ⋅ + (𝜆4/𝜇4)
,
𝛼𝐶 =
3
∑
𝑖=1
𝛼𝑖, 𝛽𝐶 ≈
𝛼1 + 𝛼2 + 𝛼3
(𝛼1/𝛽1) + (𝛼2/𝛽2) + (𝛼3/𝛽3)
,
𝛼𝐷 =
6
∑
𝑖=1
𝛼𝑖, 𝛽𝐷 ≈
𝛼1 + 𝛼2 + ⋅ ⋅ ⋅ + 𝛼6
(𝛼1/𝛽1) + (𝛼2/𝛽2) + ⋅ ⋅ ⋅ + (𝛼6/𝛽6)
.
(13)
Hence the steady state availability optimization model
becomes
Maximize 𝐴V𝑆 = [1 +
𝜆𝐴
𝜇𝐴
+
𝜆𝐵
𝜇𝐵
]
−1
s.t. 0.004 ≤ 𝜆𝐴 ≤ 0.008, 0.2 ≤ 𝜇𝐴 ≤ 0.4
0.004 ≤ 𝜆𝐵 ≤ 0.008, 0.2 ≤ 𝜇𝐵 ≤ 0.4.
(14)
By taking the fitness function as the objective function in
minimization form, the optimal values of failure and repair
0 20 40 60 80 100
−0.99
−0.98
−0.97
−0.96
−0.95
−0.94
Generation
Fitness
value
Best: −0.98027
Mean: −0.98022
Best fitness
Mean fitness
Figure 6
Table 1: Optimal design parameters.
Components Failure rate Repair rate
Cutting system 0.004 0.4
Crushing system 0.004 0.395
Bagasse carrying system 0.0045 0.3
Heat generating system 0.009 0.3
rates are calculated by executing genetic algorithm with
the help of MATLAB genetic algorithm and direct search
tool box with installed settings. The best individual is taken
by executing 20 runs and its performance graph with the
generation count is shown in Figure 6. It is found that the
technique approaches to the nearly optimal solution from
generation count 20 with a very minor difference between
the best and mean of fitness value. Thus the best system
availability and the optimal parameters after this execution
come out to be 0.980274, and 𝜆𝐴 = 0.004, 𝜇𝐴 = 0.4, 𝜆𝐵 =
0.004, 𝜇𝐵 = 0.395 within 51 generation counts, respectively.
From above analysis it is clear that the failure and repair
rates of subsystems 𝐶 and 𝐷 do not affect the working
capacity of system for long time period. For evaluation of
reliability at a time, it is best to choose the corresponding
data as their average values as there is no significant variation
in the system reliability with respect to their rates. Therefore
the optimal design policy resulting system availability as
0.980274 is stated in Table 1. For this strategy, the system
reliability at different time stages within one hour interval is
found by using (12) and coding it into MATLAB with the
condition of ignoring the imaginary part of any numerical
value and is stated in Table 2 for initial hours. The reliability
curve up to 1000 hours for optimal design policy is shown
in Figure 7. Thus we conclude that various performance
measures of the systems are easily obtained by considering
time-homogeneous Markov process and after that according
to them the impact of each subsystem can be found.
7. Discussion
In the present era of technology, industrial systems are struc-
tured with more standby units/subsystems in a particular
8. 8 Journal of Industrial Mathematics
Table 2: System reliability after 𝑡-hrs.
𝑡 (hrs) 0 10 50 100 150 200 250 500
𝑅 (𝑡) 1 0.924289 0.679017 0.461945 0.314268 0.213801 0.145452 0.021197
0
100 200 300 400 500 600 700 800 900 1000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (hrs)
R(t)
Figure 7: Reliability curve.
manner to increase the efficiency and duration of their
operation. Thus complexity in system’s structure arises as it
exhibits more than two states and cannot be represented by
reliability block diagram. In industries, performance analyses
are necessary to make them more reliable by demonstrating
their operational behaviour. To analyse the reliability and
availability of feeding system of sugar industry, Markovian
approach with genetic algorithm has been considered in this
study. From the analysis, it is found that both performance
measures of a complex system can easily be obtained by
modelling the system states as Markovian approach with
and without absorbing states. Apart from this approach,
techniques such as dynamic Petri nets, dynamic fault tree
analysis, and other computer based techniques are available
in the literature [1]. Generally, the Petri nets are same as
Markov model but its modelling process is quite tedious.
Its graph includes places, transitions, and directed arcs with
well-defined rules for transition of tokens, placed inside the
places. Dynamic Petri nets are based on the criteria of firing
of tokens, marking, reachability tree, and so forth, and it
is necessary for system analyst having the knowledge of
these important terms. More detailed explanation about Petri
nets is given in [1, 33]. In the case of complex system as
taken in this paper it is found that Markov model can be
formed in a simple and easy way by considering certain
assumptions and the system reliability and availability can
be analysed without any computational difficulty. Dynamic
Petri nets also provide system performance measures but
in a lengthy way. Another famous technique, dynamic fault
tree analysis (dynamic FTA) is a graphical representation of
conditions causing the occurrence of an undesirable event
with dynamic gates [1]. FTA is used in variety of reliability
oriented problems and involves fault trees, reliability block
diagrams, and binary decision diagrams whereas dynamic
FTA also requires the knowledge of various dynamic gates
as PAND, SEQ, SPARE, and so forth [1]. Therefore Markov
approach is found to be a simple and effective investigation
tool in comparison to other techniques for the analysis of
complex systems exhibiting more than two states.
8. Conclusion
In this paper, the application of time-homogeneous Markov
process is explained in the operating process of feeding
system of a well-popular sugar industry. It is clearly shown
that the expression for reliability function and availability for
a complex repairable system having more than two states
is easily obtained by system Markov modelling and this
method is found very useful in calculating these measures
for any industrial systems. To design the feeding system in
a way such that it will survive for long time period, we have
assumed the data regarding to its configuration and shown
the proper use of Markov process and a search technique
Genetic Algorithm. To run GA with more efficiency, popular
MATLAB software with genetic algorithm optimization tool
is executed. This study states that a system can be analysed
easily by concerning the process as Markov process and it
helps the system design analyst or plant personnel to select
the most appropriate structural components. Thus this dis-
cussion assists the system in achieving its high performance
measures for maximum duration of time.
Conflict of Interests
The authors declare that there is no conflict of interests
regarding the publication of this paper.
Acknowledgment
The corresponding author would like to thank the Ministry
of Human Resource and Development, New Delhi, India, for
providing financial support during the research work.
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