IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Draft comparison of electronic reliability prediction methodologiesAccendo Reliability
A draft version of the paper that was eventually published as “J.A.Jones & J.A.Hayes, ”A comparison of electronic-reliability prediction models”, IEEE Transactions on reliability, June 1999, Volume 48, Number 2, pp 127-134”
Provide with the kind permission of the author, J.A.Jones
Integrating fault tolerant scheme with feedback control scheduling algorithm ...ijics
In order to provide Quality of Service (QoS) in open and unpredictable environment, Feedback based
Control Scheduling Algorithm (FCSA) is designed to keep the processor utilization at the scheduling
utilization bound. FCSA controls CPU utilization by assigning task periods that optimize overall control
performance, meeting deadlines even if the task execution time is unpredictable and through performance
control feedback loop. Current FCSA doesn’t ensure Fault Tolerance (FT) while providing QoS in terms of
CPU utilization and resource management. In order to assure that tasks should meet their deadlines even
in the presence of faults, a FT scheme has to be integrated at control scheduling co-design level. This paper
presents a novel approach on integrating FT scheme with FCSA for real time embedded systems. This
procedure is especially important for control scheduling co-design of embedded systems.
System reliability and types of systems in machine designVikasSuroshe
This presentation gives brief description about, What is system reliability, types of systems. The points discussed are: System, Calculating Reliability Factor for System, System Configurations Types, Series Configuration, Parallel Configuration (Redundant System), Mixed Configuration (Combine Series-Parallel System), Reliability Block Diagram, Reliability Considerations, Advantages and Disadvantages of various configurations etc.
Draft comparison of electronic reliability prediction methodologiesAccendo Reliability
A draft version of the paper that was eventually published as “J.A.Jones & J.A.Hayes, ”A comparison of electronic-reliability prediction models”, IEEE Transactions on reliability, June 1999, Volume 48, Number 2, pp 127-134”
Provide with the kind permission of the author, J.A.Jones
Integrating fault tolerant scheme with feedback control scheduling algorithm ...ijics
In order to provide Quality of Service (QoS) in open and unpredictable environment, Feedback based
Control Scheduling Algorithm (FCSA) is designed to keep the processor utilization at the scheduling
utilization bound. FCSA controls CPU utilization by assigning task periods that optimize overall control
performance, meeting deadlines even if the task execution time is unpredictable and through performance
control feedback loop. Current FCSA doesn’t ensure Fault Tolerance (FT) while providing QoS in terms of
CPU utilization and resource management. In order to assure that tasks should meet their deadlines even
in the presence of faults, a FT scheme has to be integrated at control scheduling co-design level. This paper
presents a novel approach on integrating FT scheme with FCSA for real time embedded systems. This
procedure is especially important for control scheduling co-design of embedded systems.
System reliability and types of systems in machine designVikasSuroshe
This presentation gives brief description about, What is system reliability, types of systems. The points discussed are: System, Calculating Reliability Factor for System, System Configurations Types, Series Configuration, Parallel Configuration (Redundant System), Mixed Configuration (Combine Series-Parallel System), Reliability Block Diagram, Reliability Considerations, Advantages and Disadvantages of various configurations etc.
Objectives
To understand Weibull distribution
To be able to use Weibull plot for failure time analysis and
diagnosis
To be able to use software to do data analysis
Organization
Distribution model
Parameter estimation
Regression analysis
Estimation of Reliability Indices of Two Component Identical System in the Pr...IJLT EMAS
Progress in science & technology has made
engineering systems more powerful than ever. The intensity of
sophistication in high-tech industrial producers emerged with
reliability problems. Therefore the problem of reliability
continue to exist and more likely to require complex solutions.
Consequently, the field of reliability analysis and statistical
probability modeling of the systems and components were
growing. Ever since the theory of reliability was formally
recognized statistical and modeling of the components/ systems
analysis was used to develop various reliability measures that are
important to assess the system performance. In this research
paper, an attempt is made to find an approach of estimation
method, which could establish a formal estimation procedure to
estimate the reliability measures and also developed estimates of
the system reliability indices practically under the influence of
common cause shock failures as well as intrinsic failures. From
the results, it is seen that maximum likelihood approach used
was found useful in the estimation process to find estimate for
the reliability measures of the system, where small sample is
essential point of interest in the case of reliability analysis. The
estimates so derived using empirical procedure do possess the
property that MSE in each case is well within the prescribed
error, i.e. coincides even to the three decimal places are more.
SCHEDULING DIFFERENT CUSTOMER ACTIVITIES WITH SENSING DEVICEijait
Most periodic tasks are assigned to processors using partition scheduling policy after checking feasibility conditions. A new approach is proposed for scheduling different activities with one periodic task within the system. In this paper, control strategies are identified for allocating different types of tasks (activities) to
individual computing elements like Smartphone or microphones. In our simulation model, each periodic task generates an aperiodic tasks are taken into consideration. Different sets of periodic tasks and aperiodic tasks are scheduled together. This new approach proves that when all different activities are
scheduled with one periodic tasks leads to better performance.
Paper on the issues with mtbf published in the Spring 2011 issue of the RMSP Journal.
MTBF is widely used to describe the reliability of a component or system. It is also often misunderstood and used incorrectly. In some sense, the very name “mean time between failures” contributes to the misunderstanding. The objective of this paper is to explore the nature of the MTBF misunderstandings and the impact on decision-making and program costs.
Mean-Time-Between-Failure (MTBF) as defined by MIL-STD-721C Definition of Terms for Reliability and Maintainability, 12 June 1981, is
A basic measure of reliability for repairable items: The mean number of life units during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions.
The related measure, Mean-Time-To-Failure (MTTF) is define as
A basic measure of reliability for non-repairable items: The total number of life units of an item divided by the total number of failures within that population, during a particular measurement interval under stated conditions.
Software Reliability Growth Model with Logistic- Exponential Testing-Effort F...IDES Editor
Software reliability is one of the important factors of
software quality. Before software delivered in to market it is
thoroughly checked and errors are removed. Every software
industry wants to develop software that should be error free.
Software reliability growth models are helping the software
industries to develop software which is error free and reliable.
In this paper an analysis is done based on incorporating the
logistic-exponential testing-effort in to NHPP Software
reliability growth model and also observed its release policy.
Experiments are performed on the real datasets. Parameters
are calculated and observed that our model is best fitted for
the datasets.
Effect of stability indices on robustness and system response in coefficient ...eSAT Journals
Abstract
In Control systems, designing a robust controller such that a desired system response is obtained despite plant parameter
variations is ubiquitous problem. In this context, Coefficient diagram method is an effective method and one of the recent design
methods based on the polynomial approach introduced by Shunji Manabe. In CDM, stability indices, stability limits and time
constant are the main design parameters. The stability indices and stability limits are indicative of stability and equivalent time
constant is indicative of speed of system response. A semi-log diagram known as coefficient diagram is the design tool using
which one can analyse the important features of a design such as stability, speed of response and robustness, all in one diagram.
The right choice of the stability indices is of paramount importance in the controller design. This paper deals with the effect of
variation in the stability indices upon the system response and robustness. A type 2 fourth order plant has been considered as an
example to analyse the effects of stability indices. The stability indices are varied one by one relative to the standard Manabe form
and in each case response is observed. The transient response of the system is sensitive to lower order indices. Also, robustness in
the design is analysed by coefficient diagrams of the perturbed plant.
Keywords: Coefficient Diagram Method (CDM), robustness; Stability Indices, Coefficient Diagram
Guidelines to Understanding to estimate MTBFijsrd.com
To quantifying a reparable system or reliability we can use MTBF. It has been used for various decisions. MTBF is determining the reliability. For developing the MTBF model we can use Poisson distribution, Weibull model and Bayesian are the most popular approach. In this paper we are talking about complexities and misconceptions of MTBF and clarify in sequence what are the items and concerns that need to be consider in estimating MTBF.
Estimating Reliability of Power Factor Correction Circuits: A Comparative StudyIJERA Editor
Reliability plays an important role in power supplies, as every power supply is the very heart of every electronics equipment. For other electronic equipment, a certain failure mode, at least for a part of the total system, can often be tolerated without serious (critical) after effects. However, for the power supply no such condition can be accepted, since very high demands on the reliability must be achieved. At higher power levels, the CCM boost converter is preferred topology for implementation a front end with PFC. As a result significant efforts have been made to improve the performance of high boost converter. This paper is one the effort for improving the performance of the converter from the reliability point of view. In this paper a boost power factor correction converter is simulated with single switch and interleaving technique in CCM, DCM and CRM modes under different output power ratings and the reliability. Results of the converter are explored from reliability point of view.
Objectives
To understand Weibull distribution
To be able to use Weibull plot for failure time analysis and
diagnosis
To be able to use software to do data analysis
Organization
Distribution model
Parameter estimation
Regression analysis
Estimation of Reliability Indices of Two Component Identical System in the Pr...IJLT EMAS
Progress in science & technology has made
engineering systems more powerful than ever. The intensity of
sophistication in high-tech industrial producers emerged with
reliability problems. Therefore the problem of reliability
continue to exist and more likely to require complex solutions.
Consequently, the field of reliability analysis and statistical
probability modeling of the systems and components were
growing. Ever since the theory of reliability was formally
recognized statistical and modeling of the components/ systems
analysis was used to develop various reliability measures that are
important to assess the system performance. In this research
paper, an attempt is made to find an approach of estimation
method, which could establish a formal estimation procedure to
estimate the reliability measures and also developed estimates of
the system reliability indices practically under the influence of
common cause shock failures as well as intrinsic failures. From
the results, it is seen that maximum likelihood approach used
was found useful in the estimation process to find estimate for
the reliability measures of the system, where small sample is
essential point of interest in the case of reliability analysis. The
estimates so derived using empirical procedure do possess the
property that MSE in each case is well within the prescribed
error, i.e. coincides even to the three decimal places are more.
SCHEDULING DIFFERENT CUSTOMER ACTIVITIES WITH SENSING DEVICEijait
Most periodic tasks are assigned to processors using partition scheduling policy after checking feasibility conditions. A new approach is proposed for scheduling different activities with one periodic task within the system. In this paper, control strategies are identified for allocating different types of tasks (activities) to
individual computing elements like Smartphone or microphones. In our simulation model, each periodic task generates an aperiodic tasks are taken into consideration. Different sets of periodic tasks and aperiodic tasks are scheduled together. This new approach proves that when all different activities are
scheduled with one periodic tasks leads to better performance.
Paper on the issues with mtbf published in the Spring 2011 issue of the RMSP Journal.
MTBF is widely used to describe the reliability of a component or system. It is also often misunderstood and used incorrectly. In some sense, the very name “mean time between failures” contributes to the misunderstanding. The objective of this paper is to explore the nature of the MTBF misunderstandings and the impact on decision-making and program costs.
Mean-Time-Between-Failure (MTBF) as defined by MIL-STD-721C Definition of Terms for Reliability and Maintainability, 12 June 1981, is
A basic measure of reliability for repairable items: The mean number of life units during which all parts of the item perform within their specified limits, during a particular measurement interval under stated conditions.
The related measure, Mean-Time-To-Failure (MTTF) is define as
A basic measure of reliability for non-repairable items: The total number of life units of an item divided by the total number of failures within that population, during a particular measurement interval under stated conditions.
Software Reliability Growth Model with Logistic- Exponential Testing-Effort F...IDES Editor
Software reliability is one of the important factors of
software quality. Before software delivered in to market it is
thoroughly checked and errors are removed. Every software
industry wants to develop software that should be error free.
Software reliability growth models are helping the software
industries to develop software which is error free and reliable.
In this paper an analysis is done based on incorporating the
logistic-exponential testing-effort in to NHPP Software
reliability growth model and also observed its release policy.
Experiments are performed on the real datasets. Parameters
are calculated and observed that our model is best fitted for
the datasets.
Effect of stability indices on robustness and system response in coefficient ...eSAT Journals
Abstract
In Control systems, designing a robust controller such that a desired system response is obtained despite plant parameter
variations is ubiquitous problem. In this context, Coefficient diagram method is an effective method and one of the recent design
methods based on the polynomial approach introduced by Shunji Manabe. In CDM, stability indices, stability limits and time
constant are the main design parameters. The stability indices and stability limits are indicative of stability and equivalent time
constant is indicative of speed of system response. A semi-log diagram known as coefficient diagram is the design tool using
which one can analyse the important features of a design such as stability, speed of response and robustness, all in one diagram.
The right choice of the stability indices is of paramount importance in the controller design. This paper deals with the effect of
variation in the stability indices upon the system response and robustness. A type 2 fourth order plant has been considered as an
example to analyse the effects of stability indices. The stability indices are varied one by one relative to the standard Manabe form
and in each case response is observed. The transient response of the system is sensitive to lower order indices. Also, robustness in
the design is analysed by coefficient diagrams of the perturbed plant.
Keywords: Coefficient Diagram Method (CDM), robustness; Stability Indices, Coefficient Diagram
Guidelines to Understanding to estimate MTBFijsrd.com
To quantifying a reparable system or reliability we can use MTBF. It has been used for various decisions. MTBF is determining the reliability. For developing the MTBF model we can use Poisson distribution, Weibull model and Bayesian are the most popular approach. In this paper we are talking about complexities and misconceptions of MTBF and clarify in sequence what are the items and concerns that need to be consider in estimating MTBF.
Estimating Reliability of Power Factor Correction Circuits: A Comparative StudyIJERA Editor
Reliability plays an important role in power supplies, as every power supply is the very heart of every electronics equipment. For other electronic equipment, a certain failure mode, at least for a part of the total system, can often be tolerated without serious (critical) after effects. However, for the power supply no such condition can be accepted, since very high demands on the reliability must be achieved. At higher power levels, the CCM boost converter is preferred topology for implementation a front end with PFC. As a result significant efforts have been made to improve the performance of high boost converter. This paper is one the effort for improving the performance of the converter from the reliability point of view. In this paper a boost power factor correction converter is simulated with single switch and interleaving technique in CCM, DCM and CRM modes under different output power ratings and the reliability. Results of the converter are explored from reliability point of view.
This is a presentation to the top management as to why reliability is important and what is the difference between a maintenance engineer and a reliability engineer.
Efficiency of bond graph and external model integration for alarm processing ...IJAAS Team
The design of a supervision system based on the external model by structuring the industrial process according to several modes of operation (degraded and normal). The disadvantage of this model is that it describes the industrial process components as functions regardless of their dynamics without going into detail. Hence the interest of the bond graph model to fill the external model limits. The performance of the proposed supervisory system using both models lies in the detection and location of faults for each mode of operation. The bond graph model enriched by the concept of causality and thanks to these structural properties can clearly display the elements of the physical system taking into account their dynamics in normal and abnormal operation. The results of our research have been applied to central air conditioning system; the development of the proposed project has proceeded from the modeling stage to the reconfiguration stage of the system.
Reliability Demonstration Testing for Continuous-Type Software Products Based...idescitation
Reliability demonstration testing for software
products is performed for the purpose of examining whether
the specified reliability is realized in the software after the
development process is completed. This study proposes a model
of reliability demonstration testing for continuous-type
software such as that for controlling production lines and
operating systems of computers. Testing time and acceptance
number of software failures are designed based on variation
distance. This model has less parameters to be prespecified
than the statistical model.
Monte Carlo simulation convergences’ percentage and position in future relia...IJECEIAES
Reliability assessment is a needed assessment in today's world. It is required not only for system design but also to ensure the power delivered reaches the consumer. It is usual for fault to occur, but it is best if the fault can be predicted and the way to overcome it can be prepared in advance. Monte Carlo simulation is a standard method of assessing reliability since it is a time-based evaluation that nearly represents the actual situation. However, sequential Monte Carlo (SMC) typically took long-time simulation. A convergence element can be implemented into the simulation to ensure that the time taken to compute the simulation can be reduced. The SMC can be done with and without convergence. SMC with convergence has high accuracy compared to the SMC without convergence, as it takes a long time and has a high possibility of not getting accurate output. In this research, the SMC is subjected to five different convergence items to determine which converge simulation is the fastest while providing better performance for reliability evaluation. There are two types of convergence positions, namely input convergence and output convergence. Overall, output convergence shows the best result compared to input convergence.
Integrating Fault Tolerant Scheme With Feedback Control Scheduling Algorithm ...ijics
In order to provide Quality of Service (QoS) in open and unpredictable environment, Feedback based
Control Scheduling Algorithm (FCSA) is designed to keep the processor utilization at the scheduling
utilization bound. FCSA controls CPU utilization by assigning task periods that optimize overall control
performance, meeting deadlines even if the task execution time is unpredictable and through performance
control feedback loop.
Environmental Stress Screening (ESS) is performed on most of the Electrical/Electronic products. However Failure Rate/Time distribution analysis is not conducted always to evaluate the effectiveness of the Screening Process
An Examination of Effectuation Dimension as Financing Practice of Small and M...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Does Goods and Services Tax (GST) Leads to Indian Economic Development?iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Childhood Factors that influence success in later lifeiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Emotional Intelligence and Work Performance Relationship: A Study on Sales Pe...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Customer’s Acceptance of Internet Banking in Dubaiiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study of Employee Satisfaction relating to Job Security & Working Hours amo...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Consumer Perspectives on Brand Preference: A Choice Based Model Approachiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Student`S Approach towards Social Network Sitesiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Broadcast Management in Nigeria: The systems approach as an imperativeiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study on Retailer’s Perception on Soya Products with Special Reference to T...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study Factors Influence on Organisation Citizenship Behaviour in Corporate ...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Consumers’ Behaviour on Sony Xperia: A Case Study on Bangladeshiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Design of a Balanced Scorecard on Nonprofit Organizations (Study on Yayasan P...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Public Sector Reforms and Outsourcing Services in Nigeria: An Empirical Evalu...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Media Innovations and its Impact on Brand awareness & Considerationiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Customer experience in supermarkets and hypermarkets – A comparative studyiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Social Media and Small Businesses: A Combinational Strategic Approach under t...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Secretarial Performance and the Gender Question (A Study of Selected Tertiary...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Implementation of Quality Management principles at Zimbabwe Open University (...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Organizational Conflicts Management In Selected Organizaions In Lagos State, ...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Application of Lifetime Models in Maintenance (Case Study: Thermal Electricity Generation in Sudan)
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 6 Ver. V (Nov. - Dec. 2015), PP 26-39
www.iosrjournals.org
DOI: 10.9790/5728-11652639 www.iosrjournals.org 26 | Page
Application of Lifetime Models in Maintenance (Case Study:
Thermal Electricity Generation in Sudan)
Mohammedelameen Eissa Qurashi1
*, Ahamed Mohamed Abdalla Hamdi2
1, 2
Sudan University of Science & Technology, Faculty of Science, Department of Statistics
Abstract: The main objective of this paper is that to apply lifetime models on the fault of thermal electricity
generation in Sudan to predict faults and failures during period of working and increase its lifetime to insure
electricity production sustainability and reducing maintenance cost. Lifetimes data has been taken from Bahri
Thermal Station for electricity generation, which is, belong to the National Electricity Authority in Sudan during
the period (2011-2015). Through the lifetime models estimation fault distribution, reliability, hazard rate,
availability and MTBF have been calculated for the five machines from analysis; it is clear that, fault time for
all machines follow Weibull distribution with 2-parapmeters. The machines no (3, 4 and 6) have high reliability
whereas the machines no (1 and 5) have low reliability, when we predict the reliability according to the time we
found the that the reliability decrease and hazard rate increase and there is relationship between MTBF and
reliability.
Keywords: Lifetime, Reliability, Failure, Fault rate, Hazard rate, Weibull, Maintenance, MTBF
I. Introduction:
The concept of maintenance in the past was limited to reform, which followed the machine was out of
work. The maintenance was synonymous with reform that concerned with what has been corrupted when
actually there was fault. The causes of the fault were not discovered until it repeated and took a period of time.
After the Second World War the tough focused on controlling of maintenance expenses using mathematical
models, now the practical application revealed the ineffectiveness of many of these models and they have been
changed with more advanced models.
The machines maintenance system considered the safety gateway to authenticate the electricity
generation stability; it serves as the guard who prevents the machine from the sudden faults and plays the role on
the stability and safety of the machine which it has significant impact on reduction of production and operational
costs and it result positively in the economy activity. The research problem is that, there is no stochastic models
application for the lifetime, reliability and failure to predict failures that occur for the machines and the
consequent of technical malfunctions of the machines, which made its power, run of for the consumer and it
raise production and operational costs, which reflect on economic development
The objectives of the study are to apply lifetime models on the electricity generation machines in
Sudan, study reliability and failure model, study of probability distributions, which used in the lifetime and
compare them in terms of preference.
The data of this study have been collocated for five machines with exceptional to the machine no(2)
because it did never got fault in duration of the study. The sample size has been determine according to the
method that not tided to the number of time of failure occurs condition for each machine. The technical fault
data collected from the efficiency department in the station and it was (failure time) during the period (2011-
2015). There are two types of faults; mechanical faults and the faults due to preventive maintenance, in this
study, we used the data of mechanical faults.
This study based on the following assumptions:
Applications of lifetime on machines have a positive impact on the electricity stability.
Fault times follows Weibull distribution.
The electricity generating machines have a high reliability.
II. Theoretical Framework:
2.1: Reliability:
Reliability define as the probability of success or the probability that the system will perform it
intended function under specified design limits 1 .
Reliability that is more specific is the probability that a product are part will operate properly for
specified period of time (design life) under the design operating condition without feature. In other words,
reliability may be used as measure of the systems success in providing, it is function properly. Reliability is
once of quality characteristics that consumer require form the menu facture of products.
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DOI: 10.9790/5728-11652639 www.iosrjournals.org 27 | Page
Mathematically: reliability R(t) is the probability that a system will be successful in the interval from time 0 to
time t:
( ) ( )R t P T t 0t ……………………(1)
Where T is a random variable denoting the time -to-failure or failure time.
Unreliability F(t), a measure of failure, is defined as the probability that the system will fail by time t:
( ) ( )F t P T t for 0t
In the other words, F(t) is the failure distribution function. If the time-To-failure random variable T has a density
function f(t) , then
( ) ( )
t
R t f s ds
……………………….(2)
or, equivalently
( ) ( )
d
f t R t
dt
The density function can be mathematically described in terms of T as:
0
lim ( )
t
p t T t t
……………………..(3)
This can be interpreted as the probability that the failure time T will occur between the operating time t and the
next interval of operation, .
Consider new and successfully tested system that operates well when put into service at time 0t , the system
becomes less likely to remain successful as the time interval of course, is zero 1 .
2.2: Fault Rate:
The possibility of fault machine in specific time period 1t and 2t can be expressed with following non
reliability, equation 2 .
2 1 2
1
1 2( ) ( ) ( ) ( ) ( )
t t t
t
f t dt f t dt f t dt F t F t
or can be expressed with reliability
2
1 1 2
1 2( ) ( ) ( ) ( ) ( )
t
t t t
f t dt f t dt f t dt R t R t
The rate that a fault took place with in specific period of time is called as "Fault Rate" throughout the period 1t
indicates for no fault in the beginning of period and therefore the equation can be expressed as follows:
2
2 1 1
( ) ( )
( )
R t R t
t t R t
…………………………..(4)
It has been observed that the Fault Rate depend on time if the period 1t denoted as t t the equation (4)
stated as follow:
( ) ( )
. ( )
R t R t t
t R t
…………………………(5)
and means with rate it number of faults in each unit time.
2.3: Hazard Rate:
Define as limits of rate of faults for a period of near-zero equation can be written in the form 2 :
0
( ) ( ) 1 ( )
( ) lim
. ( ) ( )t
R t R t t dR t
h t
t R t R t dt
3. Application of Lifetime Models in Maintenance
DOI: 10.9790/5728-11652639 www.iosrjournals.org 28 | Page
( )
( )
( )
f t
h t
R t
…………………………….(6)
To find out possibility of fault machine it have age t in time period ,t t t written as:
( ).posf h t dt ………………………………(7)
The hazard rate refer to change in rate fault through age of machine. To find out hazard rate for the sample
machines N (machine consisting of n element), we will assume ( )sN t is random variable denotes to number
of machines working successfully at time t thus, the ( )sN t is binomial distribution.
( ) ( ) 1 ( )
.( )
n N n
s
N
P N t n R t R t
N N n
0,1,...,n N
The expected value for ( )sN t :
( ) . ( ) ( )sE N t N R t N t
hence:
( ( )) ( )
( ) sE N t N t
R t
N N
……………………….(8)
and reliability in time t, it is arithmetic mean for rate success in t thus:
( ) ( )
( ) 1 ( ) 1
N t N N t
F t R t
N N
……………….(9)
and rate density fall equal:
( ) 1 ( )
( ) .
dF t dN t
F t
dt N dt
2.4: System Mean Time to Failure:
Suppose that the reliability function for a system is given by R(b), the expected feature time during which a
component is expected to perform success fully, or the system mean time to feature (MTTF) 1 , given by:
0
( )MTTF tf t dt
……………………………..(10)
substituting:
( ) ( )
d
f t R t
dt
From equation (10) and performing integration by part, we obtain:
0
0 0
( ) ( ) ( )MTTF tdt R t tR t R t dt
………………(11)
The first term on the right hand side of above equation equals zero at both limits, since the system must fail after
a finite amount of operating time, therefore, we must have tR(t)→0 as t→∞ so equation (11) becomes:
0
( )MTTF R t dt
………………………………………………….(12)
Thus, MTTF is the definite integral evolution of the reliability function. In general if ( )t is defined as the
failure rate function, then by definition MTTF is not equal to .
The MTTF should be used when the feature time distribution function is specified because the reliability level
implicit by the MTTF depends on the underlying feature time distribution. Although the MTTF measure is one
of the most widely used reliability calculation, it also one of most missed calculations, it has been misinterpreted
as “guaranteed minimum life time".
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2.5: Availability:
Reliability is a measure that requires system success for an entire mission time, no failure or repairs are allowed.
The availability of a system is defined as the probability that the system is successful at time t, mathematically:
system up time
Availability =
system up time+system down time
……………………..(13)
Availability is a measure of success used primarily for repairable system, for non-repairable system availability
A(t) equals reliability R(t). In repairable system A(t) will be equal to or greater then R(t).
The mean time between failures (MTBF) is an important measure in repairable system. This implies that the
system has MTBF is an expected value of the random variable time between failures mathematically.
MTBF=MTTF+MTTR ………………………….(14)
2.6: Weibull distribution Parameters Estimation:
Let 1 2, ,..., nt t t be a random sample from Weibull distribution with p.d.f
1
1 2( , ,..., , , ) t
nf t t t t e
for 0t …………………….(15)
The likelihood function is
1
1 2
1
( , ,..., ) i
nn n
t
n i
i
L t t t t e
1 2
1 1
ln ( , ,..., ) ln ln ( 1) ln
n n
n i i
i i
L t t t n n t t
1 1
ln
ln ln 0
n n
i i
i i
L n
t t t
1
ln
0
ˆ
n
i
i
L n
t
This, the maximum likelihood estimation of and are
1
ˆ
ln
n
i i
n
T
t
……………………………………….(16)
ˆ
ˆ
n
t
……………………………………………(17)
III. Application Aspect:
The application aspect includes to what explained in the theoretical aspect and depending on statistical
software "STATGRAPHIC", we would describe the data , test the distribution of the data , estimate lifetime
models and comparison between machines in fault distribution, Reliability, hazard rate, availability and MTBF.
3.1: Description of Failure Times:
This study will be described for the failure time, for the five machines with some descriptive measures in order
to know the nature of study's data type.
Table (1): Rates of failure times for each machine
Machine Mean(hr) Std. (hr) 95% Confidence Interval for Mean
Lower Bound Upper Bound
Machine no(1) 6.764 9.249 9.249 10.217
Machine no(3) 6.442 9.023 9.023 9.1530
Machine no(4) 6.747 11.808 11.808 9.2630
Machine no(5) 8.528 10.719 10.719 13.545
Machine no(6) 15.451 15.174 15.174 22.552
Mean 7.720 11.374 11.374 9.2980
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6.764
6.442
6.747
8.528
15.451
0
2
4
6
8
10
12
14
16
18
Machine no(1) Machine no(3) Machine no(4) Machine no(5) Machine no(6)
Machines
Failuertime(hr)
Figure (1): Rates of failure times for each machine
From above table and figure, it has shown that according to the mean values for the five machines, the
machine no(6) have the highest mean failure depending on the value of the largest mean (15.45) hours, followed
by machine no(5) depending on the value of the second largest mean (8.53) hours, followed by machine no(1)
depending on the value of the third largest mean (6.76) hours, lastly machines no(1) and (4) are (6.76) and
(6.75) respectively.
3.2: Data distribution Test:
Here we test the following hypothesis:
Ho: The failure data follow Weibull distribution
H1: The failure data not follow Weibull distribution
Table (2): Kolmogorov-Smirnov test for machines
Machine Statistic Sample Size P-value
Machine no(1) 0.23796 30 0.05595
Machine no(3) 0.13482 44 0.47132
Machine no(4) 0.13482 84 0.41859
Machine no(5) 0.27464 23 0.05035
Machine no(6) 0.24790 44 0.14390
From above table, it shows the p-value of Kolmogorov-Smirnov test of all machines is greater than
significant level (0.05) that mean the failures time data follow Weibull distribution with 2-parameters, which
means the underlying distribution of the lifetime model is Weibull
3.3: Lifetime Models for Machine no(1):
The lifetime test has been conducted for machine no(1) for a period of time (100 hours) and the following
measure has been calculated:
Table (3): Results of Lifetime test for machine no(1)
Measure Value
Distribution of fault ( )f t 0.51858
Reliability ( )R t 0.48142
Hazard rate ( )h t 1.07719
Availability ( )A t 0.98
From the table (3), it has shown that:
The probability fault of the machine no(1) is ( 100) 0.51858f t during (100) hours, this indicate the
probability fault of machine no(1) is very high during this period.
The reliability for machine no(1) is weak since ( 100) 0.48142R t , this mean that the probability
for machine to work for (100) hours without fault is (0.48).
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The rate of randomly fault occurred for machine no(1) ( 100) 1.07719h t , this indicate that the rate
that occurred fault randomly during (100) hours is very high.
The probability of available time to repair machine no(1) when it fault is (0.97), this indicate that the
machine has high availability.
Table (4): Life table (times) for machine no(1)
Time
Reliability ( )R t Cum.Hazard ( )h t
0 1.00000 0.0000
100 0.48142 0.7310
200 0.24286 1.4153
300 0.12457 2.0829
400 0.06457 2.7400
500 0.03373 3.3893
600 0.01773 4.0326
From the table (4), it has shown that the reliability decreases whenever the working time of the
machine increase. When the time (t=100) hours the reliability is about (48%), at time (t=200) hours the
reliability is about (24%), at time (t=300) hours the reliability (12%), at time (t=400) hours the reliability is
about (6%), at time (t=500) hours the reliability is about (3%), at time (t=600) hours the reliability is about
(2%). The hazard rate increases whenever the working time increases too.
Estimated Reliability Function
Reliabilityprobability
0 40 80 120 160 200 240
Time
0
0.2
0.4
0.6
0.8
1
Figure (2): Reliability function vs time for machine no(1)
From the figure (2), it has shown that the reliability decreases whenever the working time of the machine
increase in until equal zero.
Estimated Cumulative Hazard Function
0 40 80 120 160 200 240
Time
0
1
2
3
4
cumulativehazard
Figure (3): Cumulative hazard function vs time for machine no(1)
From the figure (3), the hazard function increases whenever the working time increases too.
3.4: Lifetime Model for Machine no(3):
The lifetime test has been conducted for machine no(3) for a period of time (100 hours) and the
following measure has been calculated:
7. Application of Lifetime Models in Maintenance
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Table (5): Results of Lifetime test for machine no(3)
Measure Value
Distribution of fault ( )f t 0.28492
Reliability ( )R t 0.71508
Hazard rate ( )h t 0.39844
Availability ( )A t 0.97
From the table (5), it has shown that:
The probability fault of the machine no(3) is ( 100) 0.28492f t during (100) hours, this indicate that
the probability fault of this machine is low during this period.
The reliability for machine no(3) is ( 100) 0.71508R t it is weak reliability, this mean that the
probability for machine to work for (100) hours without fault is (0.72), the reliability is very high.
The rate of randomly fault occurred for machine no(3) ( 100) 0.39844h t , this indicate that the rate
occurred fault randomly during (100) hours is low.
The probability of available time to repair machine no(3) when it fault is (0.97), this indicate that this
machine has high availability.
Table (6): Life table (times) for machine no(3)
Time
Reliability ( )R t Cum.Hazard ( )h t
0 1.00000 0.0000
100 0.71508 0.3354
200 0.50892 0.6755
300 0.36153 1.0174
400 0.25653 1.3605
500 0.18186 1.7045
600 0.12883 2.0492
From the table (6), it has shown that the reliability decreases whenever the working time of the
machine increase. When the time (t=100) hours the reliability is about (72%), at time (t=200) hours the
reliability is about (51%), at time (t=300) hours the reliability (36%), at time (t=400) hours the reliability is
about (26%), at time (t=500) hours the reliability is about (18%), at time (t=600) hours the reliability is about
(13%). The hazard function increases whenever the working time increases too.
Estimated Reliability Function
0 100 200 300 400
Time
0
0.2
0.4
0.6
0.8
1
survivalprobability
Figure (4): Reliability function vs time for machine no(3)
From the figure (4), it has shown that the reliability decreases whenever the working time of the machine
increase in until equal zero.
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Estimated Cumulative Hazard Function
0 100 200 300 400
Time
0
1
2
3
4
cumulativehazard
Figure (5): Cumulative hazard function vs time for machine no(3)
From the figure (5), the hazard function increases whenever the working time increases too.
3.5: Lifetime Model for Machine no(4):
The lifetime model has been conducted for machine (4) for a period of time (100 hours) and the following
measure has been calculated:
Table (7): Results of Life time test for machine no(4)
Measure Value
Distribution of fault ( )f t 0.37294
Reliability ( )R t 0.62706
Hazard rate ( )h t 0.59474
Availability ( )A t 0.99000
From the table (7), it has shown that:
The probability fault of the machine no(4) is ( 100) 0.37294f t during (100) hours, this indicate that
the probability fault of this machine (4) is low during this period.
The reliability for machine no(4) is ( 100) 0.62706R t it is high reliability, this mean that the
probability for machine to work for (100) hours without fault is (0.63), the reliability is very high.
The rate of randomly fault occurred for machine no(4) ( 100) 0.59474h t , this indicate that the rate
that occurred fault randomly during (100) hours is middle .
The probability of available time to repair machine no(1) when it fault is (0.99), this indicate that the
machine has high availability.
Table (8): Life Tables (Times) for machine no(4)
Time
Reliability ( )R t Cum.Hazard ( )h t
0 1.00000 0.0000
100 0.62706 0.5947
200 0.44404 0.8118
300 0.32552 1.1223
400 0.24360 1.4122
500 0.18494 1.6877
600 0.14195 1.9523
From the table (8), it has shown that the reliability decreases whenever the working time of the
machine increase. When the time (t=100) hours the reliability is about (63%), at time (t=200) hours the
reliability is about (44%), at time (t=300) hours the reliability (33%), at time (t=400) hours the reliability is
about (24%), at time (t=500) hours the reliability is about (18%), at time (t=600) hours the reliability is about
(14%). The hazard function increases whenever the working time increases too.
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Estimated Reliability Function
0 100 200 300 400 500 600
Time
0
0.2
0.4
0.6
0.8
1
survivalprobability
Figure (6): Reliability function vs time for machine no(4)
From the figure (6), it has shown that the reliability decreases whenever the working time of the machine
increase.
Estimated Cumulative Hazard Function
0 100 200 300 400 500 600
Time
0
1
2
3
4
5
cumulativehazard
Figure (7): hazard function vs time for machine no(4)
From the figure (7), the hazard function increases whenever the working time increases too.
3.6: Lifetime Model for Machine no(5):
The lifetime model has been conducted for machine no(5) for a period of time (100) hours and the following
measure has been calculated:
Table (9): Measures of lifetime model for machine no(5)
Measure Value
Distribution of fault ( )f t 0.52511
Reliability ( )R t 0.47489
Hazard rate ( )h t 1.10575
Availability ( )A t 0.99
From the table (9), it has shown that:
The probability fault of the machine no(5) is ( 100) 0.52511f t during (100) hours, this indicate that
the probability fault of this machine is low during this period.
The reliability for machine no(5) is ( 100) 0.47489R t it is high reliability, this mean that the
probability for machine to work for (100) hours without fault is (0.47), the reliability is weak.
The rate of randomly fault occurred for machine no(5) ( 100) 1.10575h t , this indicate that the rate
that occurred fault randomly during (100) hours is very high.
The probability of available time to repair machine no(5) when it fault is (0.99), this indicate that this
machine has high availability.
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Table (10): Lifetable (times) for machine no(5)
Time
Reliability ( )R t Cum.Hazard ( )h t
0 1.00000 0.0000
100 0.47489 1.1058
200 0.24683 1.3991
300 0.13223 2.0232
400 0.07219 2.6285
500 0.03995 3.2202
600 0.02235 3.8011
From the table (10), it has shown that the reliability decreases whenever the working time of the
machine increase. When the time (t=100) hours the reliability is about (47%), at time (t=200) hours the
reliability is about (25%), at time (t=300) hours the reliability (13%), at time (t=400) hours the reliability is
about (7%), at time (t=500) hours the reliability is about (4%), at time (t=600) hours the reliability is about
(2%). The hazard function increases whenever the working time increases too.
Estimated ReliabilityFunction
0 40 80 120 160 200
Time
0
0.2
0.4
0.6
0.8
1
survivalprobability
Figure (8): Reliability function vs time for machine no(5)
From the figure (8), it has shown that the reliability decreases whenever the working time of the machine
increase.
Estimated Cumulative Hazard Function
0 40 80 120 160 200
Time
0
1
2
3
4
cumulativehazard
Figure (9): Hazard function vs time for machine no(5)
From the figure (9), the hazard function increases whenever the working time increases too.
3.7: Lifetime Model for Machine no(6):
The lifetime model has been conducted for machine no(6) for a period of time (100 hours) and the following
measure has been calculated:
Table (11): Measures of lifetime Model for Machine no(6)
Measure Value
Distribution of fault ( )f t 0.25874
Reliability ( )R t 0.74126
Hazard rate ( )h t 0.34905
11. Application of Lifetime Models in Maintenance
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Availability ( )A t 0.97000
From the table (11), it has shown that:
The probability fault of the machine no(6) is ( 100) 0.25874f t during (100) hours, this indicate that
the probability fault of this machine is high during this period.
The reliability for machine no(4) is ( 100) 0.74126R t it is weak reliability, this mean that the
probability for machine to work for (100) hours without fault is (0.74), the reliability is very high.
The rate of randomly fault occurred for machine no(6) ( 100) 0.349054h t , this indicate that the rate
that occurred fault randomly during (100) hours is very weak.
The probability of available time to repair machine no(6) when it fault is (0.97), this indicate that this
machine has high availability.
Table (12): Lifetable (times) for machine no(6)
Time
Reliability ( )R t Cum.Hazard ( )h t
0 1.00000 0.0000
100 0.74126 1.1058
200 0.48040 0.7331
300 0.28999 1.2379
400 0.16610 1.7952
500 0.09117 2.3951
600 0.04826 3.0312
From the table (12), it has shown that the reliability decreases whenever the working time of the
machine increase. When the time (t=100) hours the reliability is about (74%), at time (t=200) hours the
reliability is about (48%), at time (t=300) hours the reliability (29%), at time (t=400) hours the reliability is
about (17%), at time (t=500) hours the reliability is about (9%), at time (t=600) hours the reliability is about
(5%). The hazard function increases whenever the working time increases too.
Estimated Reliability Function
0 100 200 300 400
Time
0
0.2
0.4
0.6
0.8
1
survivalprobability
Figure (10): Reliability function vs time for machine no(6)
From the figure (10), it has shown that the reliability decreases whenever the working time of the machine
increase.
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Estimated Cumulative Hazard Function
0 100 200 300 400
Time
0
0.5
1
1.5
2
2.5
3
cumulativehazard
Figure (11): Hazard function vs time for machine no(6)
From the figure (11), the hazard function increases whenever the working time increases too.
3.8: Comparison between Machines:
We compare the five machines according to lifetime model, the comparison was among the following measures
probability of fault, reliability, hazard rate and availiability:
Table (13): Lifetime models comparison
( )A t( )h t( )R t( )f tmachine
0.981.077190.481420.51858Machine no(1)
0.970.398440.715080.28492Machine no(3)
0.990.594740.627060.37294Machine no(4)
0.991.105750.474890.52511Machine no(5)
0.970.349050.741260.25874Machine no(6)
0.48142
0.71508
0.62706
0.47489
0.74126
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Machine no(1) Machine no(3) Machine no(4) Machine no(5) Machine no(6)
Machines
Reliability
Figure (12): Reliability vs machines
Form above table and figure we note that ,the machines no (3,4 and 6) have high reliability and the
machines no (1 and 5) have low reliability, the machines with high reliability have a low faults probability and
hazard rate but the machines with low reliability have high faults probability and hazard rate.
Table (14): MTBF and reliability comparison
( )R tMTBFMachine
0.481426.70036Machine no(1)
0.715088.37763Machine no(3)
0.627066.18406Machine no(4)
0.474897.95355Machine no(5)
0.7412616.5139Machine no(6)
13. Application of Lifetime Models in Maintenance
DOI: 10.9790/5728-11652639 www.iosrjournals.org 38 | Page
From above table , we note that whenever mean time between renewals (repairable) increseased the reliability
increased too and that appear clearly in the machinen no(6) result which its mean between renewals is
approximately (17 hours) and the reliability (0.74).
IV. Conclusions:
The main findings of this paper are:
1. Fault time of machines follows Weibull distribution with 2-parameters which means the underlying
distribution of the lifetime model is Weibull
2. When operation time of machines increase the performance decreased or the machine got fault.
3. The machines no (3, 4 and 6) have high reliability and the machines no (1 and 5) have low reliability.
4. The hazard rate of machines increase according to the time.
5. The machines with high reliability have a low faults probability and hazard rate but the machines with low
reliability have high faults probability and hazard rate.
6. 6. Whenever mean time between failures (MTBF) for machines increase that indicate the machine has
high reliability.
7. All the machines have high availability.
Acknowledgement:
I would take this opportunity to thank my research supervisor Dr. Ahamed Mohamed Abdalla Hamdi.
Special thanks to our great teacher and my idle role Also my thanks to(Dr. Bassam Younis Ibrahim Ahamed,
Head of Statistics & Research Section Strategic Planning Division Abu Dhabi,UAE) Engineer Khalid Eltahir
Abdall-Basit and my friend Mr. Mohammed Omer Musa for their support and guidance without which this
research would not have been possible.
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APPENDIX
Failure data for five machines during period (2011-2015)
Failure time
Machine no(6)Machine no(5)Machine no(4)Machine no(3)Machine no(1)
245.980.957680
288528244848
1.73482419224
65.87160864810081704
7.775.98120240504
35.4352824010.9848
11.85481207214.38
20.78160826424962.20