Analysis of discrete-time semi-Markov model for a two-unit warm standby system subject to degradation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Neama Temraz
Keyword(s):  
Markov Model ◽  
Weibull Distribution ◽  
Discrete Time ◽  
Content Type ◽  
Regenerative Point ◽  
Semi Markov Process ◽  
Regenerative Point Technique ◽  
The Mathematical Model ◽  
Mean Time ◽  
Warm Standby

PurposeThe present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.Design/methodology/approachThe semi-Markov model under the regenerative method is used to construct the mathematical model for the system.FindingsThe effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.Originality/valueRarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

Inspecting Briquette Machine with Different Faults

2020 ◽  
Vol 13 ◽  
Author(s):  
Divesh Garg ◽  
Reena Garg ◽  
Vanita Garg
Keyword(s):  
Failure Rate ◽  
Rate Increase ◽  
Practical Importance ◽  
System Failure ◽  
Regenerative Point ◽  
Semi Markov Process ◽  
Major Fault ◽  
Environment Study ◽  
Burning Coal ◽  
Mean Time

Background: A briquette machine can be considered very useful in modern times as the need of energy consumption is increasing rapidly. Considering the harm to environment, study of briquette machine is the need of present times. In this paper, the operative unit is considered as briquette machine also known as bio-coal which is used for agroforestry waste. Objective: A single operative unit has been analyzed stochastically. The inspection of breakdown of a unit reveals the feasibility of the unit under the supervision of either ordinary or expert repairmen. Two types of fault are revealed by the repairmen either minor or major fault. Minor faults are repaired immediately by the same repairmen but whenever major fault held, the machine’s fault will be handled by expert person. Method: It is assumed that the repair needs no modification once served. Availability, Mean-time for system failure, and profits are analyzed by utilizing the Regenerative point graphical technique and semi-Markov process. Result: Study reveals that the Mean-time for system failure of the system model go on decreasing as failure rate increase and availability goes on decreasing as failure-rate increase. Moreover, the study shows that the systems profit goes down on increase of Failure-rate. Conclusion: Findings of the study supports the hypothesis that the limits of failure/repair/inspection rate will surely have effective profitability. Moreover, it is found that the utility of scale of operation can easily be derived. The practical importance of biomass briquettes for burning coal or wood is very well appreciated.

Multi-state failure phenomenon and analysis using semi-Markov model

2018 ◽  
Vol 35 (9) ◽  
pp. 2080-2091 ◽  
Author(s):  
Mahesh Narayan Dhawalikar ◽  
V. Mariappan ◽  
P.K. Srividhya ◽  
Vishal Kurtikar
Keyword(s):  
Markov Model ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Failure Rate ◽  
Degradation Process ◽  
Markov Modeling ◽  
Content Type ◽  
Availability Analysis ◽  
Unique Approach ◽  
Reliability And Availability

Purpose Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution. Design/methodology/approach The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair. Findings The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable. Research limitations/implications The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1. Practical implications These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems. Originality/value A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

RELIABILITY MEASURES OF A COLD STANDBY SYSTEM WITH PREVENTIVE MAINTENANCE AND REPAIR

2013 ◽  
Vol 20 (06) ◽  
pp. 1350022 ◽  
Author(s):  
S. C. MALIK ◽  
SUDESH K. BARAK
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Reliability Measures ◽  
Maintenance And Repair ◽  
Regenerative Point ◽  
Cold Standby ◽  
Semi Markov Process ◽  
Standby System ◽  
Regenerative Point Technique ◽  
Negative Exponential

The purpose of the present study is to determine reliability measures of a two-unit cold standby system with preventive maintenance and repair. The units are identical in nature subject to constant failure from normal mode. Preventive maintenance of the operative unit is carried out after a pre-specific time "t" up to which no failure occurs. However, repair of the unit is done at its failure. The unit works as new after repair and preventive maintenance. The switch devices are perfect. The distributions of failure time and the time by which unit undergoes for preventive maintenance are taken as negative exponential while that of preventive maintenance and repair times are assumed as arbitrary with different probability density functions. The random variables associated with failure, preventive maintenance and repair times are statistically independent. The semi-Markov process and regenerative point technique are adopted to derive the expressions for system performance measures in steady state. The graphical behavior of MTSF, availability and profit function have been observed with respect to preventive maintenance rate for particular values of other parameters and costs.

scholarly journals STOCHASTIC MODELING AND SENSITIVITY ANALYSIS OF AN INTEGRATED HARDWARE-SOFTWARE SYSTEM SUBJECT TO DIFFERENT WEATHER CONDITIONS

2021 ◽  
Vol 40 (3) ◽  
pp. 54-63
Author(s):  
Monika Saini ◽  
Ashish Kumar
Keyword(s):  
Sensitivity Analysis ◽  
Model Development ◽  
Weather Conditions ◽  
Time Dependent ◽  
Process Time ◽  
Software System ◽  
Hardware Failure ◽  
Regenerative Point ◽  
Semi Markov Process ◽  
Regenerative Point Technique

The current study covenants with stochastic investigation of an integrated hardware-software system considering hardware failure, software up-gradation upon failure, precautionary maintenance (PM) after a pre-determined process time, maximum repair time of hardware and different weather conditions. All time dependent indiscriminate variables are arbitrarily dispersed. Some important reliability measures like MTSF, availability and revenue of the system are obtained by using well established techniques semi-Markov process. Regenerative point technique has also been taken into consideration during model development. Sensitivity analysis of these measures is also performed. Finally, empirical analysis is done to demonstrate the results for a specific case. To climax the significance of the study, graphs of MTSF, availability, profit and sensitivity are also depicted.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

scholarly journals DTHMM ExaLB: discrete-time hidden Markov model for load balancing in distributed exascale computing environment

2020 ◽  
Vol 7 (1) ◽  
pp. 1743404
Author(s):  
Ulphat Bakhishoff ◽  
Ehsan Mousavi Khaneghah ◽  
Araz R. Aliev ◽  
Amirhossein Reyhani Showkatabadi ◽  
Stefania Tomasiello
Keyword(s):  
Load Balancing ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Discrete Time ◽  
Hidden Markov ◽  
Computing Environment ◽  
Exascale Computing

SIMULTANEOUS CALIBRATION TO A RANGE OF PORTFOLIO CREDIT DERIVATIVES WITH A DYNAMIC DISCRETE-TIME MULTI-STEP MARKOV LOSS MODEL

2009 ◽  
Vol 12 (05) ◽  
pp. 633-662 ◽  
Author(s):  
MICHAEL B. WALKER
Keyword(s):  
Linear Programming ◽  
Markov Model ◽  
Discrete Time ◽  
Credit Derivatives ◽  
Surface Model ◽  
Relevant Market ◽  
Market Prices ◽  
Credit Portfolio ◽  
Portfolio Credit Derivatives ◽  
Static Loss

This article describes a dynamic discrete-time multi-step Markov model for the losses experienced by a given credit portfolio, and develops a method for the simultaneous calibration of the model to all available relevant market prices (for CDO's, forward-start CDO's, options on CDO's, leveraged super-senior tranches with loss triggers, etc.) established on a given day. The implementation is via an efficient linear programming procedure, and examples are given. The approach represents an extension of previous work (Walker, 2005, 2006; Torresetti et al., 2006) on the static loss-surface model to a model containing the necessary underlying dynamics.

Fractional order plasma modeling based on linear polarization of LASER light: an Atangana–Baleanu Caputo approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tamour Zubair ◽  
Muhammad Usman ◽  
Tiao Lu
Keyword(s):  
Fractional Order ◽  
Numerical Algorithm ◽  
Laser Light ◽  
Spectral Estimation ◽  
Initial Perturbation ◽  
Physical Analysis ◽  
Content Type ◽  
Specific Geometry ◽  
The Mathematical Model ◽  
Time Evaluation

PurposeThe purpose of this offered research is to articulate a multifaceted kind of highly unstable initial perturbation and further analyze the performance of the plasma particles for time-fractional order evaluation.Design/methodology/approachFor this purpose, the authors designed specific geometry and further interpreted it into the mathematical model using the concepts of the Vlasov Maxwell system. The suggested algorithm is based on the finite-difference and spectral estimation philosophy. The management of time and memory in generic code for computational purposes is also discussed.FindingsThe main purpose is to analyze the fractional behavior of plasma particles and also the capability of the suggested numerical algorithm. Due to initial perturbations, there are a lot of sudden variations that occurred in the formulated system. Graphical behavior shows that SR parameter produces devastation as compared to others. The variation of fractional parameter between the defend domain demonstrates the hidden pictures of plasma particles. The design scheme is efficient, convergent and has the capability to cover the better physics of the problem.Practical implicationsPlasma material is commonly used in different areas of science. Therefore, in this paper, the authors increase the capability of the mathematical plasma model with specific geometry, and further suitable numerical algorithm is suggested with detailed physical analysis of the outcomes. The authors gave a new direction to study the performance of plasma particles under the influence of LASER light.Originality/valueIn the recent era, science has produced a lot of advancements to study and analyze the physical natural process, which exist everywhere in the real word. On behalf of this current developments, it is now insufficient to study the first-order time evaluation of the plasma particles. One needs to be more precise and should move toward the bottomless state of it, that is, macroscopic and microscopic time-evaluation scales, and it is not wrong to say that there exits a huge gap, to study the time evaluation in this discussed manner. The presented study is entirely an advanced and efficient way to investigate the problem into the new directions. The capability of the proposed algorithm and model with fractional concepts can fascinate the reader to extend to the other dimensions.

Development of a direct NGM(1,1) prediction model based on interval grey numbers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ye Li ◽  
Yuanping Ding ◽  
Yaqian Jing ◽  
Sandang Guo
Keyword(s):  
Genetic Algorithm ◽  
Markov Model ◽  
Prediction Model ◽  
Real Number ◽  
Content Type ◽  
Optimal Weight ◽  
Practical Applications ◽  
Number Sequences ◽  
Integral Development ◽  
Grey Number

PurposeThe purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.Design/methodology/approachA definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.FindingsThe interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.Practical implicationsUncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.Originality/valueThe main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

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