Markov Birth-death Process Research Articles

Economic and Energetic Performance Evaluation of Unreliable Production Lines: An Integrated Analytical Approach

The current context is increasingly driving researchers and industry to focus not only on the economic but also on the energetic performance of manufacturing systems. However, considerable work on the enhancement of energetic performance of complex production systems is still needed. This paper addresses a novel integrated analytical method to evaluate simultaneously the economic and energetic performances of a serial production line composed of unreliable machines and intermediate buffers. This approach is based on a discrete Markov chain formulation of machines states transitions and a birth-death Markov process for buffers states evaluation. It introduces throughput, energy consumption and energy efficiency as key performance indicators for assessing economic and energetic performances. Structural characteristics of the problem are analyzed to establish and evaluate the impact of buffers size, reliability parameters, and production rates of the machines on the energetic performance of the production line. A large experimental study, based on different instances inspired by the literature, is carried out to analyze the behavior and the complex trade-off between throughput and energy efficiency performances.

Stochastic modelling and availability analysis of a critical engineering system

Purpose The purpose of this paper is to present the technique for evaluating the performance of a condensate system of a coal-based thermal power plant situated in the northern part of India. The data which used for system availability evaluation are not precise and are uncertain and, further, collected from concerned power plant history sheets and from discussion through plant personnel. Design/methodology/approach In the proposed model, traditional Markov birth-death process using a probabilistic approach is used to analyze the performance of a complex repairable condensate system of power plant up to a desired degree of accuracy. This approach has been demonstrated by breaking the condensate system into six subsystems arranged in series with two feasible states, namely, working and failed, labeled in a transition diagram and modeled as a Markov process, using Chapman–Kolmogorov equations, which are used for development of a probabilistic stochastic model for availability analysis in a more effecting manner, considering some suitable assumptions. Findings This study of analysis of reliability and availability can help in increasing the plant production and performance. The analysis is done with the help of availability matrices, which are developed using different combinations of failures and repair rates of all subsystems. To achieve the goal of maximum power generation, it is required to run the various subsystem of the concerned system of plant, failure free for a long duration. Therefore, the present approach may be a more powerful analysis tool to access the performance of all subsystems of a condensate system in terms of availability level achieved in availability matrices. The results of present study are found to be highly beneficial to the plant management for making maintenance decisions. Originality/value The present paper suggests a suitable technique for stochastic modeling and availability evaluation of an industrial system using Markovian approach and drawing a transition diagram to represent the operational behavior of the system. The present methodology includes the advantage of the ability to model and develop a more complex industrial system and helps in improving the performance and handling the uncertainties and possibilities of an industrial system.

Performance analysis of evaporation system in sugar industry using RAMD analysis

The main aim of this study is to analyze the application of reliability, availability, maintainability and dependability in identification of most sensitive subsystem of evaporation system in sugar plant. For this analysis, transition diagram of all subsystems is drawn and respective Chapman–Kolmogorov differential equations are derived using Markov birth–death process. All failure and repair rates of each subsystem are exponentially distributed. Various measures of system effectiveness like mean time between failures, mean time to repair and dependability ratio for all the three subsystems are also computed. Sensitivity analysis of system reliability is also performed. The reliability and maintainability are estimated at various time instants. Analysis of all the subsystems shows that sulphited syrup is highly sensitive from reliability point of view. The derived measures are shared with system designers for their active deliberation.

Asymptotically Maximal Throughput in Tandem Systems with Flexible and Dedicated Servers

For a system of two tandem queues with a finite intermediate buffer, we study the asymptotically maximal throughput as the number of servers in each station grows to infinity. First, we study the system with only dedicated servers, and then we examine the system with both dedicated and flexible servers. We assume that travel times between the two stations are negligible and that each server can only work on one customer at a time. We model the system as a birth–death Markov process, derive a closed form solution for the stationary distribution, and quantify the maximal asymptotic normalized throughput as the number of servers grows to infinity. We show that flexibility is more favorable for small systems, and as the number of servers grows, the benefits of flexibility decrease. Furthermore, we prove that when the number of servers goes to infinity, there is no need of flexibility at all, as the maximum value of the throughput is obtained. However, flexibility still has a secondary beneficial effect — a little flexibility (on the order of the square root of the number of dedicated servers at each station) guarantees that all dedicated servers are busy and results in faster convergence to the maximum throughput.

Mathematical modeling of sugar plant: a fuzzy approach

Conventional reliability of a system is defined as the probability that it can perform a pre-specific function without failure in a pre-fixed time interval under a predefined environment. It is based on the assumption that system’s failure behavior is characterized in probabilistic context and binary-state assumption for the demonstration of the states. At any time, the system is either in failed or operative state. But, this assumption seems unrealistic for large complex industrial systems. The uncertainty of each component enhances the uncertainty of the whole system. In this paper, the concept of fuzzy reliability has been used for the analysis of fuzzy availability of a sugar plant. The effect of coverage factor, failure and repair rates of subsystems on systems fuzzy availability had been analyzed. Chapman–Kolmogorov differential equations have been derived with the help of Markov birth–death process. The governing differential equations are solved by Runge–Kutta method of order four using MATLAB (Ode 45 function).

Availability comparison between three dissimi-lar photovoltaic configurations

The paper deals with availability comparison between three dissimilar photovoltaic configurations using Markov Birth-Death process and probabilistic approach. The configurations consist of four subsystems arranged in series-parallel with three possible states; working with full capacity, reduced capacity and failed. Through the transition diagrams, systems of differential equations are developed and solved recur-sively via probabilistic approach. Explicit expressions for steady-state availability are derived. Availability matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. Furthermore, we compare the availability for the three configurations and find that configuration III is more reliable than system, I and II. The results have shown that the system availability increases with increase in redundant units. The results of this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimization.

Markov chain approach to availability and profit evaluation of a series-parallel system with minor and major failures

The paper deals with modeling and performance evaluation of a series-parallel with independent failures using Markov Birth-Death process and probabilistic approach. The system consists of three subsystems arranged in series and parallel configurations with three possible states, working, reduced capacity and failed. Through the transition diagram, systems of differential equations are developed and solved recursively via probabilistic approach. Failure and repair rates for all the subsystems are assumed constant. Availability and profit matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. Performance of each subsystem of series-parallel system is evaluated. The present study will help the plant management in understanding the optimum system availability and profit to be achieved, and the maintenance efforts needed to maintain an appropriate level of availability and profit and useful for timely execution of proper maintenance improvement, decision, planning and optimization.

Probabilistic approach to performance evaluation of a series-parallel system

The paper deals with modeling and performance evaluation of a series-parallel system using Markov Birth-Death process and probabilistic approach. The system consists of four subsystems arranged in series-parallel with three possible states, working with full capacity, reduced capacity and failed. Through the transition diagrams, systems of differential equations are developed and solved recursively via probabilistic approach. Explicit expressions for steady-state availability are de-rived. Availability matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. The results from this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimization.

Reliability analysis and performance optimisation of the serial process in refining system of a sugar plant

This paper deals with the reliability analysis and performance optimisation of a refining system. The refining system is a complex system and comprises of four repairable subsystems connected in series or parallel configurations. Two subsystems namely filter and sulphonation are supported by standby units with perfect switch over devices. The mathematical modelling of the system based on Markov birth-death process is carried out to derive Chapman-Kolmogorov differential equations with the assumption that the failure and repair rate of each subsystem follows exponential distribution. These equations are solved by using an adaptive step-size control Runge-Kutta method to compute the reliability of the system and steady state availability is calculated using normalising condition, initial boundary conditions and recursive method. The performance of the system is optimised with genetic algorithm. It has been found that the subsystem heater is the most critical and has more impact on performance of the system as compare to other subsystems. The results are highly beneficial to the maintenance personnel for the purpose of effective maintenance planning to enhance the overall performance of the refining system.

Performance modeling of the serial processes in refining system of a sugar plant using RAMD analysis

The main objective of this paper is to present a method to identify the critical component of the system. As traditionally, any one parameter among availability, reliability and maintainability parameters is computed to identify the critical component and its effect on performance of the system. In this paper, reliability, availability, maintainability and dependability (RAMD) parameters or indices are computed to identify the critical component of the system. Mathematical modeling of the system based on Markov birth–death process is carried out to derive Chapman–Kolmogorov differential equations. These equations are further solved and RAMD parameters are computed with mean time between failures (MTBF), mean time to repair (MTTR) and dependability ratio parameters for each component of the system. Sensitivity analysis has been conducted for finding the most critical component of the system by varying the failure and repair rates of each subsystem of the system. To show the application of the proposed method, a case of the refining system, a repairable industrial system of sugar plant has been taken for evaluating RAMD indices of the system.

Simulation and Economic Analysis of Coal Based Thermal Power Plant: A Critical Literature Review

Coal based fired power plant is a very complex unit. Today’s electric energy is playing an important role in the industrial and all-round development of every country. It is desired form of energy, because it can be produced easily and transmitted economically. Further, it can be used efficiently and easily to domestic and industrial applications. Performance evaluation of such units is becoming important because of increasing costs, competition and public demand on one way, while the risk of failure on the other. The failure-free operation of production unit seems to be impossible; also the failure occurrence is nearly an unavoidable phenomenon for all repairable industrial units and cannot be prevented completely. So, its impact and probability of occurrence should be minimized as much as possible. To increase the working time or maintain failure free operation of the plant for a long duration, it is necessary to maintain the plant at higher operational availability level. Thus working time can be increased by implementing the stand by systems parallel to active system in the plant. Formulation of the problem is carried out using Markov Birth-Death process using probabilistic approach and a transition diagram represents the operational behavior of the systems. The successful completion of a thermal power plant requires estimation of the fixed and variable costs involved in the project. The economic analysis of the coal based thermal power plant can be done on the basis of initial capital investment or fixed cost, operating cost and annual revenue.

Reliability and availability analysis of the serial processes in skim milk powder system of a dairy plant: a case study

In this paper, a numerical method is proposed to compute the long run availability and reliability with mean time between failures (MTBF) for skim milk powder system of a dairy plant. It is a complex system and comprises of six repairable subsystems viz. chiller, cream separator, pasteuriser, evaporator, drying chamber and packaging sub-systems arranged in series or parallel configurations. This analysis is based on Markov birth-death process and by assuming that the failure and repair rate of each subsystem follows exponential distribution. Mathematical formulation of the system is carried out and Chapman-Kolmogorov differential equations are derived, a numerical method, i.e., Runge-Kutta fourth order method is used to solve these differential equations. The results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the productivity of skim milk powder system.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

The advection diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in river streams. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well-suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection diffusion equation for particle activity. Yet, while this derivation is formally valid in the continuum limit, it runs into difficulty in the practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particles velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particles displacement and the dimensions of the measurement system.

Mathematical modeling and reliability analysis of the serial processes in feeding system of a sugar plant

In this paper, a numerical method is proposed for the reliability analysis of serial processes in the feeding system of a sugar plant. The feeding system is a complex system and comprises of four repairable sub-systems viz. cutting system, crushing system, bagasse carrying system and heat generating system arranged in series or parallel configurations. Three sub-systems namely cutting system, bagasse carrying system and heat generating system are supported by standby units with perfect switch over devices. Mathematical modeling of the system based on Markov birth–death process is carried out to derive Chapman–Kolmogorov differential equations. These equations are solved by using the proposed method i.e. an adaptive step-size control Runge–Kutta method. The long-run availability, reliability and mean time between failures (MTBF) for the system are computed for performance analysis of the system. These results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the feeding system of sugar plant.

Performance modeling of the skim milk powder production system of a dairy plant using RAMD analysis

Purpose – The purpose of this paper is to propose a method to compute RAMD indices to measure and improve the performance of skim milk powder production system of a dairy plant under real working conditions. Design/methodology/approach – The present work is carried out by developing performance model based on Markov birth-death process. The skim milk powder production system consists of six units. The first order governing differential equations are derived using the mnemonic rule and further solved to calculate RAMD indices i.e. reliability, availability, maintainability, dependability, MTBF, MTTR and dependability ratio for each subsystem of the system. Findings – The subsystem SS1 comprising of chiller and cream separator is the most critical from maintenance point of view, as the reliability, availability, maintainability, dependability, MTBF and dependability ratio indices are low as compared to those of other subsystems of skim milk powder production system of the dairy plant. Originality/value – The RAMD indices of the present work is very useful for finding the critical subsystem and its effect on the performance of the system working under real working conditions. Further, based on findings the maintenance priorities for various subsystems can be decided.

Redundancy effect on coal-fired power plant availability

The present study deals with the redundancy effect on operational availability of coal-fired power plant for known failure and repair rates of each component or unit in the system. For this purpose, the entire plant has been divided into four main subsystems (viz. boiler, turbine, condenser and water circulation) to predict operational availability (i.e., uptime) of these subsystems of large thermal power plant without the tangible nature of a transition diagram due to high complexity. Availability of each subsystem has been evaluated using well known Markov birth-death process in the present study. For the analysis, only the effect of redundancy on condensate extraction pump, boiler feed pump and boiler on operational availability of corresponding subsystem as well as plant has been discussed. The results predicted that the effect of boiler redundancy on coal-fired power plant found to be more sensitive in comparison to other redundant units.

The MJO in a Coarse-Resolution GCM with a Stochastic Multicloud Parameterization

Abstract The representation of the Madden–Julian oscillation (MJO) is still a challenge for numerical weather prediction and general circulation models (GCMs) because of the inadequate treatment of convection and the associated interactions across scales by the underlying cumulus parameterizations. One new promising direction is the use of the stochastic multicloud model (SMCM) that has been designed specifically to capture the missing variability due to unresolved processes of convection and their impact on the large-scale flow. The SMCM specifically models the area fractions of the three cloud types (congestus, deep, and stratiform) that characterize organized convective systems on all scales. The SMCM captures the stochastic behavior of these three cloud types via a judiciously constructed Markov birth–death process using a particle interacting lattice model. The SMCM has been successfully applied for convectively coupled waves in a simplified primitive equation model and validated against radar data of tropical precipitation. In this work, the authors use for the first time the SMCM in a GCM. The authors build on previous work of coupling the High-Order Methods Modeling Environment (HOMME) NCAR GCM to a simple multicloud model. The authors tested the new SMCM-HOMME model in the parameter regime considered previously and found that the stochastic model drastically improves the results of the deterministic model. Clear MJO-like structures with many realistic features from nature are reproduced by SMCM-HOMME in the physically relevant parameter regime including wave trains of MJOs that organize intermittently in time. Also one of the caveats of the deterministic simulation of requiring a doubling of the moisture background is not required anymore.

Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant

This paper deals with the Markov modeling and reliability analysis of urea synthesis system of a fertilizer plant. This system was modeled using Markov birth-death process with the assumption that the failure and repair rates of each subsystem follow exponential distribution. The first-order Chapman-Kolmogorov differential equations are developed with the use of mnemonic rule and these equations are solved with Runga-Kutta fourth-order method. The long-run availability, reliability and mean time between failures are computed for various choices of failure and repair rates of subsystems of the system. The findings of the paper are discussed with the plant personnel to adopt and practice suitable maintenance policies/strate- gies to enhance the performance of the urea synthesis system of the fertilizer plant.

Availability analysis and performance optimization of a butter oil production system: a case study

This paper proposes a method for time dependent system availability (TDSA) analysis of butter oil production system and the performance of the system is optimized using genetic algorithm. The mathematical formulation of the system based on Markov birth–death process is carried out and first order Chapman–Kolmogorov differential equations are developed based on the assumption that the failure and repair rate of each subsystem follows exponential distribution. The proposed method i.e. an adaptive step-size control Runge–Kutta method is used to compute TDSA and mean time between failures for butter oil production system of a dairy plant. The butter oil production system is a complex system and comprises of seven repairable subsystems. The results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the productivity and quality of butter oil.

Mathematical Modeling and Analysis of Container Manufacturing Plant in Transient State

In the present work, time dependent availability of a mechanical system i.e., container manufacturing plant is estimated. Here, Mathematical modeling has been developed on the basis of Markov birth-death process using probabilistic approach. The first order governing equations thus formulated using the mnemonic rule is solved to estimate the availability of the system in the transient state. The failure rates and the repair rates of the subsystems are taken constant. Matrix method has been applied to calculate transient state availability of the system up to desired decimal places. The time dependent availability is shown with the help of graph and the parameter MTTF is obtained. Correlation and regression coefficients between time and availability have been computed to study the variation between time and availability. The results obtained in the present work are considered to be very useful for taking all maintenance decisions associated with container manufacturing plant. Keywords: Availability, Correlation, Regression, Differential difference equation, Mathematical modeling, Mean time to failure and Mnemonic Rule.