Chapman Kolmogorov Differential Equations Research Articles

Availability evaluation of solar photovoltaic systems using markov modeling and cuckoo search algorithm

The main objective of present investigation is to evaluate and optimize the operational availability of the solar photovoltaic systems. As the solar energy is a prominent source of renewal energy and contribute a lot in global development having less environmental impacts but the safety and reliability issues of these systems also observed during the operational phase. Availability is an effective tool that is used to discourse the safety and performance issues of renewal energy sources especially solar photovoltaic systems. Here, a stochastic model is developed for solar photovoltaic system having solar photovoltaic plates, solar charger, solar battery, and inverter. The Markov birth-death process is applied for development of the mathematical model of the proposed system. The chapman-Kolmogorov differential difference equations of the proposed solar photovoltaic system used to predict the steady state availability of system. On the basis of literature, the failure and repair rates of all components of solar photovoltaic system are considered as exponentially distributed. In addition, an effort is also made to predict the optimum availability of solar photovoltaic system using well-known optimization technique cuckoo search algorithm. It is revealed that, the predicted availability of the solar photovoltaic system is 0.9988799 at population size 60 after 700 iterations. The estimated parametric values of the failure and repair rates also derived. To highlight the importance of the study the numerical and graphical results are presented and shared with the system designers and maintenance engineers.

Cloud infrastructure availability optimization using Dragonfly and Grey Wolf optimization algorithms for health systems

Cloud infrastructure provides a real time computing environment to customers and had wide applicability in healthcare, medical facilities, business, and several other areas. Most of the health data recorded and saved on the cloud. But the cloud infrastructure is configured using several components and that makes it a complex structure. And the high value of availability and reliability is essential for satisfactory operation of such systems. So, the present study is conducted with the prominent objective of assessing the optimum availability of the cloud infrastructure. For this purpose, a novel stochastic model is proposed and optimized using dragonfly algorithm (DA) and Grey Wolf optimization (GWO) algorithms. The Markovian approach is employed to develop the Chapman-Kolmogorov differential difference equations associate with the system. It is considered that all failure and repair rates are exponentially distributed. The repairs are perfect. The numerical results are derived to highlight the importance of the study and identify the best algorithm. The system attains its optimum availability 0.9998649 at population size 120 with iteration 700 by GWO. It is revealed that grey wolf optimization algorithm performed better than the Dragonfly algorithm in assessing the availability, best fitted parametric values and execution time.

Performance evaluation and optimization of process parameters for a polypropylene unit in naphtha cracker plant using PSO algorithm

The purpose of this case study is to evaluate the performance of assets in oil and gas industry. The study is carried out in polypropylene unit of naphtha cracker plant. The unit produces plastic granules from polypropylene gas and comprises number of subsystems which are complex system in nature. It consists of five important subsystems which are arranged in series and parallel configuration; Pre-contacting pot, In line mixing unit, Flash loop (Heater), Flash drum (Dynamic separator) and Bag filter. The Markov process is used to review the availability of system in the plant with the collected data. In current paper, Chapman-Kolmogorov differential equations are developed with the assistance of mnemonic rule from transition diagram of polypropylene unit. Further, the process parameters are optimised to get optimum value of availability using particle swarm optimisation algorithm tool in MATLAB (R2017a) software. The fruitful results have been observed that maximum availability 95.16 % could be achieved at particle size of 45 and 95.16 % at 70th iteration size. The results of the study are shared with maintenance personnel for setting the maintenance strategy which will helps in production enhance or increasing plant availability.

Functional safety analysis of safety-critical system using state transition diagram

The subject of research is to determine the functional safety indicators of a fault-tolerant safety-critical system, namely, the minimal cut sets’ probability for a given duration of the system’s operation, using the state transition diagram (STD). The aim is to create a new method for analyzing the functional safety of a fault-tolerant safety-critical system. This method is based on the methodology of developing models of operational reliability behavior in the form of STD. This methodology provides a detailed representation of inoperable states and their relation with pre-failure (inoperable critical) states. The task is to propose a new classification for inoperable states of the STD to obtain all possible emergencies in the same space of inoperable states. This approach allows consideration the correlations between the failures, that it is impossible to use the fault trees. Since the space of inoperable states can reach hundreds and thousands of states, a method is proposed for their automated determination according to the classification. The state space method was used to conduct the validation of the method of functional safety analysis. The following results were obtained: the system of Chapman-Kolmogorov differential equations is formed in accordance with the STD and it provides the dependence of the functional safety indicator – the minimal cut sets’ probability as a function of the operational duration of the fault-tolerant safety-critical system. This dependence is called the emergency function. The method for determining the emergency function is based on the usage of the emergency mask. Note that the proposed model of operational reliability behavior in the form of STD provides the possibility to conduct both the functional safety and the reliability indicators. The value of the minimal cut sets’ probability for a given duration of operation is determined using the fault tree for the validation of the proposed method of functional safety analysis. The fault tree was built by Reliasoft BlockSim software. The obtained value coincides with the value of the minimal cut sets’ probability, which was defined by the emergency function for the same operational duration. Thus, the designer can comprehensively analyze the feasibility of introducing redundancy (structural, temporal, functional). Conclusions: the scientific novelty of the obtained results is the following: the new method for determining safe, critical and catastrophic states in the set of inoperable states is used in the methodology of the STD developing to obtain the stochastic model of operational reliability behavior of fault-tolerant safety-critical system. This technique ensures an automated defining of emergency function by using an improved structural-automatic model.

Availability optimization of biological and chemical processing unit using genetic algorithm and particle swarm optimization

PurposeThe demand of sewage treatment plants is increasing day by day, especially in the countries like India. Biological and chemical unit of such sewage treatment plants are critical and needs to be designed and developed to achieve desired level of reliability, maintainability and availability.Design/methodology/approachThis paper investigates and optimizes the availability of biological and chemical unit of a sewage treatment plant. A novel mathematical model for this unit is developed using the Markovian birth-death process. A set of Chapman–Kolmogorov differential equations are derived for the model and a generalized solution is discovered using soft computing techniques namely genetic algorithm (GA) and particle swarm optimization (PSO).FindingsNature-inspired optimization techniques results of availability function depicted that PSO outperforms GA. The optimum value of the availability of biological and chemical processing unit is 0.9324 corresponding to population size 100, the number of evolutions 300, mutation 0.6 and crossover 0.85 achieved using GA while PSO results reflect that optimum achieved availability is 0.936240 after 45 iterations. Finally, it is revealed that PSO outperforms than GA.Research limitations/implicationsThis paper investigates and optimizes the availability of biological and chemical units of a sewage treatment plant. A novel mathematical model for this unit is developed using the Markovian birth-death process.Originality/valueAvailability model of biological and chemical units of a sewage treatment is developed using field failure data and judgments collected from the experts. Furthermore, availability of the system has been optimized to achieve desired level of reliability and maintainability.

Performance Analysis of Photovoltaic Systems Using (RAMD) Analysis

The primary aim of this present study is to examine how reliability, availability, maintainability, and dependability (RAMD) are used to describe the criticality of each sub-assembly in grid- connected photovoltaic systems. A transition diagram of all subsystems is produced for this analysis, and Chapman-Kolmogorov differential equations for each variable of each subsystem are constructed using the Markov birth-death process. Both random failure and repair time variables have an exponential distribution and are statistically independent. A sufficient repair facility is still available with the device. The numerical results for reliability, maintainability, dependability, and steady-state availability for various photovoltaic device components have been obtained. Other metrics, such as mean time to failure (MTTF), mean time to repair (MTTR), and dependability ratio, which aid in device performance prediction, have also been measured. According to numerical analysis. it is hypothesized that subsystem S4, i.e. the inverter, is the most critical and highly sensitive portion that requires special attention in order to improve the efficiency of the PV device plant. The findings of this research are very useful for photovoltaic system designers and maintenance engineers.

Simulation modelling for performance optimisation of the skim milk powder production system of a dairy plant

The purpose of this paper is to deal with the simulation modelling and performance optimisation for the skim milk powder production system of a dairy plant using genetic algorithm (GA). This analysis is based on Markov birth-death process, the mathematical formulation of the system is carried out to derive first order Chapman-Kolmogorov differential equations by assuming that the failure and repair rate of each subsystem follows exponential distribution. The proposed method is used to compute long run availability using normalising condition, initial boundary conditions and recursive method. It provides the optimum system availability level for different combinations of failure and repair rates parameters of the subsystems of the skim milk powder production system of a dairy plant concerned. 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 skim milk powder production system of the dairy plant.

Investigation of performance measures of power generating unit of sewage treatment plant

The main objective of present study to investigate the availability and profit of power generation systems established in sewage treatment plants. The sewage treatment plant is an industry in which waste sewage water has been treated and waste is used to generate power. For this purpose, a mathematical model has been proposed by considering constant failure and repair rates. The power generating unit in sewage treatment plant comprises six subsystems as sludge digester, gas holding tank, gas burner, gas scrubber, gas engine and power generation. By using appropriate redundancy technique in model development Chapman-Kolmogorov differential equations has been drawn with the help of the Markov birth death process. Availability and profit have been analysed based on making variation in the failure and repair rates. The numerical and graphical results have been depicted for a particular case. The derived results have been discussed with system designers and found useful.

Performance improvement of a crystallization system through optimization and sensitivity analysis

PurposeThis paper deals with the performance optimization and sensitivity analysis for crystallization system of a sugar plant.Design/methodology/approachCrystallization system comprises of five subsystems, namely crystallizer, centrifugal pump and sugar grader. The Chapman–Kolmogorov differential equations are derived from the transition diagram of the crystallization system using mnemonic rule. These equations are solved to compute reliability and steady state availability by putting the appropriate combinations of failure and repair rates using normalizing and initial boundary conditions. The performance optimization is carried out by varying number of generations, population size, crossover and mutation probabilities. Finally, sensitivity analysis is performed to analyze the effect of change in failure rates of each subsystem on availability, mean time to failure (MTBF) and mean time to repair (MTTR).FindingsThe highest performance observed is 96.95% at crossover probability of 0.3 and sugar grader subsystem comes out to be the most critical and sensitive subsystem.Originality/valueThe findings of the paper highlights the optimum value of performance level at failure and repair rates for subsystems and also helps identify the most sensitive subsystem. These findings are highly beneficial for the maintenance personnel of the plant to plan the maintenance strategies accordingly.

Tripod Turnstile Machines Performance Analysis for the System Safety and Security without Considering Simultaneous Failures using Reliability Approach

As the crime is increasing day by day around the world. To stop the crime many security gadgets and machines have been developed by various security agencies. The tripod turnstile machine also helps in stopping the crime and restricting the entry of unauthorized person on the premises. In this paper, the aim is to analyze the reliability measures of the two tripod turnstile machines which work in a parallel configuration. In the case of non-functionality of the machine, unauthorized persons may enter into the premises. Due to security and safety reason, organizations install these machines. Hence these machines must be highly reliable in the operation to avoid any unwanted event. In this paper, for the considered system, the transition state diagram has been drawn with the help of the Markov model. The Chapman-Kolmogorov differential equations are developed from the transition state diagram and solved using Laplace transformation. The failure and repair rates are assumed to be constant and follow negative exponential distribution. The system upstate and downstate probabilities are determined. The explicit expression of the system Availability, Reliability and MTTF are also obtained. The sensitivity analysis is also performed to determine which machine affects the system reliability the most.

Modeling and availability analysis of data center: a fuzzy approach

Data Centers are the backbone of any industry that provides a specialized environment to safeguard the company's valuable equipment and intellectual property. The successful operation of company's Data Center is typically shared among multiple departments and personnel. But, the involvement of multiple personal and departments make its configuration complex. In such situations, reliability of data center become a necessary factor. But, the traditional theory of reliability is based on the Bernoulli trials, i.e., either operative or failure. But this situation is unrealistic in case of complex systems like data center. To rectify this problem, here a mathematical model has been developed using the concept of fuzzy reliability. All the failure and repair rates are exponential distributed along with coverage factor. Chapman-Kolmogorov differential equations have been developed for the fuzzy system using Markov birth–death process. A new methodology Runge–Kutta method of order four has been used to solve Chapman-Kolmogorov differential equations using MATLAB (Ode 45 function).

A multi-stage imperfect maintenance strategy for multi-state systems with variable user demands

The main purpose of this paper is to schedule an imperfect maintenance policy for a single unit multi-state system (MSS) exhibiting more than two output states in the duration of its multiple operation stages. Firstly, a nonhomogeneous continuous time Markov chain (NHCTMC) is introduced to describe the state evolution process when the number of external shocks is modeled by a nonhomogeneous Poisson process (NHPP), and state residence probabilities of the Markov process are derived via a proposed recursive algorithm (RA) in solving the Chapman-Kolmogorov (CK) differential equations. Based on those modeling approaches, reliability measures such as the survival function and mean time to first failure (MTTFF) are evaluated where the randomly varied user demands reflecting real industrial applications are taken into consideration. We subsequently put forward a multi-stage imperfect maintenance policy by dividing system output states into three subsets concerning different degrees of degradation, incorporating a condition-based maintenance (CBM) action and a corrective maintenance (CM) activity in each operation stage. It is assumed that the CBM is a minimal repair and the effectiveness of CM is imperfect. The system will not be completely replaced by a brand new one until the number of failures reaches N in light of the investigated maintenance policy, where the expected profit in per renewal cycle is maximized to seek the optimal N analytically. An illustrative example of a bulk power electric system is presented to verify the proposed idea numerically, in which three common types of demand distributions are introduced.

Reliability, maintainability and sensitivity analysis of physical processing unit of sewage treatment plant

India is facing radical change in perspective of inadequate water resources which can reduce by using treated water. In this direction, sewage treatment plants play a key role. Sewage treatment plant comprises three units namely physical processing, chemical processing and biological process. The physical process is the most important part and it has five component arranged in series configuration. It becomes necessary to perform this process with high efficiency and reliability, availability, maintainability, and dependability (RAMD) is the methodology to analyze the performance. The failure and repair rates of the subsystems has been considered exponentially distributed. Chapman–Kolmogorov differential equations are derived using Markovian birth–death process and several measures like mean time between failures, mean time to repair and dependability ratio are derived. The sensitivity analysis of reliability of the plant has also been performed. RAMD investigation shows that: availability of system is 0.952177, reliability of the system after 20 days is 0.2018 and after 60 days 0.00823, maintainability of the plant is 0.999948, dependability ratio is 0.9541 and raw sewage sump is the most sensitive subsystem of the plant with reliability 0.382893. This work is projected to support as an informative exertion in steering a RAMD analysis of physical processing unit and vary few work is available in literature related to the performance features of physical processing units of the sewage treatment plants. The main findings may be very useful for sewage treatment plants designers.

Maintenance priorities determination for a repairable unit of a sugar plant

In the present study, a repairable unit of a sugar plant has been considered to determine the maintenance priorities of various subsystems of the unit. The selected repairable unit is crushing unit and it comprises of crusher, inter carrier and pump subsystems. Performance modeling of the unit is based on Markov approach. From the transition diagram of the unit, Chapman-Kolmogorov differential equations are derived. The equations are then solved to get the availability in steady state. It is assumed that all subsystems have constant rates of failure and repair. After that, development of decision matrices has been done for all subsystems. For various permutations of failure rates as well as repair rates, these decision matrices present different levels of availability for all the subsystems. On the basis of various values of availabilities and the graphs of failure and repair rates of subsystems, the optimum values of failure and repair rates are selected for maximum availability of each subsystem. Accordingly, priorities for maintenance are determined for various subsystems of repairable crushing unit. This will ensure maximum availability level of the crushing unit and will finally lead to the overall performance enhancement thereby maximizing the profitability of the plant.

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.

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).

Reliability and Availability Evaluation of a Series- Parallel System Subject to Random Failure

Objective: To compute the reliability/availability of casting system, a part of steel industry with a view to increase its productivity. Methods/Analysis: The reliability of casting system of a steel industry, consisting of four units, has been computed using Supplementary Variable Technique (SVT) by keeping the failure rates constant and varying the repair rates. From the transition diagram of the casting system, Chapman-Kolmogorov differential equations have been developed using mnemonic rule which are further solved using Lagrange’s method. The transient state availability of the system has been computed by Runge-Kutta fourth order method using MATLAB. Mean Time Between Failures (MTBF) has been calculated numerically. Findings: Besides increasing the plant availability and hence production, the findings of this paper may help in maintenance planning and scheduling of the said system. Novelty/Improvement: Reliability of the casting system of a steel industry has not been discussed so far.

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.

Mathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability has been used for reliability analysis of the system, and the effect of coverage factor, failure and repair rates of subsystems on fuzzy availability for fault-tolerant crystallization system of sugar plant is analyzed. Mathematical modeling of the system is carried out using the mnemonic rule to derive Chapman–Kolmogorov differential equations. These governing differential equations are solved with Runge–Kutta fourth-order method.

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.