PERFORMANCE MODELING AND AVAILABILITY ANALYSIS OF MALT SCREENER SYSTEM IN A BREWERY PLANT

Transcription

1 International Journal of Latest Research in Science and Technology Volume 3, Issue 2: Page No , March -April ISSN (Online): PERFORMANCE MODELING AND AVAILABILITY ANALYSIS OF MALT SCREENER SYSTEM IN A BREWERY PLANT Ajay Kumar, R. K. Garg, 2 P.C. Tiwari DCRUST Murthal, Sonipat 2 NIT Kurukshetra Abstract- The production process flow in a brewery comprises of various systems and subsystems arranged in series, parallel and combination of these two. The objective of the maintenance department is to achieve maximum without any failure of machine components the plant. The paper discusses the Performance modeling and analysis of a Malt Screener system in brewery plant by using Markov approach to find out all the probabilities of systems. The model for Malt Screener system has been derived on the basis of probabilistic approach using Transition Diagram (TD).The steady state availability of the Malt Screener system has found for constant repair and failure rate as calculated from the Maintenance History sheet of brewery plant situated in Haryana and the decision Matrix developed. The critical subsystem is calculated using the sensitivity analysis. The transient behavior of variation of availability is also found for Malt Screener system using the Runge-Kutta method of fourth order and simulation is done using the MATLAB tool. Keywords -,, Markov, Performance Modeling, Transition Diagram (TD) I. INTRODUCTION The probabilistic measure of the production regularity of a system is a major concern in availability studies. The process industry comprises of large complex engineering systems, subsystems arranged in series, parallel or a combination of them. For efficient and economical operation of a process plant, each system or the subsystem should work failure free under the existing operative plant conditions. Thus the importance of maintenance plan is constantly increasing and is a major factor for process industries. The main objective of Maintenance planning is to ensure that the machines, buildings, equipment etc. should perform their services of the required level of productive efficiency and available as per requirement. Reliability deals with the probability that a component or a system perform a desired function without failure under predetermined conditions for a given period of time. It focuses on study of failures of engineering components and systems during the specified time and under the specified operational and environmental conditions and their remedies. The major objective of reliability engineering is to prevent the frequency of failure, cause of failure and designing the system to have better maintainability. The availability requirements of Process industries have been increased in the last few decades. Process industries in India are expanding and modernizing at a very fast rate. Understanding the machinery and equipment performance that are coming up with high technology and energy efficient design is very essential for proper use. Designing the performance evaluating system of the process industries requires the clear understanding of the behavior and failure and repair time distributions of its various operating systems. The Process industries are characterized by large number of interlinked systems or subsystems, each with its own failure and repair rate. The overall system availability is a function of the failure and repair rates of the various subsystems. It can be used for the performance evaluation of the process industries. II. SYSTEM DESCRIPTION This system consists of the following elements as discussed below:. The elevator (A) lifts the malt to screening unit. 2. The Screening Unit (B) consists of three units in series 3. Screening unit is operated by vibrating motor (C) which is in cold standby. 4. Vacuum pump (D) is used to suction of dust particle. 5. The metallic element is separated through magnet (E) which never fails. The flow process of Malt Screener system is shown in figure. ISSN:

2 International Journal of Latest Research in Science and Technology. Malt Elevator (A) Screening Unit-(B) Screening Unit-2(B2) Vibrating Motor(C) Dust Collector Screening Unit-3(B3) Vacuum Pump (D) Magnetic Element (E) Figure Flow process of Malt Screener system III. LITERATURE REVIEW Reliability analysis techniques have been used as tools for the planning and operation of automatic and complex process industries. J.M. Kontoleon (978) studied complex repairable systems which is often important to assess system mean time to failure for a variety of component reliability characteristics and repair rate. Jai Singh et al. (995) suggested that the of a system can be improved by using the standby units of limited subsystems, where the chances of failure are high. M.A El-Damcese (995) discussed a system of n- independent reparable units that can be described by a homogeneous-time discrete- state Markov Process. G. Thangamani et al. (995) examined a live problem at a fluid catalytic cracking unit of a refinery increasing availability for cost effective operation. Sunand kumar et al. (996) discussed the behavioral analysis for shell gasification and carbon recovery process in a urea fertilizer plant and the effect of each unit on the system availability are analyzed. D.V. Raje et al. assess the availability of critical pumping system of crude distillation unit of a refinery with recourse to the Markovian model. G. Beckerb et. Al. (2000) considered nonhomogeneous semi- Markov Process as an approach to model reliability characteristics of components or small systems with complex test maintenance strategies. Gregory Levitin (200) studied the effect of limited availability of the voting units on the entire voting system reliability and pesented a method for determining indices that measure importance of voting units availability for the system. Kuo- Hsiung Wang and Jau- Chuan Ke (2002) discussed the Steady state availability and mean time to system failure of repairable system with operating units, warm standby units and repairmen in which units balking and reneging are considered. Lori E. Seward and Joel A. Nachlas (2004) constructed a model of the operational reliability and availability of multitask systems and constitute an extension to model of repairable system behavior and application of renewal theory. Francesco Martinelli (2005) consider a failure prone, single machine, single part type, limited inventory, manufacturing system subject to a nonhomogeneous Markov Failure and repair process with the failure rate depending on the production rate through a value function. Madhu jain et al. (2008) investigated a multicomponent repairable system with state dependent rate. The cost function is suggested to determine the optimal number of warm and cold standby units required for the desired level of quality of services. Komal et al. (2009) used the Genetic Algorithms based Lambda Tau (GABLT) technique to estimate the RAM parameters of these systems by utilizing available information and uncertain data. As far as reliability is concerned, it has been established as a useful tool for risk analysis, production availability studies and design of systems. has been considered as an important measure of performance for many industrial systems which are generally considered as repairable ones. Peter Bullemer et al. (200) pointed out that Process industry plants involve operations of complex human machine systems. Ahmed-Tidjani Belmansour, Mustapha Nourelfath (200) presented an analytical aggregation method for evaluating the throughput (or production rate) of tandem homogenous production lines. Ling Wang et.al. (20) discussed the how the Imperfect maintenance will decrease the expected values of cycle length and long-run availability. Kumar and Lata (202) developed a fuzzy Markov model to develop Kolmogorov s differential equations of condensate system and examined the reliability of the system. Upadhya and Srinivasan (202) developed a Discrete Event Simulation technique using Monte-Carlo methods, to estimate the availability of military systems. D. Bose et. al. (203) studied the determination of reliability and availability aspects of one of the significant constituent in a Railway Diesel Locomotive Engine and ABC analysis has been used for the maintenance of spare parts inventory. ISSN:

3 After going through a comprehensive survey of the reported literature, most of the researchers reserved their work in the development and analysis of theoretical mathematical models and none of the author has tried to solve the mathematical model using more realistic conditions. The performance optimization and numerical analysis in the Brewery plant have also not been taken up by any researcher. IV. PERFORMANCE MODELING International Journal of Latest Research in Science and Technology.... () Similarly, we can obtain The calculation of the of a system with elements exhibiting dependent failures and involving repair or standby operation is, in general, complicated and several approaches have been suggested to carry out the computations. A technique that has much appeal and works well when failure hazards and repair hazards are constant requires the use of Markov models. A stochastic process in a physical system is known as Markov process if the occurrence of any future state of the system is independent of any past state and depends only on the present state. In Markov process, we deal with two random variables either one of which can be discrete or continuous. Generally, one of the random variable refers to the state of a physical system and the other random variable refers to time. A discrete state, continuous time process is called a Markov chain. In order to find reliability/availability of a system, one has to form a system of linear differential equations using mnemonic rule. The idea for formulating the Chapman- Kolmogorov differential equations for a simple system whose transition diagram is given by figure 2. The eqns. () to (3) are Chapman-Kolmogorov differential equations which can be solved recursively or by Runge-Kutta fourth order method when the initial conditions are as follows: V. DEVELOPMENT OF AVAILABILITY MODEL models for Malt screener system has been developed on the basis of simple probabilistic considerations. First, difference-differential equations have been formulated and then these equations are solved recursively for steady state conditions. The obtained steady state probabilities are further solved using normalizing conditions i.e. Where n is the total number of states shown in transition diagram. abc(2 ABC() ABc(3 VI. RUNGE- KUTTA METHOD The eqns. () to (3) can be written as follows: Figure 2: Transition Diagram for a System Let us define, = Probability that the system is in good state at time t. = Probability that the system fails due to failure of subsystem A at time t. = Probability that the system fails due to failure of subsystem C at time t. Here, reliability/ of a system will be sum of probabilities of good states. As such, with initial conditions The variables ( ) can be calculated with the development of Runge- Kutta method, which is illustrated as below: or, Dividing both sides by, we get ISSN:

4 International Journal of Latest Research in Science and Technology. Therefore, we can find time The process can be repeated to obtain with the help of Runge-Kutta method of fourth order. at etc. Table Notations used in Performance Modeling and Analysis of Malt screener System. Transition diagram Figure 3 Full capacity (without standby) A, B, B2, B3 Full capacity (with standby) C,D Failed state a, b, b2, b3,c,d Reduced capacity.. s, i = to 6 From s to, i = to 6 from to h represents the step size. We can obtain as given below: Probability of full capacity working ( without standby unit) Probability of full capacity working (with standby unit) Probability of reduced capacity working Probability of failed state to, to, to, to TRANSITION DIAGRAM: Figure 3 Transition Diagram of Malt Screener System in brewery ISSN:

5 International Journal of Latest Research in Science and Technology. VII. ASSUMPTIONS The following assumptions are made to carry out the performance modelling and analysis of the system under consideration. At any given time the system is either in operating state or in the failed state. and repair rate are constant. A repaired sub system is as good as new. Standby sub systems are of the same nature and capacity as the active sub system. Repair facilities are always available. VIII. PERFORMANCE MODELING OF MALT SCREENER: The following differential equations equation with the transition diagram of malt screener system is formed: to infinity. Therefore, system probability becomes independent of time t and known as steady state condition. Thus, as i.e. The steady state availability of a system can be obtained by summing up all full working and reduced capacity states: Where, k represents the working as well as reduced capacity states. By putting as t in equation 0-4, the steady state probabilities are given as: (5) (0) () (6) (7) (8) (2) (9) (20) (2) Where in equation; for, n =,2,3,4: (3) (4) i=,2,3,4,j=0: i=9,20,2,22, j=7 n=6 i=8, j=7 n=2,3,4,5 i=6,7,8,0, j=5 n= i=9, j=5 n=,2,3,4,5 i=2,3,4,5,6, j= n=6 i=23, j=5 with the initial condition at time t=0 (t)= for i=0, (t)=0 for Steady state availability of malt screener: When a plant operates initially, the various constraints come into play to affect the plant operation i.e. the initial conditions. After a sufficient time, as the infant period is over, the system becomes independent of the initial conditions. This state is termed as steady state condition of a system. If designates the probability that an equipment is in succession at time t, then for smooth and continuous operation of a system without failure, time (t) will approach (22) (23) (24) (25) (26) (27) (28) (29) (30) (3) (32) (33) (34) ISSN:

6 International Journal of Latest Research in Science and Technology. IX. RESULTS AND DISCUSSION (35) The availability expression as given by eqn. 40 includes (36) (37) (38) failure events ( ) and repair priorities ( ). The different combinations of failure and repair rates can be used to compute the maximum value of system availability. Tables - 6 represent the decision matrices for various subsystems of the Malt Screener system. Where Table-2 Decision Matrix of elevator subsystem of Malt Screener system â Constant values á á=0.004, â=0.4, á3=0.05, á4=0.003, â4=, á5=0.005, â5=0.09 The probability of full working state namely determined by using Normalizing condition: i.e is â Constant values á á2=0.00, â2=0.6, á3=0.05, á4=0.003, â4=, á5=0.005, â5= x 0-3 (A) = (39) Max. (40) Figure 4 Effect of failure and repair rates of elevator Table 2 and figure 4 shows the effect of failure and repair rates of elevator subsystem on availability malt screener system. As the failure rate of Elevator is increase from ISSN:

7 0.004(once in 250 hrs) to 0.02(once in hrs), the subsystem availability decrease by.83 percentage and as repair rate increases from 0.4(once in 2.5 hr) to (once in.25 hr), the system availability increases 0.46 percentage. Table 3 Decision Matrix of Screening unit subsystem of Malt Screener system International Journal of Latest Research in Science and Technology. screener system. As the failure rate of Screening unit 2 is increase from 0.05(once in 67 hrs) to 0.055(once in 8.8 hrs), the subsystem availability decrease by 5.4 percentage and as repair rate increases from 0.65( once in.53 hr) to.05(once in 0.95 hr), the system availability increases 2 percentage Table 5 Decision Matrix of screening unit 3 subsystem of Malt Screener system â 4 á Constant values á=0.004, â=0.4, á2=0.00, â2=0.6, á3=0.05, á5= , â5=0.09 Figure 5 Effect of failure and repair rates of screening unit Table 3 and figure 5 shows the effect of failure and repair rates of Screening unit subsystem on availability malt screener system. As the failure rate of screening unit is increase from 0.00(once in 000 hrs) to 0.09 (once in. hrs), the subsystem availability decrease by.25 percentage and as repair rate increases from 0.6(once in.66 hr) to (once in hr), the system availability increases 0.06 percentage. Table 4 Decision Matrix of Screening unit 2 subsystem of Malt Screener system â Constant values á á=0.004, â=0.4, á2=0.00, â2=0.6, á4=0.003, â4=, á5=0.005, â5= Figure 6 Effect of failure and repair rates of screening unit x 0-3 Figure 7. Effect of failure and repair rates of Screening unit 3 Table 5 and figure 7 shows the effect of failure and repair rates of screening unit 3 subsystem on availability malt screener system. As the failure rate of Screening unit 3 is increase from 0.00(once in 000 hrs) to 0.005(once in 200 hrs), the subsystem availability decrease by 5.3 percentages and as repair rate increases from 0.7(once in.42 hr) to.(once in 0.90 hr), and the system availability increases 0.05 percentage. Table 6 Decision Matrix of Vibrating Motor subsystem of Malt Screener system â Constant values á á=0.004, â=0.4, á2=0.00, â2=0.6, á3=0.05, á4=0.00, â4= á6=0.005, â6= Table 4 and figure 6 shows the effect of failure and repair rates of screening unit 2 subsystem on availability malt ISSN:

8 International Journal of Latest Research in Science and Technology x 0-3 Figure 8 Effect of failure and repair rates of vibrating motor Table 6 and figure 8 shows the effect of failure and repair rates of vibrating motor subsystem on availability malt screener system. As the failure rate of vibrating motor is increase from 0.003(once in hrs) to 0.007( once in hrs), the subsystem availability decrease by 0.0 percentage and as repair rate increases from ( once in.25 hr) to.2(once in 3 hr), the system availability does not change. Table 7 Decision Matrix of Vacuum pump subsystem of Malt Screener system â Constant values á á=0.004, â=0.4, á2=0.00, â2=0.6, á3=0.05, á4=0.003, â4= Table 7 and figure 9 shows the effect of failure and repair rates of vacuum pump subsystem on availability malt screener system. As the failure rate of vacuum pump is increase from 0.005(once in hrs) to ( once in 8.8 hrs), the subsystem availability decrease by 0.0 percentage and as repair rate increases from 0.09( once in. hr) to 0.3(once in 7.69 hr), the system availability increases 0.02 percentage. Transition Behavior of malt screener System The system of differential equations () to (5) with initial conditions has been solved numerically using Runge-Kutta fourth order method. Taking data for failure and repair rates of different subsystems from maintenance history sheets, the computations have been performed up to 360 days as shown in table 8. Figure 0 shows the variation in availability with time, which reveals that the availability attains steady state after some time Table 8 Variation in with Time for malt screener System Time Failure and Repair Rates á=0.004, Variation of â=0.4, á2=0.00, â2=0.6, á3=0.05, á4=0.00, â4=0.7, á5=0.003, â5=, á6=0.005, â6=0.09, x 0-3 Figure 9 Effect of failure and repair rates of vacuum pump Time Figure-0 Variation in with Time for malt screener System X. CONCLUSIONS analysis of malt screener system in brewery has been studied extensively. The performance analysis of malt screener system of brewery plant had been carried out utilizing the Markov modeling. The decision support system ISSN:

9 has developed which showed the effects of failure and repair rates on the system performance in terms of steady state availability. The criticality of various subsystems has been found to develop the DSS which can be helpful for deciding the maintenance policy. This availability model is effectively used for analysis of availability and evaluation of performance of various subsystems of malt screener system of Brewery plant. The model developed shows the relationships between availability and various repair and failure rates for each subsystem of brewery plant. From the results we can conclude that the screening unit 2 and screening unit 3 subsystem are critical one. It can be concluded from table 4-9, that as the failure rate increases, the availability shows decreasing trend and as repair rate increases, the availability shows increasing trend. The variation in availability with time reveals that the availability attains steady state behavior after some time. REFERENCES. J.M Kontoleon Determination of MTTF from the transition probability matrix and diagram IEEE Transction on reliability, vol. R- 27, No.5, pp , Jai Singh et.al. for a system composed of four subsystems in series having standby in one subsystem. Microelectron. Reliability, Vol. 35, No. 2, pp , M.A El-Damcese Markovian-Model for systems with independent units Microelectron. Reliability, Vol. 35, No. 7, pp , G. Thangamani, T.T. Narendran Assessment of availability of a fluid catalytic cracking unit through simulation Reliability Engineering and system safety, 47, , Sunand Kumar, Dinesh Kumar and N.P Mehta Behavioural analysis of shell gasification and carbon recovery process in urea fertilizer plant Microelectron. Reliability, Vol. 36, No. 5, pp , D. V. Raje, R.S. Olaniya, P.D. Wakhare Availibility assessment of a two unit standby pumping system Reliability Engineering and system safety, 68, , G.Becker, L. Camarinopoulous, G. Zioutas A semi Markovian model allowing for inhomogenitities with respect to process time Reliability Engineering and system safety, 70, 4-48, Gregory Levitin Analysis and optimization of weighted voting systems consisting of voting units with limited availability Reliability Engineering and system safety, 73, 9-00, 99. International Journal of Latest Research in Science and Technology. 9. Kuo- Hsiung Wang and Jau- Chuan Ke Probabilistic analysis of a repairable system with warm standbys plus balking and reneging Applied Mathematical Modelling,27, , Lori E. Seward and Joel A. Nachlas analysis for multitask production system The international Journal of Flexible manufacturing system, 6, pp.9-0, Francesco Martinelli Control of manufacturing systems with two value, production dependent failure rate Automatica, 4, , Madhu Jain, G.c. Sharma, Rakhi Sharma Performance modeling of state dependent system with mixed standbys and two modes of failure Applied Mathematical Modelling,32,72-724, Komal, S.P Sharma, Dinesh Kumar RAM analysis of repairable industrial systems utilizing uncertain data Applied soft computing, , Peter Bullemer et al. Specific recommendations include how to analyze plant incident reports to better understand the sources of systemic failures and improve plant operating practices Journal of Loss Prevention in the Process Industries. Vol. 23, pp , Ahmed-Tidjani Belmansour, Mustapha Nourelfath An aggregation method for performance evaluation of a tandem homogenous production line with machines having multiple failure modes Reliability Engineering and System Safety. Vol. 95, pp.93-20, Ling Wang et.al. Imperfect maintenance will decrease the expected values of cycle length and long-run availability Applied Mathematical Modelling, Vol. 35, pp , Kumar, A. and Lata, S. (202), Reliability Evaluation of Condensate System using Fuzzy Markov Model, Annals of Fuzzy Mathematics and Informatics, Vol. 4, No. 2, pp Upadhya, K.S. and Srinivasan, N.K. (202), Estimation Using Simulation for Military Systems, International Journal of Quality and Reliability Management, Vol. 29, Issue 8, pp D. Bose, G. Ghosh, K. Mandal, S.P. Sau and S. Kunar (203), Measurement and Evaluation of Reliability, and Maintainability of a Diesel Locomotive Engine International Journal of Engineering Research and Technology, Volume 6, Number 4, pp ISSN: