PERFORMANCE ANALYSIS OF A PROCESS

PERFORMANCE ANALYSIS OF A PROCESS

PERFORMANCE ANALYSIS OF A PROCESS INDUSTRY TO PROVIDE DECISION SUPPORT SYSTEM

1Rahul kumar, 2Dr. R. K. Gupta, 3Mukesh Verma, 4Pardeep Kumar, 5Sonia Sapra

1MTech Scholar, SSIET, Dreabassi

2,3 Department of Mechanical Engineering, SSIET, Derabassi

4 Department of Mechanical Engineering, ACE, Ambala

5 Department of Applied Science and Humanities, ACE, Ambala

1rahulkumar.ace@gmail.com, 2docrkg2005@yahoo.com, 3vermamukesp9@gmail.com 4pardeepkamboj@yahoo.com, 5soniasapra023@gmail.com

1. INTRODUCTION

   System availability is defined as combination of reliability and maintainability which is a measure of performance of the system under specified conditions. Complex plant consists of systems/subsystems connected in series, parallel or a combination of these. Availability and maintainability of systems/subsystems in operation must be maintained at highest in order to have higher productivity which is ultimate goal of every industry. To achieve high production goals, system should remain operative (failure free run) for maximum possible duration.

2. LITERATURE REVIEW

   Various researchers gave number of theories in the field availability and reliability for complex

   manufacturing industries. Tewari et. al.[2002] discussed behavioural analysis of crushing system in a sugar plant. Blischke [2003], Yadav et al. [2003] and Dai et al. [2003] performed reliability and availability analysis for several complex systems. Ocon et al. [2004] and Murthy et al. [2004] proposed a reliability and analysis technique using different modeling methods. Edwards et al. [2004] discussed the importance of simulation, an effective tool in improving the maintenance schedule in an automotive engine production facility and for effecting changes to decision maker's strategy over time. Gupta et al. [2005] evaluated reliability parameters of a butter manufacturing unit in a dairy plant taking into consideration exponentially distributed failure rates of various components. Lapa et al. [2006] presented a methodology for preventive maintenance policy evaluation based upon a reliability model using Genetic Algorithm. Zio et al. [2007] presented a Monte Carlo simulation model for the evaluation of the availability of a multi state and multi output offshore installation. Khanduja et al. [2008] discussed development of decision support system for washing unit of a paper plant. Gupta et al. [2009] developed a Markov model for performance evaluation of coal handling unit of a thermal power plant. Garg et al. [2010] discussed about the availability and maintenance scheduling of a repairable block-board manufacturing system. Kajal [2012] discussed the performance optimization for milk processing unit of a dairy plant at National Dairy Research Institute (N. D. R. I.), Karnal using Genetic Algorithm (G.A.). Guan [2012] developed an efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations. Pardeep [2013] developed a decision Support System for soft drink (beverage) Manufacturing plant using Markov Birth-death process. Wang [2013] discussed new approach, nested extreme response surface (NERS)

   which efficiently tackle time dependency issue in time- variant reliability analysis.

3. SYSTEM DESCRIPTION

   Milk Powder manufacturing system consists of the following components:

   Preheating System (A): It is used to heat the roller. The steam is allowed to move onto the roller still drums surface achieve a temperature high enough to dry the milk film. The flow is allowed over the entire drum length.

   Agitator (B): It works on the centrifugal force principle. Chilled milk from chiller is taken to the agitator where fat is separated from the milk. The skimmed milk is stored in milk silos for preparing milk powder. It consists of three components in series- motor, bearing and high speed gearbox. Failure of any one component causes failure of this system.

   Pasteurizer (C): It pasteurizes the milk coming from pumping system. Here the cream is heated around 800 to 820 for no holding time. The purpose is to destroy pathogenic organism, to destroy undesirable organism, to inactivate the enzymes present and to make possible removal of volatile flavors. It consists of a motor and bearing in series.

   Drum drier and scraping machine (D): The drum revolves and a thin film of milk is adhered to it which is dried by the time of a complete revolution and then scrapped by a blade. This machine consists of gearbox, motor, two drums and bearings in series.

   Pulverized Machine (E): The scrapped milk is collected and fed into pulverized machine which converts it into the fine powder form. This fine powder is then packed and stored. This machine consists of gearbox, motor, two roller and bearing in series.

4. ASSUMPTIONS AND NOTATIONS

   The following notations and assumptions are used for the purpose of mathematical modeling :

   1. Assumptions

      1. A repaired system is as good as new,

   2. Notations

   The following symbols are associated with the system: A,B,C,D,E : Subsystems in good operating state

   a,b,c,d,e : Indicates the failed state of A,B,C,D,E i : Mean constant repair rate

   i : Mean constant failure rate

   Pi(t) : Probability that at time t all units are good and system is in ith state

   System working at full capacity System working at reduced capacity

   System in failed state

   Performance Evaluation: The performance evaluation of the Milk Powder manufacturing system has been carried out with the help of probabilistic approach based upon Markov birth-death process. The differential equations are developed based on transition diagram as shown in figure 1, as follows:

   0

   + 1 + 2 + 3 + 4 + 5 = 11 +

   22 + 33 + 49 + 55 . (1)

   1

   + 11 = 1 . (2)

   2

   + 22 = 2 . (3)

   3

   + 33 = 3 . . (4)

   5

   + 55 = 5 . (5)

   + ( + + + + ) = +

   performance wise, for a specified duration.

   4 1 2 3

   5 6 4 1 6

   1. Failure and repair rates are constant over time and statistically independent.

   2. There is no simultaneous failure i.e. not more than one failure occurs at a time.

   3. Standby systems are of the same nature as that of active systems.

   4. Sufficient repair facilities are provided.

   27 + 38 + 510 + 4 . (6)

   6

   + 16 = 14 (7)

   7 2 7 2 4

   + = . (8)

   8

   + 38() = 34().(9)

   + = (10)

   9 4 9 6 4

   10

   + 510 = 54 (11)

   In the process industry, we require long run availability

   = 1

   1

   1

   , 2

   = 2

   2

   , 3

   4

   = 3

   3

   , 5

   = 5 ,

   5

   of the system, which is obtained by putting 0 at

   t and taking probabilities independent of t.

   For steady state availability, transition rates are taken to be constant.

   1 + 2 + 3 + 4 + 5 1 = 11 + 22 +

   33 + 44 + 55 (12)

   11 = 1 . (13)

   22 = 2 . (14)

   33 = 3 (15)

   55 = 5 . . (16)

   (1 + 2 + 3 + 5 + 6)4 = 16 + 27 + 38 +

   510 + 4 . . (17)

   16 = 14 . (18)

   27 = 24 (19)

   38 = 34 . . (20)

   49 = 64 . . (21)

   510 = 54 . (22)

   Solving the above equations, we get the values of all state probabilities in terms of full working state probability i.e. Po:-

   1 = 1 . (23)

   2 = 2 (24)

   3 = 3 . . . (25)

   4 = 10 (26)

   5 = 5 27

   6 = 1 10 . . 28

   7 = 2 10 . 29

   8 = 3 10 . 30

   = 6 . . 31

   9 4 1 0

   10 = 5 10 32

   Where,

   1 = 2 11 22 3355

   1 = 1 + 2 + 3 + 4 + 5

   2 = 1 + 2 + 3 + 5 + 6

   Using Normalizing conditions, i.e. Sum of all probabilities is equal to one

   10

   = 1

   =0

   1 62 3 5 1 2 3 5 1

   0 = 1

   1+ + + + 1+ + + + +

   4

   Now Steady state availability is summation of all working state prob.

   = 0 + 4 = 0 + 10

   = 1 + 1 0

   Where P0 = Probability of initial working state (0) with full capacity

   Availability index which is derived from the above equation can be used for maintenance planning and scheduling of Milk Powder Manufacturing system.

   Availability Analysis: The failure and repair rates of various subsystems of Milk Powder Manufacturing System are taken from the maintenance history sheet of plant. The performance analysis deals with quantitative analysis of all factors viz. states of nature and courses of action which also influence the maintenance decisions associated with system. The availability matrixes are generated to calculate the various availability levels for different combinations of failure and repair rates. The models are developed under the real decision making environment i.e. decision making under risk (probabilistic model) for the purpose of performance evaluation. Such models are used to implement the proper decision regarding maintenance of Milk Powder Manufacturing System of VITA plant.

5. RESULTS AND DISCUSSION

   Table 1 to 5 show the effect of failure and repair rates of Pre-Heater, Agitator, Pasteurizer, Drum Drier and Scraping Machine, Pulverized Machine on the steady state availability of Milk powder manufacturing system.

   Table 1 reveals that as failure rates of preheating system increases from 0.0005 (once in 2000 hours) to 0.00079 (once in 1266 hr), the availability decreases by 2.17%. Similarly as repair rates of Preheating system increases from 0.009 (once in 111 hr) to 0.025 (once in 40 hr), availability increases by 2.54%.

   Table 2 depicts that as failure rate of Agitator increases from 0.008 (once in 125 hours) to 0.02 (once in 50 hr), the availability decreases by 6.88%. Similarly as repair rates of Agitator increases from 0.11 (once in 9 hr) to

   0.35 (once in 3 hr), availability increases by 3.6 %.

   Table 3 shows that as failure rates of Pasteurizer increases from 0.005 (once in 200 hours) to 0.014 (once in 72 hr), the availability decreases by 7.08 %. Similarly as repair rates of Pasteurizer increases from

   1. (once in 13 hr) to 0.78 (once in 2 hr), availability increases by 4.07 %.

      Table 4 depicts that as failure rate of Drum Drier and Scraping Machine increases from 0.0008 (once in 125 hours) to 0.02 (once in 50 hr), the availability decreases by 0.49 % . Similarly as repair rates of Drum Drier and Scraping Machine increases from 0.05 (once in 20 hr) to 0.10 (once in 10 hr), availability increases by 0.11 %.

      Table 5 depicts that as failure rate of Pulverized Machine increases from 0.00009 (once in 11112 hours) to 0.0005 (once in 2000 hr), the availability decreases by 3.39 %. Similarly as repair rates of Pulverized Machine increases from 0.008 (once in 125 hr) to 0.040 (once in 25 hr), availability increases by 0.63 %.

6. CONCLUSION

   The developed availability model is used for performance evaluation of various subsystems of Milk powder manufacturing system. The availability matrix depicts the system performance for different combinations of failure and repair rate of various subsystems.

   On the basis of repair rates, the maintenance priorities should be given as per following order:

   1. Pasteurizer

   2. Agitator

   3. Pre-heater

   4. Pulverized Machine

   5. Drum Drier and Scraping Machine

   These results might be highly beneficial to the plant management for performance evaluation and availability improvement of Milk powder manufacturing system.

7. REFERENCES

[1]. Blischke, W.R., Murthy, D.N.P., Case studies in reliability and maintenance,

Wiley, New York (2003).

[2]. Edwards, J.S., Alifantis, T., Hurrion, R.D., Ladbrook, J., Robinson, S. and Waller, A., Using a simulation model for knowledge elicitation and knowledge management, Simulation Modelling Practice and Theory, (2004), Vol. 12, No. 7-8, pp. 527-540.

[3]. Garg, S., Singh, J. and Singh, D.V., Availability and maintenance scheduling of a repairable block-board manufacturing system, International Journal of Reliability and Safety, (2010), Vol. 4, No. 1, pp. 104-

118.

[4]. Guan, X. An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations, Reliability Engineering and System Safety, (2012), Vol. 97, pp. 1-13.

[5]. Gupta, P., Lal, A.K., Sharma, R.K. and Singh, J. Numerical analysis of reliability and availability of the series processes in butter oil processing plant, International Journal of Quality and reliability Management, (2005), Vol. 22, No. 3, pp. 303-316.

[6]. Gupta, S., Tewari, P.C. and Sharma, A.K. A Markov model for performance evaluation of coal handling unit of a thermal power plant, Journal of Industrial and Systems Engineering (JISE), (2009), Vol. 3, No. 2, pp.

85-96.

[7]. Kajal, S., Tewari, P.C. Performance Optimization for Skim Milk Powder Unit of a Dairy Plant Using Genetic Algorithm, International Journal of Engineering, (2012), Vol. 25, No. 3, pp. 211-221.

[8]. Khanduja, R., Tewari, P.C., Decision support system of washing unit of a paper plant, Industrial Engineering Journal, Navi Mumbai, (2008 A), Vol. 1, No. 5, pp. 26-

30.

[9]. Kumar, P.,Tewari, P.C, Decision Support System for critical subsystems of a Beverage Plant International Conference on Production and Industrial Engineering, (2013), pp. 1481-1486.

[10]. Lapa, C.M.F., Pereira, C.M. and De Barros, M.P., A model for preventive maintenance planning by genetic algorithms based in cost and reliability, Reliability Engineering and System Safety, (2006), Vol.91, pp. 233- 240.

[11]. Murthy, D.N.P., Bulmer, M. and Eccleston, J.A., Weibull model selection for reliability modelling, Reliability Engineering and System Safety, (2004), Vol. 86, pp. 257-267.

[12]. Ocon, R.P., Cazorla, D.M., A multiple system governed by a quasi-birth death process, Reliability Engineering and System Safety, (2004), Vol. 84, pp. 187-196.

[13]. Tewari, P.C., Kumar, D. and Mehta, N. P., Decision support system of refining system of sugar plant, Journal of Institution of Engineers (India), (2002), Vol. 84, pp. 41-44.

[14]. Zio, E., Cadini, F., A Monte Carlo method for the model-based estimation of nuclear reactor dynamics, Annals of Nuclear Energy, (2007), Vol. 34, No. 10,pp. 773-781.

Figure 1 Transition Diagram of Milk Powder Manufacturing System

.

Table 1: Availability Matrix for Pre-heater

1	1	0.0005	0.00057	0.00065	0.00071	0.00079
0.009		0.8314	0.8261	0.8201	0.8156	0.8097	2=0.008, 3=0.005
0.010		0.8353	0.8304	0.8250	0.8209	0.8155	4=0.0008,
							5=0.00009
0.015		0.8471	0.8437	0.8401	0.8372	0.8334	6=0.0008
0.018		0.8511	0.8483	0.8451	0.8427	0.8396	2=0.11, 3=0.08
							4=0.0008, 5=0.008
0.025		0.8568	0.8547	0.8524	0.8506	0.8483

Table 2 Availability Matrix for Agitator

2	2	0.008	0.01	0.012	0.016	0.02
0.11		0.8314	0.8191	0.8072	0.7843	0.7626	1=0.0005, 3=0.005
0.18		0.8515	0.8436	0.8358	0.8207	0.8061	4=0.0008, 5=0.00009
							6=0.0008
0.25		0.8606	0.8548	0.8491	0.8378	0.8268
							1=0.009, 3=0.08
0.30		0.8645	0.8597	0.8549	0.8454	0.8321

0.35

0.8674

0.8632

0.8591

0.8508

0.8427

4=0.0008, 5=0.008

Table 3 Availability Matrix for Pasteurizer

3 3	0.005	0.007	0.009	0.011	0.014
0.08	0.8314	0.8146	0.7984	0.7828	0.7606	1=0.0005, 2=0.008
						4=0.0008, 5=0.00009
0.15	0.8521	0.8426	0.8333	0.8242	0.8109
						6=0.0008
0.32	0.8651	0.8606	0.8561	0.8516	0.8449
						1=0.009, 2=0.11
0.65	0.8711	0.8689	0.8667	0.8644	0.8611
						4=0.0008, 5=0.008
0.78	0.8721	0.8703	0.8684	0.8665	0.8638

Table 4 Availability Matrix for Drum Drier and Scraping Machine

4	4	0.0008	0.0050	0.01	0.015	0.02
0.05		0.8314	0.8291	0.8274	0.8263	0.8265	1=0.0005, 2=0.008
0.06		0.8315	0.8304	0.8290	0.8281	0.8274	3=0.005, 5=0.00009
							6=0.0008
0.07		0.8316	0.8308	0.8295	0.8287	0.8282
							1=0.009, 2=0.11
0.08		0.8325	0.8310	0.8299	0.8292	0.8287
							3=0.008, 5=0.008
0.1		0.8325	0.8314	0.8305	0.8299	0.8295

Table 5 Availability Matrix for Pulverized Machine

5 5	0.00009	0.0002	0.0003	0.0004	0.0005
0.008	0.8314	0.8220	0.8137	0.8055	0.7975
						1=0.0005, 2=0.008
0.016	0.8353	0.8306	0.8263	0.8220	0.8178
						3=0.005, 4=0.0008
0.024	0.8366	0.8335	0.8306	0.8277	0.8249	6=0.0008
0.032	0.8373	0.8349	0.8327	0.8306	0.8284	1=0.009, 2=0.11
						3=0.008, 4=0.05
0.040	0.8377	0.8358	0.8340	0.8323	0.8306