Development of performance evaluation system for screening unit of a paper plant.

Khanduja, Rajiv ; Tewari, P.C. ; Kumar, Dinesh 等

Introduction

Due to automation in the process industries, maintenance is considered as an integral part of the production process. It is done by optimal utilization of maintenance resources and by ensuring high performance level. For increasing the productivity, availability and reliability of equipment/subsystems in operation must be maintained at highest order. To achieve high production goals, the units should be remain operative (run failure free) for maximum possible duration. However, practically these units are subjected to random failures due to poor design, wrong manufacturing techniques, lack of operative skills, poor maintenance, overload, delay in starting maintenance and human error etc. These causes lead to non-availability of an industrial system resulting into improper utilization of resources (man, machine, material, money and time). So to achieve high production and good quality targets, there should be highest system performance (maximum possible long run system availability) for which maintenance operations should be managed well. The paper plants are complex and repairable engineering systems, comprising of various units namely chipping, cooking, washing, bleaching, screening, stock preparation and paper production etc. These units are arranged in hybrid configuration. The important process of a paper industry, upon which the quality of paper depends, is screening process. In the process of paper formation, the chips from storage are fed in to a digester to form the pulp, which is processed through system called knotter, decker, opener and washing. These systems have been discussed in detail in [2-4]. The washed pulp is kept in a chamber where chlorine, at a controlled rate, is pressed through the pulp for a few hours. The pulp is passed over a filter and washer in four stages to get chlorine free white pulp. The white bleached pulp so obtained, is first passed through a screen to separate out oversize and odd shape particles. It is then processed through a cleaner and finally sent to paper making machine.

System Description

The screening unit comprises of four main subsystems, which are as follows:

1. Medium Consistency (M.C) Pump subsystem (A): It consists of one M C Pump which is used to flow the pulp from washer with consistency 4 -5% with fresh water.

2. Screen subsystem (B): It consists of one screen to remove the knots and other undesirable foreign materials from the pulp .Its failure can cause a sudden and complete failure of the unit.

3. Cleaner subsystem ([C.sub.I]): It consists of three cleaners in parallel to mix the water with the pulp by centrifugal action. Failure of anyone cleaner results in poor quality of paper. Complete failure of this unit reduces the efficiency of plant but system remains operative.

4. Decker subsystem ([D.sub.J]): It consists of one decker to reduce the blackness of the pulp if any by controlling the water contents. Its failure causes complete failure of the unit.

Assumptions

The following assumptions are addressed for the purpose of mathematical analysis of the screening unit:

1. There are no simultaneous failures among the subsystems.

2. The repair process begins soon after a particular unit fails.

3. Failure and repair events are statistically independent.

4. A repair unit is as good as a new one.

5. Failure and repair rates of the subsystems are constant.

6. System may work at a reduced capacity / efficiency.

Notations

The following notations are addressed for the purpose of mathematical analysis of the screening unit:

A,B,[C.sub.I],[D.sub.J] : represent good working states of respective M.C.Pump, screen,cleaner and decker.

a,b,[c.sub.I],[d.sub.J] : represent failed states of respective M.C.Pump, screen, cleaner and decker.

[[lambda].sub.1], [[lambda].sub.2],[[lambda].sub.3] [[lambda].sub.4] : respective mean constant failure rates of A,B,[C.sub.I], [D.sub.J].

[[mu].sub.1], [[mu].sub.2],[[mu].sub.3], [[mu].sub.4] : respective mean constant repair rates of a,b,[c.sub.I].[d.sub.J].

d/dt : represents derivative w.r.t 't'.

[P.sub.i](t) : represents the state probability that the system is in ith state at time t

System Modeling

Simple probabilistic approach gives the difference differential equations, associated with the transition diagram Fig.1 (Markov graph) of the screening unit [1, 6-9].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[d/dt+[[mu].sub.1]][P.sub.3](t)=[[lambda].sub.1][P.sub.0](t) (4)

[d/dt+[[mu].sub.2]][P.sub.4](t)=[[lambda].sub.2][P.sub.0](t) (5)

[d/dt+[[mu].sub.4]][P.sub.5](t)=[[lambda].sub.4][P.sub.0](t) (6)

[d/dt+[[mu].sub.1]][P.sub.6](t)=[[lambda].sub.1][P.sub.0](t) (7)

[d/dt+[[mu].sub.2]][P.sub.7](t)=[[lambda].sub.2][P.sub.0](t) (8)

[d/dt+[[mu].sub.4]][P.sub.8](t)=[[lambda].sub.4][P.sub.0](t) (9)

[d/dt+[[mu].sub.1]][P.sub.9](t)=[[lambda].sub.1][P.sub.0](t) (10)

[d/dt+[[mu].sub.2]][P.sub.1]0(t)=[[lambda].sub.2][P.sub.0](t) (11)

[d/dt+[[mu].sub.4]][P.sub.1]1(t)=[[lambda].sub.4][P.sub.0](t) (12)

With initial conditions at time t = 0

[P.sub.i] (t) = 1 for i = 0 = 0 for i [not equal to] 0

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Steady State Analysis

Since the paper industry is a process industry, its every unit should be available for a long period. Therefore, long run availability of the system is computed by substituting

d/dt =0 and t [right arrow] [infinity] for equations (1) - (12) and solving them recursively:

[P.sub.1] = B[P.sub.0] [P.sub.4] = [B.sub.2][P.sub.0] [P.sub.7] = [B.sub.2]B[P.sub.0] [P.sub.1]0 = [B.sub.2][B.sub.3]B[P.sub.0]

Where [B.sub.i] = [lambda]i/[mu]i

[P.sub.2] = [B.sub.3]B[P.sub.0] [P.sub.5] = [B.sub.4][P.sub.0] [P.sub.8] = [B.sub.4]B[P.sub.0] [P.sub.1]1 = [B.sub.4][B.sub.3]B[P.sub.0]

i= 1,2,3,4

[P.sub.3] = [B.sub.1][P.sub.0] [P.sub.6] = [B.sub.1]B[P.sub.0] [P.sub.9] = [B.sub.1][B.sub.3]B[P.sub.0]

B= [[lambda].sub.3] /([[lambda].sub.3] +[[mu].sub.3])

Using Normalizing condition i.e. sum of all the state probabilities is equal to one [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The steady state availability (Av.) of this screening unit is given by summation of all the full working and reduced capacity states.

Av. = [P.sub.0] +[P.sub.1]+[P.sub.2]

Av. = [P.sub.0] + B[P.sub.0]+[B.sub.3]B[P.sub.0]

Av. = [P.sub.0][1 + B + [B.sub.3]B]

Av. = [1 + B + [B.sub.3]B] [(1 + [B.sub.1] + [B.sub.2]+[B.sub.4]) (1+B +[B.sub.3]B)]

Av. = 1/ [1+[B.sub.1] +[B.sub.2]+[B.sub.4]]

Therefore, availability of the screening unit (Av.) represents the performance evaluation model of screening unit of a paper plant.

Performance Evaluation Analysis

This performance evaluation model includes all possible states of nature, that is, future events ([lambda]i) and the identification of all the courses of action, that is, repair priorities ([[mu].sub.i]). The model developed is used to implement the maintenance policies for a screening unit in paper plant. The various performance levels may be computed for different combinations of failure and repair rates / priorities. On the basis of analysis, one may select the best possible combination ([lambda]i, [mu]i), that is, optimal maintenance strategies and hence maintenance operations management can be done sucessfully.

Table 1 and graph in fig.3 show the effect of M.C. Pump subsystem parameters i.e. failure and repair rates ([lambda]i, [mu]i) on the performance i.e. availability of screening unit. It is observed that for some known values of failure / repair rates of screen and decker ([[lambda].sub.2] = 0.01, [[mu].sub.2] = 0.25, [[lambda].sub.4] = 0.02, [[mu].sub.4] = 0.10), as failure rate of M.C. Pump increases from 0.05 (once in 20 hrs) to 0.09(once in 11.11 hrs), the unit availability decreases by about 13%. Similarly as repair rate of M.C. Pump increases from 0.10(once in 10 hrs) to 0.50(once in 2 hrs), the unit availability increases considerably by about 17%.

[FIGURE 3 OMITTED]

Table 2 and graph in figure 4 depict the effect of screen subsystem parameters i.e. failure and repair rates ([lambda]i,[mu]i) on the availability of screening unit. It is observed that for some known values of failure / repair rates of M.C. Pump and decker ([[lambda].sub.1] = 0.05, [[mu].sub.1] = 0.20, [[lambda].sub.4] = 0.02, [[mu].sub.4] = 0.10), as failure rate of screen increases from 0.01 (once in 100 hrs) to 0.09(once in 11.11 hrs), the unit availability decreases considerably by about 29%. Similarly as repair rate of screen increases from 0.05(once in 20 hrs) to 0.45(once in 2.22 hrs), the unit availability increases by about 7%.

[FIGURE 4 OMITTED]

Table 3 and graph in figure 5 reveal the effect of decker subsystem parameters i.e. failure and repair rates ([lambda]i,[mu]i) on the availability of screening unit .It is observed that for some known values of failure / repair rates of M.C. Pump and screen ([[lambda].sub.1] = 0.05, [[mu].sub.1] = 0.20, [[lambda].sub.2] = 0.01, [[mu].sub.2] = 0.25), as failure rate of decker increases from 0.020 (once in 50 hrs) to 0.08(once in 12.5 hrs), the unit availability decreases by about 19%. Similarly as repair rate of decker increases from 0.10(once in 10 hrs) to 0.30(once in 3.33 hrs), the unit availability increases by about 7%.

[FIGURE 5 OMITTED]

Conclusions

It can thus be concluded that the performance evaluation system is effectively used for the availability analysis of various sub-systems of screening unit of a paper plant. It also shows the relationship among various failure and repair rates ([lambda]i,[mu]i) for each subsystem, that is, M.C Pump,screen and decker subsystems of a paper plant. It provides the various availability levels for different combinations of failure and repair rates for each subsystem as shown in table 1-3. It also helps in determining the optimal maintenance strategies, which will ensure the maximum overall availability of a screening unit of a paper plant. The optimum values of failure and repair rates for each subsystem are given in table 4 as shown above. Therefore, the results of this paper will be highly beneficial to the plant management for the corrective and timely execution of proper maintenance strategies and hence to enhance the performance of screening unit of the paper plant These findings will also ensure the effective and efficient maintenance operations management for the screening unit of the paper plant concerned.

References

[1] Dhillon B S and Singh C (1981), Engineering Reliability-New Techniques and Applications, John Willey and Sons, New York.

[2] Kumar Dinesh., Singh I P and Singh Jai (1988), "Reliability analysis of the feeding system in the paper industry", Microelectron. Relaibility, Int.J. Vol.28, pp.213-215.

[3] Kumar Dinesh, Singh Jai and Pandey P C (1989), "Availability analysis of the washing system in the paper industry", Microelectron. Relaibility,, Int.J. Vol.29, pp.775-778.

[4] Kumar Dinesh., Singh Jai and Pandey P C (1993), "Operational behavior and profit function for a bleaching and screening system in the paper industry", Microelectron. Relaibility, Int.J. Vol. 33, pp.1101-1105.

[5] Sheu C and Krajevski L J (1994), "A decision model for corrective maintenance management", International journal of production research. vol. 32, pp.1365-1382.

[6] Sunand Kumar, Dinesh Kumar and N P Mehta (1996), "Behavioural analysis of shell gasification and Carbon recovery process in urea Fertilizer Plant", Microelectron. Relaibility, Int.J. Vol.36,No.5, pp.671-673.

[7] Sunand Kumar, Dinesh Kumar and N P Mehta (1999), "Maintenance Management for Ammonia Synthesis System in urea Fertilizer Plant", International journal of Management and System (IJOMAS) Vol.15,No.3, pp.211-214.

[8] P C Tewari et al. (2003) "Decision Support System of refining system of Sugar Plant " I.E. (INDIA) Journal of Production Engineering, Volume 84, pp.41-44.

[9] Tewari et al., 'Decision Making Model for Steam Generation System using Genetic Algorithm', Proceedings of National Conference held at Goa September 10-12, 2004.

[10] Singhal A K and Jain S (2005), " Reliability Analysis & Risk Assessment of Steam Power Plant using Mixed Redundancy", Proceedings of 14th ISME International Conference in Mechanical Engg. In Knowledge Age", New Delhi.

[11] Braglia, M., Fantoni, G. and Frosolini, M., 2007, The house of reliability", International Journal of Quality & Reliability Management, Vol. 24 No. 4, pp. 420-440.

[12] Kumar, S., Chattopadhyay, G. and Kumar U., 2007, Reliability improvement through alternative designs--A case study, Reliability Engineering and System Safety, 92 pp.983-991.

Rajiv Khanduja *, P.C. Tewari ** and Dinesh Kumar ***

* Assistant Professor Mechanical Engineering Department, JMIT, Radaur, Haryana e-mail: [email protected]

** Assistant Professor, Mechanical Engineering Department, NIT, Kurukshetra, Haryana e-mail: [email protected]

*** Professor, Mechanical & Industrial Engineering Department, IIT, Roorkee, Uttranchal

Table 1: Performance Matrix for M.C. Pump Subsystem of
Screening Unit Availability (Av.)

[[mu].sub.1]/
[[lambda].sub.1]   0.10     0.20     0.30     0.40     0.50

0.05               0.5747   0.6711   0.7109   0.7326   0.7462
0.06               0.5434   0.6493   0.6944   0.7194   0.7352
0.07               0.5154   0.6289   0.6787   0.7067   0.7246
0.08               0.4900   0.6097   0.6637   0.6944   0.7142
0.09               0.4672   0.5917   0.6493   0.6825   0.7042

[[mu].sub.1]/
[[lambda].sub.1]

0.05               [[lambda].sub.2] = 0.01
0.06               [[mu].sub.2] = 0.25
0.07               [[lambda].sub.4] = 0.02
0.08               [[mu].sub.4] = 0.10
0.09

Table 2: Performance Matrix for Screen Subsystem of Screening
Unit Availability (Av.)

[[mu].sub.2]/
[[lambda].sub.2]   0.05     0.15     0.25     0.35     0.45

0.01               0.6060   0.6593   0.6711   0.6763   0.6792
0.03               0.4878   0.6060   0.6369   0.6511   0.6593
0.05               0.4081   0.5607   0.6060   0.6278   0.6489
0.07               0.3508   0.5217   0.5780   0.6060   0.6228
0.09               0.3076   0.4878   0.5524   0.5857   0.6060

[[mu].sub.2]/
[[lambda].sub.2]

0.01               [[lambda].sub.1] = 0.05
0.03               [[mu].sub.1] = 0.20
0.05               [[lambda].sub.4] = 0.02
0.07               [[mu].sub.4] = 0.10
0.09

Table 3: Performance Matrix for Decker Subsystem of Screening
Unit Availability (Av.)

[[mu].sub.4]/
[[lambda].sub.4]   0.10     0.15     0.20     0.25     0.30

0.020              0.6711   0.7025   0.7194   0.7299   0.7371
0.035              0.6097   0.6564   0.6825   0.6993   0.7109
0.050              0.5586   0.6160   0.6493   0.6711   0.6864
0.065              0.4901   0.5802   0.6191   0.6451   0.6000
0.080              0.4784   0.5484   0.5917   0.6211   0.6423

[[mu].sub.4]/
[[lambda].sub.4]

0.020              [[lambda].sub.1] = 0.05
0.035              [[mu].sub.1] = 0.20
0.050              [[lambda].sub.2] = 0.01
0.065              [[mu].sub.2] = 0.25
0.080

Table 4: Optimal Values of failure and repair rates of M.C.
Pump, screen, decker

         Failure Rates             Repair Rates
Sr.No.   ([lambda]i)               ([mu]i)

1.       [[lambda].sub.1] = 0.05   [[mu].sub.1] = 0.50
2.       [[lambda].sub.2] = 0.01   [[mu].sub.2] = 0.45
3.       [[lambda].sub.4] = 0.02   [[mu].sub.4] = 0.30

         Max. Availability
Sr.No.   Level Approx. (%)

1.       75%
2.       68%
3.       74%