Sensitivity analysis of a biscuit making plant

Introduction

Modern products have vided range from simple to complex; hence bakery plants should have quality design with optimal availability and optimal system parameters. The competition and challenge in modern engineering bakery plants is to guarantee optimal manufacturing costs and minimum design cycle time to attain performance and reliability. This chapter discusses sensitivity analysis to analyze transient behavior of repairable biscuit manufacturing plant using RPGT, based on Markov modeling for modeling system parameters equations. The effect of failure and repair of units is examined to realize optimum level of performance of system parameters. Now a day availability/maintainability analysis of process industries is having increased importance which may benefit the industry with higher productivity and lower maintenance activities with costs. Different performance measures used in process industry are indicates to define the performance of a plant in terms of system parameters. Most of these parameters are linked to operational stage while a few of these are useful to design the units at an early stage. A biscuit manufacturing plant in Bahadurgarh (Rohtak) in Haryana has 6. The system is discussed for steady-state conditions. Ri (t): Reliability of the system at time t, given that the system entered the un-failed Regenerative state 'i' at t= 0. Ai (t): Probability of the system in up time at time't', given that the system entered Regenerative state 'i' at t= 0. Bi (t): Reliability that the server is busy for doing a particulars job at time't'; given That the system entered regenerative state 'i' at t= 0. Vi (t): The expected no. of server visits for doing a job in (o,t] given that the system Entered regenerative state 'i' at t= 0. ',': denote derivative μi: Mean sojourn time spent in state i, before visiting any other states; 𝜇 𝑖 = ∫ 𝑅 𝑖 (𝑡)𝑑𝑡 ∞ 0

: The total un-conditional time spent before transiting to any other regenerative states, given that the system entered regenerative state 'i' at t=0. ni: Expected waiting time spent while doing a given job, given that the system entered regenerative state 'i' at t=0; ξ: Base state of the system. fj: Fuzziness measure of the j-state.

Vertex i Primary Circuits (CL1)

Secondary Circuits (CL2) 0 (0,1,0), (0,2,0), (0,3,0), (0,4,0), (0,5,0) (1,6,1), (1,8,1), (1,7,1), (1,9,1) Nil

(2,0,2) (0,1,0), (0,3,0), (0,4,0), (0,5,0) 3 (3,0,3) (0,1,0), (0,2,0), (0,4,0), (0,5,0) 4 (4,0,4) (0,1,0), (0,2,0), (0,3,0), (0,5,0) 5

(5,0,5) (0,1,0), (0,2,0), (0,3,0), (0,4,0)

Mean Sojourn Times RI (t): Reliability of the system at time t, given that the system in regenerative state i.: Mean sojourn time spent in state i, before visiting any other states;

Evaluation of Parameters: The Mean time to system failure and all the key parameters of the system under steady state conditions are evaluated, applying Regenerative Point Graphical Technique (RPGT) and using '0' as the base-state of the system as under:

The transition probability factors of all the reachable states from the base state 'ξ' = '0' are: Probabilities from state '0' to different vertices are given as

Mtsf (T0):

The regenerative un-failed states to which the system can transit (initial state '0'), before entering any failed state are: 'i' = 0,1 taking 'ξ' = '0'.

Availability of the System (A0):

The regenerative states at which the system is available are 'j' = 0, 1 taking base state 'ξ' = '0' the total fraction of time for which the system is available is given by

Where D = V0,0µ0+V0,1µ1+V0,2µ2+V0,3µ3+V0,4µ4+V0,5µ5+V0,6µ6+V0,7µ7+V0,8µ8+V0,9µ9

Busy Period of the Server: The regenerative states where server is busy are j = 1 ≤ i ≤ 9 and taking ξ = '0', the total fraction of time for which the server remains busy is

B0 = V0,1μ1+V0,2μ2+V0,3μ3+V0,4μ4+V0,5µ5+V0,6µ6+V0,7µ7+V0,8µ8+V0,9µ9

Expected Number of Inspections by the repair man:

The regenerative states where the repair man visits a fresh are j = 1, 2, 3, 4, 5, taking 'ξ' = '0', the number of visit by the repair man is given by

Sensitivity Analysis: Effect of failure rates of units on system parameters and varying repair rates, we have MTSF (T0): For fixed failure rates On watching the table and graph drawn for fixed failure rates of units (taking failure rates of units (mi = 0.10 Ɐ 'i') and varying repair of units, it is concluded that there not much gain in the value of T0, however there is a slight increase in the value of T0 an increasing repair rate of unit 'A'. Hence it is recommended that there is no benefit in the value of T0 on increasing the repair rates of units i.e. increasing repair rates of units will not contribute much in the value of T0. Keeping failure rates of units fixed (mi = 0.10 Ɐ 'i') and increasing repair rates of units, there is no gain in the value of A0 as is observed from the table and graph. Hence systems have fixed A0 for fixed failure rates of units and are independent of the repair rates of units. However there is a small gaining A0 on increasing repair rate of unit A0. Keeping failure rates of units (mi = 0.10 Ɐ 'i'). There is not much significance reduction in bus period of the server on increasing the repair rates of units, except or unit 'A' there is a marginal reduction in value of B0 is clear from the table and graph drawn. Hence better/ repair expert facilities are of not much use. Fixing failure rates of unit at 0.10 and increasing the repair of individual units, table and graph for values of V0 is drawn, which shows that better repair facilities do not reduce the value of V0, there is a very small scope to optimize value of V0 with the increase in repair rate of unit 'A' or we can say that value of V0 may solely depend on failure rates of units.

Effect of failure rates of units on system parameters

For fixed repair rate hi = 0.80 Ɐ i On moving from top to down in table and from the graph it is concluded that value of T0 decreases with the increase in failure rates of value units, but is least effected with the increase in failure rate of unit 'A', as on failure of unit 'A' alternatively dung is managed manually. For a good system value of T0 should be as large possible, hence it is recommended that unit B, D, E, F should be best in quality and design as for as possible. From the table and graph, we see that keeping repair rate of all units fixed and increasing failure rates of units. There is decrease in the value of A0 but is least effected with the increase in failure rates of unit 'A' over the others. For an idea system value of A0 should be as large as possible hence failure rates of units should be very small or which all units of the system should be best in quality and design or best value of A0. For a good system value of B0 should be as small as possible, from the table and graph we see that value of B0, increase with the increase in failure rates of units and also increases by equal proportions, so keep value of B0 small failure rates of all units should be as small as possible for which management should arrange and provide all units of best in quality and design, which may increase the cost for best values of B0. For a system of repute value of V0 should be as small as possible as large value of V0 will increase the maintenance cost and being bad name to the industry. From the table and graph it is observed that value of V0 increases with the increase in failure rates of units (keeping repair rates fixed). Moreover, increase in failure rates of individual units, increases the value of V0 by equal proportions. So for an ideal system it is recommended that to keep value of V0 smallest possible, all the units should be best in quality and design with lowest possible failure rates.

Conclusion

Over all it is concluded that for optimum values of system parameters, all units should be best in quality and design with smallest possible failure rates. Improvement in repair facilities does not have more significant contribution to optimize the system parameter values.

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