Evaluation of Reliability Parameters of a Sugar Manufacturing Plant

: In this paper, Investigations have been carried out for the evaluation of reliability in three different cases i.e., if the reliability of each component of the complex system is R, if failure rates follow Weibull time distribution & Exponential distribution and MTTF of a sugar manufacturing plant by using Boolean function technique. The sugar plant under consideration is a complex system which consists of various subsystems viz., washing, sugar cane cutter, crushing system, Defecation, Filtration, Evaporation, Crystallization, centrifugal, refining. The units such as Defecation, Filtration, Evaporation, centrifugal have two states.


Introduction:
The considered sugar manufacturing plant consists of nine subsystems.The first subsystem is washing and it clearly wash the cane sugar without any dust.The second subsystem is sugar cane cutter, where cutters start cutting of cane in fine small pieces and then the pieces go to the third subsystem namely crushing subsystem, the sugar cane juice will be extracted.This juice goes into the subsystems like defecation, filtration, evaporation, crystallization, centrifugal.At the end the crystals of sugar enter into refining unit.Finally, we get crystal clear sugar as an output.

Assumptions:
1.The reliabilities of all constituent components of the system are known.2. The states of all components are independent.3. The state of each component and of the whole system is either good or bad 4. The failure times of all components are arbitrary.5.All components are always operating (no stand by or switched redundancy) 6.There is no repair facility.

FORMATION OF MATHEMATICAL MODEL:
By using Boolean Function Technique, the conditions of capability for the successful operation of the system in terms of logical matrix are expressed as:   (1)

SOLUTION OF THE MODEL:
By the application of algebra of logic, equation (1) may be written as ( , , , , , , , )  3) may be written as: • Email: editor@ijfmr.com

SOME PARTICULAR CASES:
Case I: When reliability of each component R then equation (55) yields 13 12 11 10 9 Case III: When failure rates follow exponential time distribution Exponential distribution is nothing but a particular case of Weibull distribution for 1 p  and is very useful for practical problems purpose.Therefore, the reliability of considered system as a whole at an instant "s" is expressed as:

Conclusion:
In this paper, we have considered a sugar plant for analysis of various reliability parameters by employing the Boolean function technique and algebra of logics.Table 1 computes the reliability of the system with respect to time when failure rates follow exponential and Weibull time distributions.From the graph "reliability Vs Time"(Fig2) reveals that the reliability of the complex system decreases approximately at a uniformly rate in case of exponential time distribution, but decreases very rapidly when failure rates follow Weibull distribution.Table 2 and graph "M.T.T.F Vs Failure rate"(Fig.3) yields that MTTF of the system decreases catastrophically in the beginning but later it decreases approximately at a uniform rate.

56) Case II: When failure rates follow Weibull time distribution:
 Also, an important reliability parameter, viz; Mean time to failure (M.T.T.F) in this case is given by • Email: editor@ijfmr.comIJFMR2301557 Volume 5, Issue 1, January-February 2023 17 i  and j  "s has mentioned earlier.Exponential Distribution Weibull Distribution • Email: editor@ijfmr.comIJFMR2301557 Volume 5, Issue 1, January-February 2023 18 7. Numerical computation for MTTF: Setting i   one can compute table 2 from equation (59)

Table 2 Fig.3
Kumar, Evaluation of Reliability and MTTF of a Power Plant with the aid of Boolean Function Expansion Algorithm, Microelectronic Reliability,U.K.,26,1986.PP.821-824.