مدلسازی ریاضی و تحلیل عملکرد از سیستم تولید نخ شانه زده : بر اساس چند داده

The paper describes the availability of combed sliver production system, a part of yarn production plant. The units under study are specialized single purpose machines. Performance analysis of the system is carried out to identify the key factors. The optimum value of ‘r’, where ‘r’ represent the number of repairman to repair the twelve carding machines (r ≺ 12), is calculated to maximizing the steady state availability of the system. The problem is formulated using probability consideration and supplementary variable technique. Probability considerations at various stages give differential-difference equations, which are solved using Lagrange method to obtain the state probabilities. The numerical analysis carried out helps in increasing the production rate by controlling the factors affecting the system i.e. availability optimization.

Reliability, in general, can be defined as the probability of a system/device performing its anticipated purpose adequately for the intended period of time under the given operating conditions. Reliability is an important consideration in the planning, design and operation of the system. The process industries are the backbone of a country for its development. The process industries must provide continuous and long-term production to meet the ever-increasing demand at lower costs. The reliability and availability analysis of process industries can benefit in terms of higher production and lower maintenance. The need and application of reliability technology in the process industries is well understood by many researchers. Singh [1] analyzed the problem of system reliability with identical units having statically independent and dependent (common cause) failures. Singh [2] computed the state probabilities of a complex system with preemptive repeat priority repairs and failure of non-failed components. Subramanian and Anantharaman [3] carried out reliability analysis of a complex standby redundant system and estimated the comprehensive cost function. Dijkhuizen and Heijden [4] have given a series of mathematical models and optimization techniques, with which the optimal preventive maintenance intervals can be determined from an interval availability point of view. Kumar [5] and [6], Gupta et al. [7], Garg and Singh [8] and some other workers applied reliability technology to various industrial systems obtaining important results. Todinav [9] is proposed a new method for optimization of the topology of engineering systems based on reliability allocation by minimizing the total cost. The present paper consists of a brief discussion of method of calculating some important reliability characteristic such as reliability function, failure frequency and renewal frequency. A yarn production plant situated in Himachal Pradesh (India) is chosen for study. Here, the production of combed sliver, a part of a yarn production system has been discussed in detail. The combed sliver production system further consists of four sub-systems blow room (B), carding machine (C), unilap machine (U) and comber machine (M), all working in series. Sub-system M is having multiple units working in parallel. The sub-system C is a 5-out-of-12: G system i.e. there are 12 carding machines working in parallel and the system works till there are at least 5 carding machines in good and operating state. Combed sliver production sliver fails either when there remain only four carding machines in working position, or sub-system B or U comes to failed state. When there remain only four carding machines are in working state, the system is under breakdown and the collective repair (including corrective and preventive maintenance) of all the carding machines is performed. In routine, normally eight or ten units remain in working states. The twelve carding machines are repaired with the help of ‘r’ repairmen where (r < 12). The optimum value for ‘r’ is calculated which maximizes the steady state availability of the system operating with ten or more carding machines. The production capacity of the plant is 34.56 tones combed yarn per day at optimum level. The target of the management to produce 29 tones combed yarn per day. This target can be achieved if at least ten carding machines remain in operative state. With this consideration, the performance of the system is examined. Numerical analysis is carried out making use of software package MATLAB.

The foremost outcome of the analysis is that it inferences the minimum number of repairmen needed for keeping ten or more carding machines out of twelve carding machines in working states with system availability .9739 is three. Once the minimum number of repairmen is fixed, the effect of failure and repair rates of the constituent components of the system is studied. It is found out that failure and repair rates of unilap machine and repair rates of carding machines highly affect the availability of the system. So the paper concludes that repair rates of carding machine and unilap machine must be improved which could be achieved with appropriate maintenance planning and thus the availability of the system could be improved. This information is vital for the management and helps in devising a comprehensive scheduling plan for utilizing suitable repair facility in order to achieve the optimum availability.