Mathematical Modelling the Assembly Cell Operation in the Context of Increasing Its Reliability

Abstract

In the article, by limiting the mathematical description to one assembly cell connected with the workpiece dispenser, the considerations concerning the time redundancy are partially eliminated and the preferred material redundancy, in the form of the workpiece reserves in the dispensers, is achieved thanks to the reserve of the assembly cell productivity. Additionally, it has been assumed in the article that all random variables have the Erlang distribution of two-grade. Two cases were presented in the model: when the workpiece dispenser fails and when the dispenser has absolute reliability. INTRODUCTIONThe assembly line is a group of assembly cells equipped with assembling machines and auxiliary operation work stands which are located in accordance with the sequence of the operations performed and which are connected with mechanical transport equipment [1,2]. In order to simplify and facilitate analysing phenomena on the assembly line, the events occurring in the elementary component of the assembly line are studied. The elementary components of the line under scrutiny may be the following: module, work centre, flexible production machine, assembly cell [3]. The results obtained are generalized and approximated with regard to next elementary components of the line. This approach enables drawing conclusions which concern functioning of the whole line.On the one hand, the task of increasing the assembly line reliability can be accomplished on the basis of increasing the reliability of separate units which constitute the whole system [4,5]. On the other hand, the task can be accomplished by applying the apparatus and time redundancy [6]. The second method is used much more frequently since it enables simultaneous increasing of the automated system flexibility [7]. Time redundancy consists in introducing time reserve during which failures of individual line components do not lead to interruption of the line functioning [8]. The time reserve is not introduced to the facility but to the rule (algorithm) which governs the utilization of the facility [9,10]. Practical experience indicates that, in order to assure the production stability, guarantee reserves should increase in parallel with the production increase, widening of nomenclature and acceleration of the production renewal rate, which consequently leads to freezing of the company circulating assets [11][12][13][14]. Introduction of time redundancy on the assembly line necessitates defining the following: time redundancy implementation method, conditions for time redundancy utilization and spatial distribution of time redundancy (for each line component or for a group of components) [15].Frequently, in order to achieve time redundancy, intermediate production feeders (dispensers) are located on the line between separate assembly line cells [16,17]. Application of feeders (dispensers) enables increasing line reliability and capacity which results in reduced loss due to line failures [18].Research problems focusing on description of the assembly line model...