Mathematical Models for Productivity Rate of Automated Lines with Reliability Attributes of Mechanisms Ryspek Usubamatov 1, a * and Tan Chan Sin 1, b 1,2 School of Manufacturing Engineering, Campus Tetap Pauh, University Malaysia Perlis, 02600 Arau, Perlis, Malaysia a ryspek@unimap.eadu.my, b tcs5077@hotmail.com Keywords: Productivity, Reliability, Automated lines Abstract. Automated lines with complex structures consist of stations and mechanisms with different levels of reliability. Most publications that present the mathematical models for productivity of automated lines are based on simplifications to derive the approximate equations of productivity. Simplification is based on the premise that all stations of the automated lines have one level of reliability, and balancing of technological process on stations is conducted evenly, etc. However, manufacturers need correct and clear mathematical models to enable the calculation of the productivity of the automated lines with high accuracy. This paper presents the analytical approach to the productivity rate of the automated lines with stations and mechanisms, with different failure rates, and processing times. The proposed mathematical models allow for the output of automated lines to be modelled with results that are close to actual productivity. Introduction Mathematical models for the productivity rate of the industrial machines with complex designs are primary attributes, to evaluate the efficiency of manufacturing system. Methodology for calculation of the system productivity is presented by several key publications that consider all aspects of manufacturing processes [1-4]. Efficiency of expensive production systems like automated lines with complex design depends on reliability of main mechanisms and units. Reliability problem in industry is not new and its attributes of engineering are well presented and made it possible to describe analytically manufacturing problems [5-7]. The theory of reliability provides standard attributes and modes of calculation that can be used for the mathematical modeling of reliability of manufacturing systems. However, known attributes of reliability describe properties of an industrial machine separately from its productivity rate and other indices. In literature, there are publications which describe the reliability of manufacturing systems using a probabilistic approach that allow for the calculation of the average magnitudes of searching parameters [6-7]. Several publications are dedicated to studying the productivity and reliability attributes of automated lines with different designs [8]. Analysis of the equations for productivity of multi-station automated lines of different structures shows that for simplification, the attributes of reliability of stations are accepted by average magnitude. Such simplification formulates equations for productivity rate of the automated lines which are unable to give accurate results in calculation [3]. Mathematical models of industrial machines’ productivity rate are derived according to the level of consideration of the manufacturing processes. This article presents the equations of productivity that include the technological and technical aspects of the manufacturing systems and do not consider aspects of maintenance of machines at prescribed planned overhaul repair time. The reliability theory represents the indices by the following attributes: the machine failure rate λ = 1/m w ; mean time to work m w ; mean time to repair m r ; and availability A. These attributes of reliability are used to develop analytical equations for the productivity rate of machines with complex designs like automated lines of different structures. This paper presents mathematical models of productivity rate of automated lines, which stations failure rates are different and results of productivity calculations will have values close to the actual output. Applied Mechanics and Materials Vol. 695 (2015) pp 521-525 Submitted: 16.06.2014 © (2015) Trans Tech Publications, Switzerland Revised: 15.09.2014 doi:10.4028/www.scientific.net/AMM.695.521 Accepted: 15.09.2014 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 1.9.65.108-05/11/14,06:42:01)