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,
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