«by Saumil Mahendra Ambani A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy (Mechanical ...»
ANALYTICAL ESTIMATION OF
THROUGHPUT DISTRIBUTION FOR SERIAL
MANUFACTURING SYSTEMS WITH
MULTI-STATE MACHINES AND ITS
Saumil Mahendra Ambani
A dissertation submitted in partial fulﬁllment
of the requirements for the degree of
Doctor of Philosophy (Mechanical Engineering) in The University of Michigan 2011
Professor Jun Ni, Co-Chair Assistant Research Scientist Lin Li, Co-Chair Professor Kazuhiro Saitou Associate Professor Amy Ellen Mainville Cohn ⃝ c Saumil Ambani 2011 Dedicated to my parents ii
A special thanks to every Wu group member for the fun picnics, IAB’s, rides (dropping me home every night) and whatnots. A special shoutout to Grace, George, Adam, Seungchul, Xiaoning, Ahmad and Shiming. I would also like to thank all of my ‘other friends’ for providing me with food, bed, tea and an ear when each was needed. Thank you Devesh, Amit, Paul, Abhijeet, Ashwani, Devyani, Biju, Prasanna, Kaustubh, Saurabh, Anna, Kritika, Harish, Shaurjo, Anurag, Trushal, Naveen, Juil... and lots more.
I want to take this opportunity to dedicate my research to my parents. Words will never be enough to thank you. Also, what better time to say the ﬁrst nice thing about my brother in years! Nikhil, thanks for always supporting me and encouraging me! And Priti, my sister in law, I can’t be grateful enough for providing me a home iii away from home, the yummiest puﬀs and the cutest wonder, Mr. Neil- You three rock!
Last but not the least, I would like to thank my ﬁancee and also my best friend, Madhura, for all her support and love over the years. For always believing in me and carrying me through all my highs and lows. I could not have done this without you.
WE did it!
TABLE OF CONTENTSDEDICATION..........
eP M Eﬃciency of the machine in presence of PM ed M Eﬃciency of the machine in presence of deterministic PM P e∗ M Optimal eﬃciency of the machine in presence of PM P
1.1 Motivation An accurate estimate of a system’s performance is necessary for design, improvement and management of a manufacturing system. A system’s performance can be characterized using many performance measures, several of which include, throughput, work in process (WIP), probability of blockage, probability of starvation and residence time. Of these, throughput, deﬁned as the number of parts produced by the last machine of a manufacturing system over a given period of time, has attracted signiﬁcant attention over the past ﬁfty years (see reviews by Dallery and Gershwin ; Papadopoulos and Heavey ; Li et al.  and monographs by Buzacott and Shanthikumar ; Gershwin ; Altiok ).
From a manufacturing system modeling perspective, the steady state behavior of a manufacturing system has been well studied, with focus on estimating average (ﬁrst order) performance of a system (see, for instance, monographs by Buzacott and Shanthikumar ; Papadopoulos et al. ; Gershwin ; Yao ; Altiok ; Liberopoulos et al. ; Li and Meerkov ). Due to uncertainties, such as machine failures, the throughput of a manufacturing system is considered a random variable.
standard deviation associated with the weekly production of a manufacturing system might be over 10% of its mean. Meerkov and Zhang , in their recent study of transient analysis of manufacturing systems, stated that a production line with cycle time of 1 minute, initially empty buﬀers and operating time of 8 hours (1 shift), could lose up to 10% of the estimated production, within a given shift. Such high variability may result in customer requirements not being met on time, several times. By estimating the throughput distribution of a manufacturing system, higher order estimates of the internal and external performance measures of a manufacturing system can be obtained, using which, higher predictability and dependability of a manufacturing system can be achieved.
Over the past two decades, in a parallel area of research, condition monitoring of machines has developed signiﬁcantly, largely due to the introduction of low-cost electronics, intelligent sensing devices and data capture equipment, and its successful application to many industries, including processing, services and manufacturing.
Condition monitoring aims towards increasing system reliability and reducing maintenance costs, and has resulted in a gradual shift from time based maintenance to condition based maintenance (Fararooy and Allan ).
In contrast to existing manufacturing system machine models, wherein machines are represented as two state models (with operating and failure states); the modern condition based maintenance (CBM) models consider machines as multi state models (Chen and Trivedi ; Chan and Asgarpoor ; Ambani et al. ) with multiple degradation and failure states. Introduction of multi-state machine models in manufacturing system modeling can lead to inclusion of real time condition monitoring within manufacturing system decision making.
used in high volume production and characterize the inter-relationship of manufacturing stations and buﬀers, which may be used to model the key features of manufacturing environments with simplifying assumptions (Dincer and Deler ). Further, complex manufacturing systems with assembly, rework, disassembly operations etc., can also be divided into several simpler serial manufacturing systems for analysis (Li ). Hence, the study of serial manufacturing systems is fundamental and essential to analyzing complex manufacturing systems.
Based on the above considerations, the study of throughput distribution of a serial manufacturing system with multi-state machines, can lead to improved predictability and dependability of manufacturing systems, and can aid the development of a real time decision making framework to include condition monitoring of machines.
Accomplishing the above tasks will result in improved system reliability and reduced maintenance costs.
1.2 Background and Scope A manufacturing system consists of material (parts), work stations (machines) and storage areas (buﬀers). The work stations may consist of machines, work cells or departments within a factory, while the buﬀers may consist of simple containers, material handling devices or other forms of storage locations. In this dissertation, work areas are referred to as machines, storage areas as buﬀers and material as parts.
A manufacturing system with machines and buﬀers arranged in a consecutive order, with buﬀers present between every two machines, is known as a serial manufacturing system. Figure 1.1 shows the block diagram of a serial manufacturing system, where Mi is the ith machine and Bj is the j th buﬀer of the system. Serial
Depending on the characteristics of the machines and buﬀers, a manufacturing
system may be deﬁned as follows:
1. Synchronous/ Asynchronous: If the cycle times of all machines are identical, the manufacturing system is called synchronous. If the cycle times are not identical, the system is called as asynchronous (Li and Meerkov ).
2. Saturated/ Unsaturated : If the ﬁrst machine of the manufacturing system never starves (unlimited supply of raw materials) and the last machine of the system never blocks (inﬁnite demand), then the system is called saturated, otherwise unsaturated (Dallery and Gershwin ). Most practical systems are unsaturated, but in order to focus on the internal dynamics of a system, manufacturing systems are often assumed as saturated.
3. Reliable/ Unreliable: Manufacturing systems with 100% reliable machines are referred to as reliable systems. If machines of a manufacturing system can undergo failures, the system is referred to as unreliable.
Further, depending on the nature of machine failures, an unreliable system may be classiﬁed to have time dependent failures (TDFs) or operation dependent failures (ODFs). TDFs depend on the time spent by a machine in its up state, while ODFs depend on the number of operations carried out by a machine. Both
of which is found in (Buzacott and Haniﬁn ; Buzacott and Shanthikumar ). TDFs simplify manufacturing system analysis and help in obtaining closed form expressions (Li et al. ), making the system (analytically) more
4. Finite/ Inﬁnite buﬀers: The size of buﬀers in a manufacturing system dictates the coupling between machines. For example, in presence of ﬁnite buﬀers, the failure of one machine may lead to downtime of other machines; whereas, in presence of inﬁnite buﬀers, the machines behave as if in complete isolation.
In this study, a manufacturing system is considered to be synchronous, saturated, unreliable, serial manufacturing systems with ﬁnite buﬀers and time dependent failures. Other features of manufacturing systems that are equally important, but out of the scope of this dissertation are structure and quality. A manufacturing system, depending on the arrangement of machines and buﬀers (layout), may result in different structures, such as, serial, parallel, closed loop, rework loop, assembly and disassembly (see Li and Meerkov  for detailed description of structural considerations). In presence of material or machine errors, a manufacturing system may produce defective parts, resulting in quality considerations. Several studies have been done to optimally position an inspection station in a manufacturing system (Rebello et al. ; Shin et al. ; Kogan and Raz ; Kalade et al. ; Shiau et al. ; Volsema et al. ), to maximize production of good parts. Another important study related to quality, is determining the relation between quantity and quality of products for a system (Jacobs and Meerkov ; Han et al. ; Chiang ).
1. Analysis: Given a manufacturing system with machine and buﬀer characteristics, manufacturing system analysis focuses on estimating the performance of a system. Few common performance measures found in literature are throughput, WIP, probability of blockage, probability of starvation and probability of meeting given demand. Depending on the duration of interest, three types of
analysis may be pursued:
(a) Steady State Analysis: The steady state analysis of a manufacturing system focuses on the average performance of a system, while the system is in its steady state. Most results and studies in literature focus on this type of analysis (Buzacott and Shanthikumar ; Papadopoulos et al. ;
Gershwin ; Yao ; Altiok ; Liberopoulos et al. ; Li
(b) Transient Analysis: Study of a manufacturing system during the initial phase of operations, before reaching steady state, is studied in transient analysis. Although equally important, this area has received limited attention in the past and has been recognized as a critical area for future studies (Mitra ; Narahari and Viswanadham ; Mocanu ;
(c) Interval Analysis: Analysis of a manufacturing system over a given ﬁnite duration of time, wherein the system may or may not be in steady state, is called as interval analysis. This approach is usually used to obtain the cumulative performance of a system over a given period of time, for
2. Continuous Improvement: Redistributing resources within a manufacturing system in order to improve the performance of an existing system is known as continuous improvement. An example of this type of study is bottleneck identiﬁcation (Lawrence and Buss ; Kuo et al. ).
3. Design: Given a desired performance, obtaining the minimum requirements for machines and buﬀers is referred to as design of manufacturing systems. Few studies related to this area are found in (Papadopoulos et al. ; Papadopou
This study focuses on the interval analysis of an unreliable, saturated, serial manufacturing system with time dependent failures. More speciﬁcally, the main goal of this dissertation is to estimate the throughput distribution and related performance measures of the above described system, over a given period of time.
1.3 Literature Review 1.3.1 Throughput Analysis Several deﬁnitions related to throughput are found in literature. The commonly
found deﬁnitions are:
1. Throughput is deﬁned as the expected number of parts produced by a produc
2. For a system in steady state, the average number of parts produced by the last machine of a production system per unit of time is known as throughput (Li
and Meerkov ).
3. The number of parts (a random variable) produced by a manufacturing system (transfer line with buﬀer inventories) per unit time is deﬁned as the throughput rate (Dincer and Deler ).