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«by Saumil Mahendra Ambani A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical ...»

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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

Doctoral Committee:

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


I would like to express my sincere gratitude to my advisor, Professor Jun Ni, for his valuable guidance, advice and support through my research and dissertation. For challenging me to pursue things that I thought were not possible and for pushing me to achieve them. I would also like to thank Dr. Lin Li for pushing me to work harder and for having my back when the going got tough! I am grateful to my dissertation committee members, Professor Kazuhiro Saitou and Professor Amy Cohn for devoting their precious time to my research, providing valuable feedback and for being very accommodating. I would also like to thank Prof Semyon Meerkov for his excellent in class teaching and out of class guidance.

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!




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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

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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 [1992]; Papadopoulos and Heavey [1996]; Li et al. [2009] and monographs by Buzacott and Shanthikumar [1993]; Gershwin [1994]; Altiok [1997]).

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 [1993]; Papadopoulos et al. [1993]; Gershwin [1994]; Yao [1994]; Altiok [1997]; Liberopoulos et al. [2006]; Li and Meerkov [2009]). Due to uncertainties, such as machine failures, the throughput of a manufacturing system is considered a random variable.

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standard deviation associated with the weekly production of a manufacturing system might be over 10% of its mean. Meerkov and Zhang [2008], 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 [1995]).

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 [2002]; Chan and Asgarpoor [2006]; Ambani et al. [2009]) 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.

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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 [2000]). Further, complex manufacturing systems with assembly, rework, disassembly operations etc., can also be divided into several simpler serial manufacturing systems for analysis (Li [2004]). 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

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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 [2009]).

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 [1992]). 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

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of which is found in (Buzacott and Hanifin [1978]; Buzacott and Shanthikumar [1993]). TDFs simplify manufacturing system analysis and help in obtaining closed form expressions (Li et al. [2006]), making the system (analytically) more

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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 [2009] 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. [1995]; Shin et al. [1995]; Kogan and Raz [2002]; Kalade et al. [2004]; Shiau et al. [2007]; Volsema et al. [2007]), 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 [1991]; Han et al. [1998]; Chiang [2006]).

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three areas:

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 [1993]; Papadopoulos et al. [1993];

Gershwin [1994]; Yao [1994]; Altiok [1997]; Liberopoulos et al. [2006]; Li

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(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 [1988]; Narahari and Viswanadham [1994]; Mocanu [2005];

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(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

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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 [1995]; Kuo et al. [1996]).

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. [1993]; Papadopou

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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

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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

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and Meerkov [2009]).

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 [2000]).

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