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Интернет-журнал «Науковедение» ISSN 2223-5167 http ://naukovedenie.ru/ Том 7, №3 (2015) http ://naukovedenie. ru/index.php?p=vol7-3 URL статьи: http://naukovedenie.ru/PDF/26TangVN315.pdf DOI: 10.15862/26TangVN315 (http://dx.doi.org/10.15862/26TangVN315)
Okai George Essah Yaw
Tver State Technical University Tver Russia PhD Student
Presbyterian University College, Ghana
Lecturer
E-mail: [email protected]
Klushin Alexander Yurievich
Tver State Technical University Tver Russia Associate Professor E-mail: [email protected]
Bogatikov Valery Nikolayevich
Tver State Technical University Tver Russia Professor E-mail: [email protected]
System Analysis and Modeling of the Manufacturing Processes of Solid-Based Pharmaceutical Dosage Form Using
Finite Automata
Abstract. The objective of this paper is to conduct a system analysis and develop a model of the manufacturing processes of pharmaceutical solid dosage forms with much emphasis on tablets. The system analysis was carried out with much emphasis on both the manufacturing processes and the equipment used at each stage of the manufacturing system. The development of a finite automata model for the manufacturing processes of pharmaceutical solid dosage forms was briefly discussed. Classification of the technological processes within the manufacturing of solid-based dosage forms was also discussed. From the resulting finite automata scheme and a transition table developed, a clearer picture of the technological processes in the manufacturing system was shown. The Finite Automata model developed in this paper can be used to solve the problem of choosing an optimal manufacturing model. It can also be used to improve the efficiency and reliability in the production of the pharmaceutical solid dosage forms.
Keywords: manufacturing process; finite automata; pharmaceutical manufacturing; modeling; system analysis; solid dosage; transition; state; technological process; pharmaceutical industry.
For citation
Okai George Essah Yaw, Klushin A.Yu., Bogatikov V.N. System Analysis and Modeling of the Manufacturing Processes of Solid-Based Pharmaceutical Dosage Form Using Finite Automata // On-line journal "Naukovedenie" Vol 7, №3 (2015) http://naukovedenie.ru/PDF/26TangVN315.pdf (open access). DOI: 10.15862/26TangVN315
Introduction
The processes within most manufacturing systems are carried out sequentially in a predefined transition from one state to another reaching desirable or pre-specified state. Each product goes through its own states until it reaches completion or the final state [1].
Currently the pharmaceutical industry is experiencing significant changes in connection with prevailing economic situations and the high demands on quality from the regulatory bodies. There is also lots of competition among the manufacturers of generic pharmaceutical products. With the emergence and popularity of other alternative treatment of patients, there is the likelihood of reduced profit margins for pharmaceutical industries. Despite the challenges faced, the pharmaceutical manufacturing processes remain relatively inefficient and poorly understood as compared with other chemical process industries [11, 12, 13].
The objective of this paper is to do a system analysis of the manufacturing processes of pharmaceutical solid dosage forms with much focus on the technological processes of tablets manufacturing. The system analysis will be done with emphasis on both the manufacturing processes and the equipment used at each stage of the manufacturing. The development of a finite automata (FA) model for the manufacturing processes of pharmaceutical solid dosage forms is also discussed.
The reason for using FA for the modeling of the manufacturing processes of solid-based pharmaceutical dosage forms is because, the manufacturing processes of solid-based pharmaceutical dosage has finite states of manufacturing processes. There is also a finite link from one state to another which is expressed in terms of machine sequence. The best approach for modeling the manufacturing processes of solid-based pharmaceutical dosage forms should include all stages of the manufacturing and the transitions from the raw material to the finished product [2].
A finite-state machine (FSM) or finite- automata (FA) is a mathematical model of computation used to design both computer programs and sequential logic circuits. It can also be described as a device that can be in one of a finite set of states. In certain conditions, it can switch to another state and this is called a transition. It is considered as an abstract machine that can be in one of a finite number of states. The machine can be in only one state at a given time. The state it is in at any given time is called the current state. It can make a transition from one state to another when initiated by a triggering event or condition. Any FSM can generally be defined by a set of its states, and the activating conditions for each transition [3, 9].
The function of FA can be observed in many devices around us performing a predefined sequence of actions depending on the sequence of events inputted. Typical examples are the elevators which drop riders off at upper floors before going down, a combination lock which require the input of combination numbers in the proper order and the automatic teller machine which gives out information or cash when the correct sequence of inputs are followed.
The Manufacturing Process of Solid-Based Pharmaceutical Dosage Forms
The manufacture of pharmaceutical products goes through a series of technological processes to convert active pharmaceutical ingredients from either natural or artificial sources into suitable products before they are administered to humans and animals. Active pharmaceutical ingredients are carefully combined with the pharmaceutical necessities, such as binders, fillers, bulking agents and flavouring, preservatives and antioxidants. These raw materials may be dried, milled, blended, compressed and granulated to achieve the desired properties before they are manufactured as a final formulation. Tablets and capsules or in other words, solid dosage form drugs are the most common oral dosage forms. The technological processes of manufacturing solid dosage products consists of the following generalized operations: the weighing and dispensing of the raw materials; preparation
of a binder; mixing the active drug substances with a binder; wet granulation; drying; dry granulation; dusting; tableting and packaging [4, 5, 6].
The technological processes of manufacturing all forms of pharmaceutical products consist of several stages. The first stage for all forms of pharmaceutical products starts with preparatory works, which consists of preparation of the factory premises, auxiliary materials preparation, equipment testing and configuration, preparation of packaging materials, preparation of active drug substances and excipients. After the preparatory stage, all the other stages of manufacturing in accordance with the standards of a particular dosage form are followed. Quality controls are enforced at each stage within the whole drug manufacturing process. The manufacturing process ends at the packaging stage [7]. A generalized technological flowchart of the production of solid dosage forms is shown in figure 1.
The technological processes of manufacturing solid dosage forms can be divided into four main technological stages:
1. The technological stage of getting the raw materials into powdered form;
2. The technological stage of obtaining the correct texture and mixture for the dosage form;
3. The technological stage of obtaining the finished solid dosage;
4. The technological stage of packaging and labeling.
At each stage of the solid dosage manufacturing process, a specific type of equipment is used [6]. A developed classification of the technological stages and the equipment used is shown in table 1.
Table 1
Classification of the technological stages and the equipment used at each stage
(compiled by the author)
No. Technological stage Manufacturing Process Equipment
1 The technological stage of getting the raw materials into powdered form. Grinding/Milling Pharmaceutical Grinding Machine
Sieving Pharmaceutical Sieving Machine
2 The technological stage of obtaining the correct texture and mixture for the solid dosage form. Mixing Granulator/Mixer
Wet Granulation Granulator
Dry Granulation Granulator
Drying Pharmaceutical Powder Dryer
3 The technological stage of obtaining the finished solid dosage. Tablet Pressing Tablet Press Machine
Capsule Filing Capsule Filling Machine
Tablet De-Dusting Tablet De-Dusting Machine
4 The technological stage of packaging and labeling. Tablet Packaging Tablet Packaging Machine
Capsule Packaging Capsule Packaging Machine
Fig. 1. Flowchart diagram of the technological processes of solid dosage manufacturing
(compiled by the author)
Development of FA Model for the Manufacturing Process of Solid-Based Pharmaceutical Dosage Forms
FA models have been applied many times to model and develop a control for manufacturing systems. In the manufacturing processes of solid-based pharmaceutical dosage forms, the state of each machine or equipment changes after an input instruction is executed. Each state is determined by the prior state and also by the input. The equipment basically starts at an initial state and sequentially changes from one state to another state until it reaches the final state. A typical manufacturing system is made up of a set of machines that perform various operations at a specific stage of the manufacturing process. Raw materials are processed to completion by transiting them through various equipment according to a predefined manufacturing plan. After a particular stage is completed, the processed raw materials proceed to the next state until the final state of production is reached [8, 10].
In most manufacturing systems, operations run sequentially reaching desirable or pre-specified states. Each product goes through its own states until it reaches completion or the final state [1]. As a result of the fact that the manufacturing process of solid-based pharmaceutical dosage runs sequentially and FA models are abstract models of real systems, we were inspired to use FA to model and conduct system analysis of the manufacturing processes. The manufacturing system of solid-based pharmaceutical dosage forms has finite states of manufacturing processes with a finite link from one state to another that can be expressed in terms of machine sequence.
According to [3], an FA is formally a 5-tuple which is mathematically represented as:
A = (X, Y, Q, 5, X),
Where :
• X ={x1(t), X2(t),..., Xn(t)} - finite set of input symbols,
• Y ={y1(t),y2(t),. yk(t)} - finite set of output symbols,
• Q ={q1(t),q2(t),.qs(t)} - a finite set of states,
• qo(t) eQ -the initial or start state,
• X : QxX^Y - the output function,
• 5: QxX^Q -the transition function.
In this paper, a detailed model for the manufacturing processes of solid-based pharmaceutical dosage using FA was developed. This is to provide an algebraic theoretic treatment and analysis of the model with the aim of developing functional relations among the different equipment and sub processes of the manufacturing systems. The model will therefore, be based on pre-defined assumptions of finite automata having the following notational symbols as shown in Table 2. In table 3 the finite set of input operations for the manufacturing processes are shown. The finite set of output operations for the manufacturing processes is shown in table 4.
Table 2
The finite set of states of the manufacturing processes (compiled by the author)
Notation of States The Set of Operational States Within the Manufacturing Process Technological Stage
qo Loading the grinder with raw materials The grinding of raw material state.
qi In the grinder there is a technological process (grinding) going on within a giving period.
q2 Grinding process is completed
q3 Pouring out of grinded raw material from the grinder
q4 Grinder is empty and ready for another batch of raw material
q5 Loading of the pharmaceutical sieving machine with the grinded raw materials The sieving of raw material state.
q6 The sieving machine is undergoing a technological process (sieving) until completion of the process
q7 Sieving process is completed
qs Retrieving of the processed products from the sieving machine
q9 Sieving machine is empty and ready for another batch of raw material
qio Loading the mixer with weighed and measured active materials and excipients The mixing of all ingredients state.
qii The mixer is undergoing a technological process (mixing) until desired texture is achieved
qi2 Mixing process is completed
qi3 Pouring out of the mixture into a holding container
qi4 Mixer is empty and ready for another batch of raw material
qi5 Loading of granulator with the mixture from the mixer The granulation process state.
qi6 Granulation process going on in the granulator
qi7 Granulation process is completed
qis Wet granules are poured out of the granulator into a holding container
qi9 Granulator is empty and ready for another batch of raw material to be loaded
q2o Loading of dryer with wet granule The drying process state.
q2i Drying process is going on in the dryer until the correct moisture level is achieved
q22 Drying process is completed
q23 Cooling process is going on in the dryer
q24 Cooling process is completed
q25 Pouring out of the dried granules from the dryer
q26 Dryer is empty and ready for another batch of raw material
q27 Loading of the tablet press with the dried granules from the dryer The tablet pressing state.
q28 The tablet press is pressing the granules into tablets in accordance with the giving shape and weight
q29 The tableting process is completed
q3o A batch of tablets are released from the tablet press and kept in appropriate containers to be transported to the next stage
q3i Tablet press is empty and ready for another batch of raw materials to be loaded
q32 Loading of the tablets into the tablet packaging machine The packaging state.
q33 The packaging machine is undergoing the process of packaging the tablets into defined sets
q34 Packaging process is completed
q35 The packaged tablets are collected and sent to storage
q36 Tablet packaging machine is empty and ready for the next batch of packaging
Table 3
The finite set of input operations for the manufacturing processes (compiled by the author)
Input Notation Finite Set Of Input Operations
X1 Grinder is switched on
X2 Grinder is switched off
X3 Input procedures to pour out processed materials from grinder
X4 Input procedures to reset grinder to initial state
X5 Transportation of grinded materials from the grinder to the sieving machine
X6 Input signals to switched on the sieving machine
X7 Input signals to switched off the sieving machine
X8 Input signals to obtain the sieved products from the sieving machine
X9 Input procedures to reset sieving machine to initial state
X10 Transportation of the processed materials from the sieving machine to the mixer
X11 Mixer is switched on
X12 Mixer is switched off
X13 Input procedures to empty the content of the mixer into a container
X14 Procedure to reset mixer machine to initial state
X15 Transportation of the products from the mixer to the granulator
X16 Granulator is switched on
X17 Granulator is switched off
X18 Input procedures to pour out wet granule from the granulator
X19 Procedure to reset granulator to initial state
X20 Transportation of wet granule to a dryer
X21 Dryer is switched on
X22 Dryer is switched off
X23 Input signal to start cooling process
X24 Input signal to end cooling process
X25 Procedure to empty dryer
X26 Procedure to reset dryer to initial state
X27 Transportation of dry granules to the tablet press
X28 Tablet press is switched on
X29 Tablet press is switched off
X30 Procedure to empty tablet press
X31 Procedure to reset tablet press to initial state
X32 Transportation of tablets to packaging machine
X33 Input signal to switch on packaging machine
X34 Input signal to switch off packaging machine
X35 Procedure to empty the packaging machine
X36 Procedure to reset packaging machine to initial state
Table 4
The finite set of output operations for the manufacturing processes (compiled by the author)
Output Notation Finite Set of Output Operations
yi Grinder is on and functioning
У2 Grinder is off and the processed materials are at the desired texture
У3 Grinded raw materials are poured out and kept in the holding vessel
У4 Grinder adjusted to the initial state
У5 A batch of raw material from the grinder arrives at the sieving machine
У6 Sieving machine is switched on and functioning
У7 All raw materials are sifted and the sieving machine is switched off
У8 Sifted products are collected and kept in a holding container
У9 Sieving machine is adjusted to the initial state and ready for next batch of raw materials
У10 A batch of raw material from the sieving machine arrives at the mixer
У11 Mixer is switched on and functioning
У12 Mixer is switched off and the processed raw materials are at the needed texture
У13 The processed materials are poured out from the mixer and kept in a holding container
У14 The mixer adjusted to initial state and ready for next batch of raw materials
У15 A batch of raw material from the mixer arrives at the granulator
У16 Granulator is on and functioning
У17 Granulator is switched off and the desired wet granules obtained
У18 Wet granules are poured out from the granulator and kept in the holding container
У19 Granulator is adjusted to initial state and ready for next batch of raw materials
У20 A batch of wet granules arrives at the dryer
У21 Dryer is on and heating up for the drying process
У22 The dryer is off and the granules are at the needed moisture level
У23 Cooling process started
У24 Cooling process completed
У25 All dried granules are removed from the oven of the dryer and kept in a container
У26 Dryer adjusted to initial state and ready for next batch of materials to be dried
У27 A batch of dried granules arrives at the tablet press machine
У28 Tablet press is on and functioning
У29 Tablet press is switched off after all the granules had been pressed into tablets
У30 Tablet press is emptied of all tablets and the tablets are kept in holding containers
У31 Tablet press adjusted to initial state and ready for next batch of raw materials
У32 A batch of tablets arrives at packaging machine
У33 Packaging machine is switched on and functioning
У34 Packaging machine is switched off after all the loaded tablets are packaged
У35 The packaging machine is emptied and the packaged products sent to the storage
У36 Packaging machine is adjusted to initial state
From table1, table 2 and table 3, the finite set of input symbols X, the finite set of output symbols Y, and the finite set of states Q are:
• Q ={ qo,qi, q2, q3, q4 ,q5, q6, q7, qs, q9, qio, qii, qi2, qi3, qi4, qi5, qi6, qi7, qi8, qi9, q20, q2i, q22, q23, q24, q25, q26, q27, q28, q29, q30, q3i, q32, q33, q34, q35,q36}
• X = { xi, X2, X3, X4 ,X5 , X6, X7, Xs, X9, Xio, Xii, Xi2, Xi3, Xi4, Xi5, Xi6, Xi7, Xis, Xi9, X20, X2i, X22, X23, X24, X25, X26, X27, X28, X29, X30, X3i, X32, X33, X34, X35,X36 }
• Y = { yi, y2, y3, y4 ,y5 , y6, y7, ys, y9, yi0, yii, yi2, yi3, yi4, yi5, yi6, yi7, yi8, yi9, y20, y2i, y22, y23, y24, y25, y26, y27, y28, y29, y30, y3i, y32, y33, y34, y35, y36}
Construction of the Finite Automata Model and Transition Table for the Manufacturing Process
The FA model of the manufacturing process of the solid dosage form was developed by taking into consideration the processes and activities in line with the different machines or equipment used in the system. In this case the state in which the manufacturing process will be found in at any given time was determined by which equipment is either switched on or off. Within the same equipment, the state of manufacturing can also have sub states while the processing is going on.
The FA model that was developed for the whole manufacturing process of the solid dosage form, thirty six sub states where identified for this paper. These sub states can be grouped under the following technological processing states:
• The technological process of grinding raw materials state
• The technological process of sieving raw materials state
• The technological process of mixing all ingredients state
• The technological process of forming granules state
• The technological process of drying process state
• The technological process of tablet pressing state
• The technological process of packaging state
Based on these defined parameters the FA model of the manufacturing process was designed as shown in figure 2.Table 5 is a state transition table which shows what state the manufacturing process will move to, based on the current state and the inputs. A state table is basically a truth table in which some of the inputs are the current state, and the outputs include the next state, along with other outputs. The vertical (or horizontal) dimension indicates current states, the horizontal (or vertical) dimension indicates next states, and the row/column intersections contain the event which will lead to a particular next state of the manufacturing process.
Fig. 2. Detailed model of the Solid Dosage Manufacturing process as a finite automata scheme
(compiled by the author)
Table 5
The state transition table of the detailed model of solid dosage manufacturing process
(compiled by the author)
Чо 9i Q2 яз 44 9s (¡6 Qi (Is 49 910 (¡11 912 Qn 914 9 is 916
?# *i/YI
hlb
(¡2 Хз/Уз
Ь X4M
Я4 Vvo Х5/У5
45 Хб/Уб
4t hlb
9l Xa/Vs
9s hlb
99 hlb Х10/У10
(¡10 Хц/Уи
111 X12/V12
qи Х13/У13
Х14/У14
q и hAo %/Vis
9 is WVm
Conclusion
From the resulting transition table and the FA scheme developed, a clearer picture of the technological processes in the manufacturing system was shown. The FA scheme developed can be used in solving the problem of choosing an optimal manufacturing model for the pharmaceutical solid dosage forms. This can be done by critically observing and analyzing the transitions, the input functions and the output function and the conditions that triggers a transition. This model create an opportunity to conduct further research the can lead to the reengineering of the manufacturing system for optimal production levels and synchronizing of processes to save time and resources.
Substantial work remains to be done in the area of modeling the manufacturing processes of pharmaceutical solids-based dosage, specifically on the performance of the equipment and the efficient flow of raw materials within the process. Another area where further modeling is needed is in the area of predicting the properties of the solid dosage with data mining technology and other statistical models.
REFERENCES
1. Kim N., Shin D., Wysk R.A. and Rothrock L. Using Finite State Automata for Formal Modeling of affordances in Human-Machine Cooperative Manufacturing System: International Journal of Production Research, vol. 48, No. 5. 2010-pp. 1303 - 1320.
2. Garcia-Diaz A. and Lee H. An Industrial Application of Network-flow Models in Cellular Manufacturing Planning. Planning, Design, and Analysis of Cellular manufacturing System Elsevier Science. 1995.
3. Савельев А.Я. Прикладная теория цифровых автоматов Учебник для вузов по специальности ЭВМ. Москва: Издательство «Высшая школа», 1987 272с.: ил.
4. Погорелов В.И. Фармацевтическая технология. Ростов-на-Дону: Феникс, 2002. 467 с.
5. Ажгихин И.С., Гандель В.Г. Избранные лекции, по курсу технологии лекарств заводского производства. М., 1972. ч. 2". 189 с.
6. Tait, Keith Pharmaceutical Industry, Encyclopedia of Occupational Health and Safety [Электронный ресурс]. 2011. Режим доступа: // http://www.ilo.org/oshenc/part-xii/pharmaceutical-industry/item/385-pharmaceutical-industry#PHC_fig2(дата обращения-19.04.2014).
7. Таптунов, В.Н. Интеллектуальная система информационной поддержки выбора технологических схем производства твердых лекарственных препаратов. дисс. кан. техн. наук: 05.13.01 В.Н. Таптунов. - РХТУ им. Д.И. Менделеева, Москва, 2012. - 148 с.
8. Ibrahim Z., Ibrahim A.A. and Garba I. A. modeling of Sokoto cement production process using a finite automata scheme: An analysis of the detailed model. International Journal of Computational Engineering Research (IJCER) Vol.04 Issue, 5 - 2014.
9. Lewis H., Papadimitriou C.H. Elements of the Theory of Computation (2nd Edition). Publisher: Prentice-Hall. 1997-pp. 361 pages.
10. Smith P., Esta C., Jha S. and Kong S. Deflating the Big Bang: Fast and Scalable Deep Packet Inspection with Extended Finite Automata, Seattle, Washington, USA. 2008.
11. Suresh, P.; Basu, P.K. Improving pharmaceutical product development and manufacturing: Impact on cost of drug development and cost of goods sold of pharmaceuticals. J. Pharm. Innov. 2008, 3, pp. 175-187.
12. Shah, N. Pharmaceutical supply chains: Key issues and strategies for optimisation. Comput. Chem. Eng. 2004, 28, pp. 929-941.
13. McKenzie, P.; Kiang, S.; Tom, J.; Rubin, A.E.; Futran, M. Can pharmaceutical process development become high tech? AIChE J. 2006, 52, pp. 3990-3994.
УДК 007
Окаи Джордж Эссах Яо
ФГБОУ ВПО «Тверской государственный технический университет»
Россия, Тверь Аспирант
Пресвитерианский университетский колледж, Гана
Преподаватель E-mail: [email protected]
Клюшин Александр Юрьевич
ФГБОУ ВПО «Тверской государственный технический университет»
Россия, Тверь Кандидат технических наук, доцент E-mail: [email protected]
Богатиков Валерий Николаевич
ФГБОУ ВПО «Тверской государственный технический университет»
Россия, Тверь Доктор технических наук, профессор E-mail: [email protected]
Системный анализ и моделирование процессов производства твердых лекарственных форм с помощью конечных автоматов
Аннотация. Целью данной работы является проведение системного анализа и разработка модели процессов производства твердых лекарственных форм с большой упор на таблетки. Системный анализ был обсужден с акцентом на производственные процессы и оборудование, используемые на каждом этапе производственной системы. Разработка модели конечных автоматов для производственных процессов фармацевтических твердых лекарственных форм была обсуждена в статье. Эти модели используются при разработке алгоритмов управления процессом смены состояний в аппаратах периодического действия. Классификация технологических процессов в производстве твердых лекарственных форм также была обсуждена в статье. В статье описана технологический процесс производства твердых лекарственных форм, а также была построена блок-схема системы производства твердых лекарственных форм. Из полученного схемы конечных автоматов и созданная таблица переходов, все основные функции технологических процессов в производственной системе было показано. В модели конечных автоматов, которая была разработана в данной работе могут быть использованы при решении задачи выбора оптимальной производственной модели. Модель может также использоваться для повышения эффективности и надежности производства фармацевтических твердых лекарственных форм.
Ключевые слова: производственный процесс; конечные автоматы; производство фармацевтических средств; моделирование; системный анализ; твердые лекарственные препараты; переход; состояние; технологический процесс; фармацевтическая промышленность.
ЛИТЕРАТУРА
1. Kim N., Shin D., Wysk R.A. and Rothrock L. Using Finite State Automata for Formal Modeling of affordances in Human-Machine Cooperative Manufacturing System: International Journal of Production Research, vol. 48, No. 5. 2010-pp. 1303 - 1320.
2. Garcia-Diaz A. and Lee H. An Industrial Application of Network-flow Models in Cellular Manufacturing Planning. Planning, Design, and Analysis of Cellular manufacturing System Elsevier Science. 1995.
3. Савельев А.Я. Прикладная теория цифровых автоматов Учебник для вузов по специальности ЭВМ. Москва: Издательство «Высшая школа», 1987 272с.: ил.
4. Погорелов В.И. Фармацевтическая технология. Ростов-на-Дону: Феникс, 2002. 467 с.
5. Ажгихин И.С., Гандель В.Г. Избранные лекции, по курсу технологии лекарств заводского производства. М., 1972. ч. 2". 189 с.
6. Tait, Keith Pharmaceutical Industry, Encyclopedia of Occupational Health and Safety [Электронный ресурс]. 2011. Режим доступа: // http://www.ilo.org/oshenc/part-xii/pharmaceutical-industry/item/385-pharmaceutical-industry#PHC_fig2(дата обращения-19.04.2014)
7. Таптунов, В.Н. Интеллектуальная система информационной поддержки выбора технологических схем производства твердых лекарственных препаратов. дисс. кан. техн. наук: 05.13.01 В.Н. Таптунов. - РХТУ им. Д.И. Менделеева, Москва, 2012. - 148 с.
8. Ibrahim Z., Ibrahim A.A. and Garba I.A. modeling of Sokoto cement production process using a finite automata scheme: An analysis of the detailed model. International Journal of Computational Engineering Research (IJCER) Vol.04 Issue, 5- 2014.
9. Lewis H., Papadimitriou C.H. Elements of the Theory of Computation (2nd Edition). Publisher: Prentice-Hall. 1997-pp. 361 pages.
10. Smith P., Esta C., Jha S. and Kong S. Deflating the Big Bang: Fast and Scalable Deep Packet Inspection with Extended Finite Automata, Seattle, Washington, USA. 2008.
11. Suresh, P.; Basu, P.K. Improving pharmaceutical product development and manufacturing:Impact on cost of drug development and cost of goods sold of pharmaceuticals. J. Pharm. Innov. 2008, 3, pp. 175-187.
12. Shah, N. Pharmaceutical supply chains: Key issues and strategies for optimisation. Comput. Chem. Eng. 2004, 28, pp. 929-941.
13. McKenzie, P.; Kiang, S.; Tom, J.; Rubin, A.E.; Futran, M. Can pharmaceutical process development become high tech? AIChE J. 2006, 52, pp. 3990-3994.
Рецензент: Калабин Александр Леонидович, Д.Ф-М.Н, профессор, зав. кафедрой «Программное обеспечение вычислительной техники», ФГБОУ ВПО «Тверской государственный технический университет».
