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Flow diagram

A flow diagram is a diagrammatic representation that visually illustrates the sequence of steps, decisions, and operations in a process, system, or algorithm, using standardized symbols connected by arrows to indicate direction and flow. It encompasses various forms, such as flowcharts for algorithms, process flow diagrams for manufacturing, and data flow diagrams for information systems. These diagrams are essential tools in fields such as engineering, business process management, computer programming, and quality control, providing a clear overview of workflows to identify inefficiencies, plan improvements, or document procedures.^[1] Flow diagrams originated in industrial engineering in the early 20th century and evolved through standardization efforts in the mid-20th century, particularly in computing and information processing (see Historical Development). They include types like business process models for organizational workflows and support modern applications across industries, including healthcare and energy (see Applications).

Core Concepts

Definition and Purpose

A flow diagram is a graphical representation of a process, system, or workflow, utilizing standardized symbols to depict individual steps, decision points, and the directional connections between them.^[2]^[3] This visualization tool maps out the sequence of activities, enabling a clear depiction of how elements interact within a structured operation.^[4] The primary purposes of flow diagrams are to simplify the representation of complex sequences, identify inefficiencies such as bottlenecks, communicate procedural details effectively to diverse audiences, and support systematic analysis or planning efforts.^[5]^[6] In fields like engineering and information systems, they serve as a bridge for conveying operational logic between technical experts and non-specialists.^[7] Unlike static charts, which focus on displaying data distributions or static relationships, flow diagrams emphasize directional flow and sequential logic to model the dynamic progression of events or data through a system.^[8]^[9] Key benefits include enhanced comprehension of intricate workflows, assistance in troubleshooting by revealing potential failure points, and provision of a reusable format for documentation and training.^[10]^[11] These diagrams often incorporate basic elements such as nodes for processes or decisions and arrows to denote flow direction.

Elements and Symbols

Flow diagrams utilize a standardized set of visual elements to represent processes, decisions, data flows, and sequences, enabling clear communication of complex systems or workflows. These elements include shapes for specific functions and lines for connections, adhering to established conventions that promote uniformity across diagrams. The use of consistent symbols ensures that diagrams are interpretable by diverse audiences, from engineers to business analysts.^[12] The core symbols in flow diagrams are designed to denote distinct types of actions or states. Rectangles typically represent processes or steps, indicating operations where data is transformed or tasks are performed. Diamonds signify decision points, where paths branch based on conditions or outcomes, often with yes/no branches. Ovals mark the start and end points of the diagram, providing clear boundaries for the process. Arrows, or flowlines, illustrate the direction and sequence of flow between elements, guiding the viewer through the diagram's logic. Parallelograms are used for input/output operations, highlighting where data enters or exits the system.^[12]^[13]

Symbol Shape	Name	Meaning
Rectangle	Process	A step or operation that processes data or performs an action.^[12]
Diamond	Decision	A branching point based on a condition or choice.^[12]
Oval	Terminator (Start/End)	The initiation or conclusion of the process.^[12]
Arrow	Flowline	Direction of sequence or data flow between elements.^[7]
Parallelogram	Input/Output	Data entry or output to/from the system.^[12]

Connectors such as circles or off-page references link distant parts of a diagram, maintaining continuity without excessive lines, while annotations—often text labels or callouts—provide additional details for clarity. Branches from decision symbols use arrows to depict alternative paths, ensuring logical progression is evident. These components collectively form the diagram's structure, with lines typically flowing left-to-right or top-to-bottom for readability.^[7]^[13] Variations in symbol sets exist to accommodate specific contexts, with basic notations focusing on the essential shapes above for general use, while extended notations incorporate specialized forms like double-lined rectangles for predefined subprocesses or trapezoids for manual operations. For instance, in information processing diagrams, symbols may differentiate storage types (e.g., sequential vs. direct access), but core shapes remain consistent to avoid confusion.^[13] Effective use of these elements requires adherence to guidelines that enhance comprehension. Symbols should maintain consistent sizing and proportions to ensure visual harmony. Color-coding can categorize elements (e.g., blue for processes, red for decisions), but should be applied sparingly to prevent distraction. Diagrams must avoid clutter by limiting complexity, using hierarchies for detailed sub-processes, and incorporating clear labels that read left-to-right. These practices, drawn from standardization efforts, promote scalability and universal interpretability.^[7]^[13]^[14]

Historical Development

Origins in Early 20th Century

The origins of flow diagrams emerged within the early 20th-century industrial efficiency movement, rooted in Frederick Winslow Taylor's scientific management principles, which sought to optimize workflows through systematic analysis of worker tasks and production processes.^[15] Taylor's methods, developed in the 1880s and 1890s at factories like Midvale Steel, involved time studies to measure motions and eliminate waste, laying the groundwork for visualizing sequences to achieve the "one best way" of performing work.^[15] Building directly on Taylorism, Frank and Lillian Gilbreth advanced motion studies in the 1910s, introducing therbligs in 1915 as 16 elemental motions—such as search, grasp, and transport empty—to dissect and refine workflows for reduced fatigue and higher productivity.^[16] Their techniques, including micro-motion filming and cyclegraphs, enabled detailed breakdown of physical tasks in industries like bricklaying, where motions were reduced from 18 to as few as 4.5 per unit.^[16] This focus on granular workflow analysis influenced the shift toward graphical representations in efficiency consulting. A pivotal milestone came in 1921 when the Gilbreths presented "Process Charts: First Steps in Finding the One Best Way to Do Work" to the American Society of Mechanical Engineers, unveiling the first structured flow process chart using symbols for operations, inspections, transports, delays, and storage, connected by arrows to map material and information flows in manufacturing.^[17] In the 1920s, these diagrams gained traction in chemical engineering for visualizing process sequences, as exemplified by P.A. Amos's 1912 charts for flour manufacturing and C.E. Knoeppel's 1920 graphic methods for production control, which depicted material paths between equipment to streamline industrial operations.^[18] Such tools were initially adopted in manufacturing blueprints to chart physical workflows, supporting the broader efficiency drive in assembly lines and resource allocation.^[18] Early flow diagrams, however, were constrained by their hand-drawn nature, absence of universal symbols, and emphasis on linear, physical movements of materials and workers rather than abstract or logical flows.^[17] Lacking elements like decision points or variability, they prioritized deterministic "one best way" sequences suited to repetitive tasks, limiting applicability to complex or adaptive processes.^[17]

Evolution and Standardization

Following the informal origins of process charting in early industrial engineering, flow diagrams experienced rapid evolution in the post-World War II period, particularly through their adaptation to computing applications. In the mid-1940s, Herman Goldstine and John von Neumann introduced a systematic notation for flow diagrams to visualize the logical flow of computer programs, representing operations, decisions, and data movements in a structured manner that influenced early software design practices.^[19] This integration marked a shift from mechanical process representation to algorithmic modeling, as detailed in their 1947 report on planning and coding of problems for the ENIAC computer. Concurrently, in 1947, the American Society of Mechanical Engineers (ASME) formalized the first widely adopted standard for flowchart symbols in the "ASME Standard: Operation and Flow Process Charts," establishing consistent shapes for operations, inspections, transports, delays, and storages to promote uniformity in industrial and engineering documentation.^[20] The 1960s and 1970s brought further standardization efforts to address growing complexity in information processing and systems design. The American National Standards Institute (ANSI) released X3.5-1969 and its revision X3.5-1970, "Flowchart Symbols and Their Usage in Information Processing," which defined precise symbols for input/output, processing, connectors, and flow directions, tailored for computing contexts.^[7] In 1969, the International Organization for Standardization (ISO) issued Recommendation R 1028 for flowchart symbols in information processing, adopting similar principles to ensure international consistency and reducing variations in symbol interpretation across global engineering projects.^[21] These standards laid the groundwork for later evolutions, including the Unified Modeling Language (UML) in the 1990s, developed by Grady Booch, Ivar Jacobson, and James Rumbaugh and standardized by the Object Management Group (OMG) in 1997, which incorporated activity diagrams as an advanced form of flow diagrams for object-oriented software modeling. Similarly, the 2000s saw the emergence of Business Process Model and Notation (BPMN), initiated by the Business Process Management Initiative in 2004 and adopted by OMG in 2006 with version 2.0 in 2011, providing a richer notation for business processes with elements like gateways, events, and pools to handle orchestration and choreography. Technological advancements drove significant changes in how flow diagrams were created and utilized. The 1980s marked a transition from paper-based drafting to computer-aided design (CAD) software, exemplified by the release of AutoCAD in 1982, which allowed for digital creation, editing, and scaling of diagrams, enhancing accuracy and facilitating iterative revisions in engineering workflows. By the 2020s, artificial intelligence has introduced automation in diagramming, with tools leveraging natural language processing to generate flow diagrams from textual descriptions, streamlining the process for non-experts while maintaining adherence to standards like BPMN.^[22] Standardization has profoundly impacted flow diagrams by minimizing interpretive ambiguity, enabling seamless global collaboration, and supporting interoperability in multidisciplinary teams, as evidenced by the widespread adoption of ANSI/ISO symbols in software and manufacturing documentation.^[23] However, challenges persist in domain-specific adaptations, where industries often extend core symbols—such as adding chemical engineering icons to PFDs—leading to hybrid notations that balance universality with specialized needs, sometimes complicating cross-domain communication.^[24]

Varieties of Flow Diagrams

Process Flow Diagrams

Process flow diagrams (PFDs) are graphical representations employed in chemical and process engineering to illustrate the primary flow paths, equipment, and major material and energy transfers within industrial processes, such as those in refineries, petrochemical plants, and manufacturing facilities. These diagrams provide a high-level overview of the process topology, focusing on the sequence of operations without delving into minor details like valve specifications or instrumentation wiring. PFDs serve as foundational tools for communicating process design intent among engineers, operators, and stakeholders.^[3]^[25] Key features of PFDs include standardized symbols for process units—such as circles for pumps and rectangles for reactors and heat exchangers—connected by directed lines representing piping and streams that convey inputs, outputs, and utilities like steam or cooling water. Each major equipment item is assigned a unique identifier, for example, "P-101" for the first pump in process section 1, while streams are numbered sequentially and annotated with quantitative data such as mass flow rates (e.g., 50,000 kg/h), molar flows (e.g., 1,500 kmol/h), temperatures (e.g., 25°C), pressures (e.g., 1.5 atm), and phase compositions (e.g., vapor fraction or component mole percentages). These elements enable the integration of mass and energy balances directly into the diagram or accompanying tables, distinguishing PFDs from simpler general flow diagrams by emphasizing verifiable physical quantities for process simulation and validation. Basic symbols in PFDs are adapted from standards like ISO 10628 for consistency across engineering drawings.^[26]^[27]^[3]^[25] In chemical engineering applications, PFDs support process design by outlining equipment sizing and stream routing, facilitate optimization through identification of energy inefficiencies (e.g., heat recovery via exchangers), and enable safety analyses such as hazard identification in high-pressure systems. For instance, in oil refining, a PFD for a crude distillation unit depicts the flow from a preheated crude oil stream (e.g., 100,000 barrels/day at 350°C) through a furnace, atmospheric tower, and heat exchangers, capturing side streams like naphtha and kerosene while balancing mass inputs against outputs like gases and residues. This quantitative framework allows engineers to perform techno-economic evaluations and ensure compliance with operational constraints.^[25]^[3]^[28]

Data Flow Diagrams

Data flow diagrams (DFDs) are graphical representations that model the flow and transformation of data within an information system, emphasizing how data moves between processes, entities, and storage without detailing control logic or timing. Developed in the 1970s as part of structured analysis techniques, the Yourdon/DeMarco notation provides a standardized way to depict these flows, originating from Tom DeMarco's seminal work Structured Analysis and System Specification (1978), which introduced DFDs to facilitate clear system modeling for analysts and developers.^[29] This notation focuses on logical data interactions, making it particularly useful for abstracting complex systems into understandable visuals.^[30] In Yourdon/DeMarco notation, DFDs consist of four primary components: processes, represented as circles or bubbles to indicate data transformations (e.g., a "Validate Order" process); external entities, shown as rectangles for sources or destinations of data outside the system (e.g., a "Customer"); data stores, depicted as open-ended rectangles or parallel lines for persistent data repositories (e.g., "Inventory Database"); and data flows, illustrated by arrows labeled with specific data items (e.g., "Order Details") to show movement between components.^[31] These elements connect to form a network where processes act as transformers, data stores as holding tanks, and flows as pipelines, ensuring balanced inputs and outputs across the diagram for consistency.^[32] DFDs are structured hierarchically across levels of detail to progressively refine the system view. The context diagram (Level 0 overview) represents the entire system as a single process interacting with external entities via major data flows, providing a high-level boundary.^[30] This decomposes into a Level 0 diagram, which breaks the system into primary subprocesses (numbered sequentially, e.g., 1.0 for main functions), maintaining data balance with the context level.^[31] Further levels (e.g., Level 1) decompose individual processes into finer subprocesses (e.g., 1.1, 1.2), allowing detailed analysis without altering higher-level balances, with the number of levels depending on system complexity.^[33] DFDs play a crucial role in system analysis and design, particularly for requirements gathering and specifying information systems by visualizing data requirements and interactions early in development.^[34] They aid in identifying inefficiencies, ensuring data integrity, and communicating designs to stakeholders in software engineering and database modeling.^[30] For instance, in an e-commerce order processing system, a Level 0 DFD might show the "Customer" entity sending "Order Request" data to a "Process Order" subprocess, which interacts with an "Orders Database" store and outputs "Confirmation" to the customer, while flowing "Inventory Update" to another subprocess—highlighting data paths without physical implementation details.^[35]

Flowcharts and Control Flow Diagrams

Flowcharts are graphical representations of algorithms and processes that illustrate the sequence of operations using standardized symbols to depict sequential, decision, and loop structures. They originated in the 1940s as a tool for planning and coding computer programs, with early examples appearing in the work of Adele Goldstine and John von Neumann, who used flow diagrams to outline computational steps for the ENIAC computer in their 1947 report. These diagrams typically employ a set of symbols defined by standards such as ISO 5807, including ovals for start and end points, rectangles for process steps, diamonds for decision points, and parallelograms for input/output operations, connected by arrows to show the flow direction. Sequential structures represent linear execution of steps, decision structures branch based on conditions (e.g., yes/no paths from a diamond), and loop structures incorporate repetition, often via connectors returning to prior points. Control flow diagrams extend flowchart principles to software engineering, focusing on execution paths, conditional branching, exception handling, and concurrency within programs. In software design, they map how control passes between code blocks, including interrupts or parallel threads, and are particularly formalized in UML activity diagrams, which use rounded rectangles for actions, diamonds for decisions, and bars for forks/joins to model concurrent flows. These diagrams help visualize program behavior under various inputs, such as handling errors via exception paths or synchronizing multi-threaded operations. A simple example of a flowchart is the bubble sort algorithm, which repeatedly steps through a list, compares adjacent elements, and swaps them if out of order until no swaps are needed; it begins with a start oval, loops through comparisons in rectangles and decisions in diamonds, and ends when the list is sorted.^[36] For more complex scenarios, control flow diagrams in embedded systems depict execution in resource-constrained environments, such as a microcontroller managing sensor inputs with interrupt-driven paths for real-time responses, using nodes for basic blocks and edges for conditional jumps to ensure reliable operation under timing constraints.^[37] Flowcharts and control flow diagrams offer advantages in programming, such as aiding debugging by revealing logical errors in execution paths and serving as training tools to communicate algorithmic logic to teams.^[38] However, they have limitations, including poor scalability for large programs where diagrams become overly complex and difficult to maintain, often requiring simplification or decomposition into sub-flows.^[23]

Specialized Types

Sankey diagrams represent flows of energy, materials, or costs where the width of each stream is proportional to the quantity it depicts, facilitating visualization of balances and efficiencies in physical processes.^[39] Originating from a 1898 diagram by Irish engineer Captain Matthew Henry Phineas Riall Sankey illustrating energy distribution in a steam engine, these diagrams emphasize conservation principles by showing inputs, transformations, and outputs without loss except as specified waste.^[40] In energy applications, such as analyzing power plant efficiency, Sankey diagrams quantify how thermal energy from fuel converts to electrical output, with arrow widths revealing losses like heat rejection in cooling systems, often highlighting that only about 30-40% of input energy becomes usable electricity in coal-fired plants.^[41] This proportional scaling aids in identifying inefficiencies, as seen in U.S. manufacturing Sankey diagrams where offsite fuels and electricity flows are tracked to end-use sectors.^[41] Influence diagrams provide a graphical framework for decision analysis under uncertainty, using nodes to represent decision variables (rectangles), chance variables (ovals) for random events, and value nodes (diamonds) for objectives, connected by directed arcs indicating probabilistic or informational influences.^[42] Introduced by Ronald A. Howard and James E. Matheson in 1981 as a compact alternative to extensive decision trees, they model complex interdependencies in problems like resource allocation or risk assessment, where arcs denote conditional dependencies or relevance.^[43] For instance, in medical decision-making, an influence diagram might link patient symptoms (chance nodes) to diagnostic tests (decision nodes) and treatment outcomes (value nodes), incorporating uncertainties like test accuracy to compute expected utilities.^[44] This structure supports quantitative evaluation through Bayesian inference, enabling sensitivity analysis on uncertainties to guide optimal choices.^[45] Network flow diagrams model optimization problems as directed graphs with nodes for origins, destinations, and intermediates, and edges assigned capacities and costs to represent constrained resource movements.^[46] These diagrams underpin algorithms for maximum flow or minimum-cost flow, where flow conservation at nodes ensures balanced inflows and outflows except at sources and sinks.^[47] In transportation networks, they optimize shipment routing; for example, in a supply chain from factories to warehouses, edge capacities limit truckloads, and costs reflect distances or fuel, solving for minimal total expense while satisfying demands, as in the classic Hitchcock transportation problem formulation.^[48] Such models, solvable via linear programming, scale to real-world logistics where capacities might constrain flows to 100 units per route, demonstrating efficiency gains like 15-20% cost reductions in optimized freight systems.^[46] Among emerging specialized types, alluvial diagrams extend flow visualization to categorical data transitions over time or stages, with parallel vertical axes linked by curved bands whose widths indicate category frequencies and changes between them.^[49] First formalized in a 2010 paper by Martin Rosvall and Carl T. Bergstrom for mapping network evolution, they reveal patterns like voter shifts across elections or species migrations in ecological networks, where band thickness proportionally shows group sizes, such as 40% of a population moving categories between periods.^[50] Fault tree diagrams, conversely, depict system reliability through top-down logic trees starting from an undesired top event (e.g., system failure) branching via AND/OR gates to basic failure causes, developed in the early 1960s by Bell Telephone Laboratories for the U.S. Air Force's Minuteman ICBM project and later applied in NASA's Apollo program.^[51] In aerospace reliability engineering, they quantify failure probabilities—such as a 10^{-6} per hour rate for redundant avionics—by propagating bottom-up event likelihoods, aiding fault identification in post-1960s designs like satellite systems.^[52]

Applications

Engineering and Manufacturing

In engineering, process flow diagrams (PFDs) serve as foundational tools for designing and optimizing plant layouts by illustrating the sequence of equipment, material flows, and operational paths in chemical and process industries. These diagrams enable engineers to visualize the overall process topology, including major unit operations and interconnections, which is crucial for initial design phases and ensuring efficient spatial arrangements in facilities.^[3] For simulation of production lines, PFDs integrate with discrete-event simulation software to model throughput and resource allocation, allowing virtual testing of scenarios to predict performance before physical implementation.^[53] Additionally, PFDs often interface with computer-aided design (CAD) systems during prototyping, where flow representations inform 3D modeling of components and assemblies, facilitating iterative design refinements in mechanical engineering workflows.^[54] In manufacturing, flow diagrams are extensively applied to map assembly line processes, depicting sequential steps from raw material input to final product output, such as in automotive or electronics production where they outline stations for cutting, welding, and quality checks. A prominent example is value stream mapping (VSM), a lean manufacturing technique that visualizes material and information flows to eliminate waste; building on Toyota's Production System (developed in the mid-20th century) and popularized in the 1990s.^[55]^[56]^[57] The benefits of flow diagrams in these contexts include effective bottleneck detection through visual identification of process delays and throughput modeling to forecast production capacity and efficiency gains. For instance, in an automotive engine assembly line case study, implementing a process flow analysis identified non-value-added activities, leading to a reduction in cycle time via targeted kaizen improvements without major capital investment.^[58]^[59]^[60] However, challenges arise in handling production variability, as static diagrams may not fully capture real-time fluctuations in demand or machine reliability, necessitating dynamic updates or hybrid simulations.^[61] Compliance with standards like ISO 9001 further complicates their use, requiring flow diagrams to document controlled processes for quality management audits while adapting to evolving regulatory demands in manufacturing environments.^[62] As of 2025, flow diagrams are integrated with AI for automated process synthesis in chemical engineering.^[63]

Information Systems and Software Development

In software development, Data Flow Diagrams (DFDs) serve as a foundational tool for eliciting and analyzing requirements by visually depicting the movement of data between processes, external entities, and data stores within a system. This modeling technique enables developers to identify functional dependencies, ensuring that outputs are clearly derived from inputs without ambiguity in the specification.^[64] Formal representations of DFDs, such as those using predicate transformers or algebraic semantics, further enhance this process by providing rigorous semantics that support verification and refinement during the design phase.^[65] Data flow modeling, as exemplified by DFDs, thus offers a structured way to bridge user requirements with implementation details in information systems. Control flow diagrams complement DFDs by outlining the sequential and conditional execution paths in software, facilitating code reviews and debugging efforts. These diagrams, often rendered as macro flowcharts, have been experimentally validated to improve documentation effectiveness, with studies showing they reduce comprehension time and error rates in maintenance tasks when kept concise relative to code length.^[66] In system analysis, flow diagrams extend to visualizing database schema interactions and API endpoint flows, where they map data transformations and request-response patterns to ensure integration coherence. For instance, in cloud migration projects, DFDs are applied to decompose monolithic applications into distributed components, illustrating how data streams evolve from centralized to service-oriented architectures. Since the 2000s, flow diagrams have integrated into Agile and DevOps methodologies to support iterative development and continuous integration. Cumulative flow diagrams track work-in-progress limits and bottlenecks in Agile sprints, promoting efficient resource allocation in team-based environments. Similarly, in the Scaled Agile Framework (SAFe), continuous flow diagrams monitor feature delivery across large-scale programs, enabling real-time adjustments for velocity and quality. Tools like the Unified Modeling Language (UML) incorporate activity diagrams—essentially object-oriented flow diagrams—to model behavioral flows in object-oriented design, allowing traceability from requirements to code while accommodating parallel processes and object interactions.^[67] The benefits of flow diagrams in these contexts include enhanced traceability, which links artifacts across the development lifecycle to maintain alignment, and error reduction through early detection of inconsistencies in data or control paths. In the 2020s, evolving trends emphasize their role in microservices architectures, where diagrams model inter-service data flows to optimize scalability via horizontal partitioning and incorporate security paths for threat identification, such as API gateway protections and encrypted channels. This approach ensures resilient, distributed systems capable of handling dynamic loads while mitigating vulnerabilities in decentralized environments.

Business Processes and Management

In business process modeling, flow diagrams serve as essential tools for visualizing and standardizing workflows within organizations. The Business Process Model and Notation (BPMN), developed by the Object Management Group, offers a graphical standard that depicts sequences of activities, decision points, and interactions, enabling stakeholders to design, execute, and monitor processes effectively.^[68] This notation bridges technical and non-technical audiences, facilitating clearer communication and iterative improvements in operational efficiency. Swimlane diagrams, a key variant often integrated into BPMN through pools and lanes, partition processes by roles or departments to highlight responsibilities and handoffs. By organizing elements into horizontal or vertical lanes, these diagrams clarify accountability in cross-functional settings, reducing misunderstandings and enhancing collaboration in complex workflows.^[68] In management applications, flow diagrams underpin methodologies like Six Sigma, which emerged in the 1980s to drive process improvement through data-driven analysis. Six Sigma practitioners use flowcharts to map current-state processes, identifying bottlenecks, waste, and non-value-added activities, thereby supporting targeted optimizations that align with organizational goals.^[69] For supply chain management, these diagrams trace the flow of materials, information, and finances across entities, revealing opportunities to minimize delays and costs in end-to-end operations. A prominent example is the order-to-cash cycle, where flow diagrams outline sequential steps from customer order entry and fulfillment to invoicing and payment receipt. This visualization aids in streamlining the cycle, accelerating cash flow, and mitigating errors in revenue-generating processes.^[70] Strategically, flow diagrams support risk assessment by mapping potential disruptions and response pathways, consistent with the iterative process outlined in ISO 31000.^[71] In compliance auditing, they align with the COSO framework by illustrating internal control activities, ensuring traceability and adherence to regulatory requirements across operations.^[72] Such applications yield benefits like cost reduction by pinpointing redundancies and enabling proactive adjustments.^[69] Modern adaptations integrate flow diagrams with Enterprise Resource Planning (ERP) systems, where they model automated workflows for real-time visibility and scalability in dynamic environments.^[73] Post-2020, amid accelerated remote work adoption, these diagrams have evolved to depict hybrid models, incorporating virtual collaboration steps to manage distributed teams and maintain productivity in flexible structures.^[74] As of 2025, flow diagrams also serve as standard tools in clinical trial reporting per updated CONSORT guidelines.^[75] This builds briefly on prior standardization efforts in business diagramming for enhanced interoperability.^[68]

Creation and Tools

Manual and Hand-Drawn Methods

Manual and hand-drawn methods for creating flow diagrams rely on simple, accessible tools to facilitate initial conceptualization and collaborative development of processes. Common materials include graph paper or plain sheets for layout, pencils or pens for sketching, and erasers for revisions, allowing for flexible iterations without specialized equipment. Stencils or templates, often made of plastic or metal, are used to draw standardized symbols accurately, ensuring uniformity in shapes like rectangles and diamonds. These analog approaches are particularly suited to engineering and team environments where quick visualization is needed.^[76]^[77] A typical step-by-step process begins with identifying the key steps of the process, such as inputs, operations, decisions, and outputs, often brainstormed in a group setting. Next, sketch the flow using a top-down or left-to-right layout to mimic natural reading order and enhance readability; for instance, start with an oval for the beginning and connect elements sequentially with arrows. Iterate by reviewing the draft for clarity, adjusting connections to avoid crossings, and incorporating feedback from stakeholders during sessions like whiteboard brainstorming. This method is ideal for initial exploration in meetings, where participants can rearrange elements in real time.^[69]^[77] The advantages of hand-drawn flow diagrams include low cost and accessibility, requiring no software or power sources, making them practical for field use or resource-limited settings. They offer a tactile experience that fosters team collaboration, as seen in whiteboard sketches during engineering reviews, where physical manipulation of notes or drawings encourages dynamic input and immediate problem identification. Additionally, manual creation promotes deeper conceptual understanding by forcing focus on core logic rather than technical details.^[69]^[77] Despite these benefits, limitations arise in scaling complex diagrams, where hand-drawing becomes error-prone for large processes due to imprecise measurements and difficulty maintaining proportions. Revisions can be labor-intensive, often requiring redrawing entire sections, and legibility suffers without uniform spacing or consistent line weights. To mitigate these, employ best practices such as uniform symbol sizing (e.g., maintaining a 1:2/3 width-to-height ratio), clear lettering in uppercase (at least 0.16 inches high), and even spacing between elements to prevent clutter. Basic symbols, drawn per standards like ANSI X3.5, include rectangles for processes and diamonds for decisions to ensure consistency.^[76]^[7]

Software Tools and Digital Creation

Digital tools for creating flow diagrams have revolutionized the process by enabling efficient, scalable visualization compared to manual methods, allowing users to produce complex diagrams with precision and ease.^[78] Among the most widely used software are Microsoft Visio, introduced in the early 1990s as a product of Shapeware Corporation and acquired by Microsoft in 2000, which supports a broad range of diagram types including flowcharts and process maps.^[79] Lucidchart, launched in 2008, offers cloud-based diagramming with intelligent features tailored for collaborative environments.^[80] Draw.io (now diagrams.net), an open-source tool released in the 2010s, provides free, accessible diagramming without licensing costs and integrates with various platforms.^[81] For specialized applications like process flow diagrams (PFDs) in engineering, AutoCAD Plant 3D extends AutoCAD's capabilities to generate P&IDs and PFDs with industry-standard symbols and data validation.^[82] Key features of these tools include drag-and-drop interfaces for placing symbols and connectors, automated routing to optimize line paths and avoid overlaps, and versatile export options such as PDF for print-ready documents and SVG for scalable web use.^[83] Cloud-based options like Lucidchart and draw.io emphasize real-time collaboration, enabling multiple users to edit diagrams simultaneously with version history and commenting.^[84] The typical creation workflow begins with importing data from sources like spreadsheets or databases to populate diagram elements, followed by selecting pre-built templates for standards such as BPMN or UML to accelerate setup. Users then customize connections and annotations before simulating flows to validate logic, as seen in Bizagi Modeler, which supports BPMN 2.0 notation for modeling, executing, and analyzing business processes.^[85] Emerging trends in the 2020s include AI-driven auto-generation, where tools like Lucidchart's AI assistant convert text descriptions or code snippets into diagrams, reducing manual effort.^[22] Additionally, integrations with integrated development environments (IDEs) such as draw.io's extension for Visual Studio Code or plugins for IntelliJ IDEA allow developers to generate diagrams directly from code, enhancing software design workflows.^[86]

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Flowchart. Symbol. Name. (Alternates). Description. Process. An operation or action step. Terminator. A start or stop point in a process. Decision. A question ...
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[PDF] ISO 5807:1985 - iTeh Standards
3.3 flowchart: Graphical representation of the definition, analysis, or method of solution of a problem in which symbols are used to represent operations, data, ...
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How to choose the most effective flow chart - Microsoft
Sep 30, 2022 · Make flow charts easy to read, consistent, use contrast, and use online makers. Consider end-user, clear titles, and avoid jargon.Missing: authoritative | Show results with:authoritative
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Scientific Management - Encyclopedia of Greater Philadelphia
Frederick Winslow Taylor, “Father of Scientific Management,” developed a methodology that changed the shape of industrial manufacturing in the early twentieth ...Missing: workflow analysis
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[PDF] Frank and Lillian Gilbreth and the Manufacture and Marketing of ...
Given Taylor's use of Gilbreth's bricklaying innovations as illustrations for his popular Principles of Scientific Management [46], and the American. Federation ...Missing: origins | Show results with:origins
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[PDF] 100 Years of Graphical Business Process Modelling
In December 1921, Frank B. and Lillian Moller Gilbreth held a presentation entitled “Process. Charts” at the Annual Meeting of The American Society of ...
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Flow Diagrams: Rise and Fall of the First Software Engineering ...
Drawings of water are the earliest, least abstract forms of flow diagram. Representations of ideal or generalised sequences for manufacturing or actual ...<|control11|><|separator|>
[25]
Flow Diagrams, Assertions, and Formal Methods - ACM Digital Library
Oct 7, 2019 · This paper examines the early history of the flow diagram notation developed by Herman Goldstine and John von Neumann in the mid-1940s.<|control11|><|separator|>
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A.S.M.E. standard operation and flow process charts ... 1947 c.2.
ASME standard operation and flow process charts, developed by the ASME Special committee on standardization of therbligs, process charts, and their symbols, ...
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Generating Diagrams Instantly With Lucid AI - Lucidchart
The perfect toolkit for AI-driven diagramming · Create AI-powered flowcharts · Quickly customize diagrams · Optimize every process · Integrate with AI.Missing: 2020s | Show results with:2020s
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Flow Diagrams: Rise and Fall of the First Software Engineering ...
Aug 7, 2025 · This paper examines the early history of the flow diagram notation developed by Herman Goldstine and John von Neumann in the mid-1940s. It ...
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DEXPI process: Standardizing interoperable information for process ...
DEXPI Process is a proposed standard for modelling information about process design, as it is presented on block flow and process flow diagrams.
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Process Flow Diagram - an overview | ScienceDirect Topics
A process flow diagram (PFD) is defined as a graphical representation that describes a process, its constituent tasks, and their sequence, aiding in the ...
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Process Flow Diagrams (PFDs) – Foundations of Chemical and ...
Process flow diagrams (PFDs) include major equipment, process flow streams, and utility streams. Equipment is labeled by position, and utilities by descriptor.
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2.2 Refining of Petroleum into Fuels | EGEE 439
Simple flow diagram of an oil refinery. Crude oil is the first process, and it breaks the products down into LPG, straight-run gasoline, naphtha/kerosene/diesel ...
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Structured Analysis and System Specification - Google Books
Evaluation and refinement of data flow diagrams. Data flow diagrams for system specification. Part 3: Data dictionary. The analysis phase data dictionary.
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This guide provides everything you need to know about data flow diagrams, including definitions, history, and symbols and notations.Data Flow Diagram Symbols · How to Make a Data Flow...
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In this chapter, we will explore one of the three major graphical modeling tools of structured analysis: the dataflow diagram. The dataflow diagram is a ...<|control11|><|separator|>
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DFD Using Yourdon and DeMarco Notation - Visual Paradigm Online
A data-flow diagram (DFD) is a way of representing a flow of data of a process or a system that aims to be accessible to a computer specialist and ...DFD Using Yourdon and... · The Elements of DFD · Data-flow Diagram Example...
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DFD Tutorial: Yourdon Notation - Visual Paradigm Online
Yourdon and Coad method includes components for creating data-flow diagrams and also object state diagrams. Some unique attributes of their DFD notation include ...DFD Tutorial: Yourdon Notation · Flowchart vs DFD
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What Is a Data Flow Diagram (DFD)? - IBM
A data flow diagram (DFD) is a visual representation of the flow of data through an information system or business process.
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Data Flow Diagram Examples Symbols, Types, and Tips - Lucidchart
A data flow diagram shows the way information flows through a process or system. It includes data inputs and outputs, data stores, and the various subprocesses ...
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Sample flowchart for a sorting algorithm. This flowchart illustrates...
This flowchart illustrates the conditional constructs, loops, and other elements of control flow that comprise an algorithm for sorting, from smallest to ...
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Jul 11, 2025 · A Control Flow Graph (CFG) is the graphical representation of control flow or computation during the execution of programs or applications.<|control11|><|separator|>
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Jan 3, 2025 · Advantages of using a Flowchart · Flowcharts are a better way of communicating the logic of the system. · Flowcharts act as a guide for blueprint ...
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Apr 12, 2007 · Sankey diagrams are named after Captain Matthew Henry Phineas Riall Sankey. Here is some biographical information on Mr. Sankey.
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2018 Manufacturing Static Energy Sankey Diagrams
The Sankey diagrams show the fuel, steam, and electricity entering U.S. manufacturing plants from offsite sources. Renewable electricity generated onsite is ...Missing: balances | Show results with:balances
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Decision Influence Diagrams and Their Uses - SpringerLink
In 1981, Howard and Matheson introduced the idea of representing a Bayesian decision problem in terms of a graph called an influence diagram.
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[PDF] Influence Diagrams - Gwern
An influence diagram is a way of describing the dependencies among aleatory variables and decisions. An influence diagram can be used to visualize the.
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Dec 1, 2005 · This note explains why the original introduction of influence diagrams, lacking formal underpinning of these features, has had only mild influence on automated ...
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Influence Diagrams - ResearchGate
Aug 7, 2025 · Basically, the influence diagram is a qualitative description of the decision problem. [27] The influence diagram shows the utility function in ...
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[PDF] Chapter 5 Network Flows
Network flows involve how objects move through a network, represented by nodes and directed edges. Min-cost-flow problems involve flow variables and ...
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[PDF] Chapter 10: Network Flow Programming
Network flow programming is formulating and solving network problems via linear programming, where any network flow problem can be cast as a minimum-cost ...
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[PDF] Network Models - MIT
The transportation problem is a network-flow model without intermediate locations. To formulate the problem, let us define the following terms: ai = Number of ...
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Alluvial Diagram - Data Viz Project
Alluvial diagram is a variant of the Parallel Sets but for categorical variables and often to display trends over time and phases. Family. Diagram. Function.
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Using the Alluvial diagram to display variable characteristics for ...
Jun 23, 2023 · Alluvial diagrams were first used in the 2010 paper Mapping Change in Large Networks by Martin Rosvall and Carl T. Bergstrom, in which they used ...
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[PDF] 1 Fault Tree Analysis – A History Clifton A. Ericson II The Boeing ...
Fault Tree Analysis (FTA) is a tool for analyzing failure paths in a system. It was developed for the Air Force around 1961 and used in the Apollo project.
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[PDF] Fault Tree Analysis - NASA Technical Reports Server (NTRS)
Fault tree analysis is a top-down approach to identify process hazards and graphically display ways something can go wrong.
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Use Plant Simulation software for discrete-event simulation and throughput optimization to improve manufacturing performance of your production systems.
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How to Make a Production Flow Chart for Manufacturing Processes ...
Dec 21, 2022 · A production flow chart is used to illustrate the manufacturing process of a product. It shows the stages, equipment used and quality control checks.
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A production system based on the philosophy of achieving the complete elimination of waste in pursuit of the most efficient methods.
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Toyota's success and use of lean manufacturing practices helped promote value stream mapping as a modern best practice for high efficiency business teams during ...
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Dec 11, 2024 · In this article, we will explore how process mapping can help identify bottlenecks in your business processes, leading to improved efficiency and productivity.
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[PDF] Reduction of Cycle Time in Vehicle Engine Assembly Line Using ...
This research aims to identify the Non-Value Added (NVA) activities in Station 2 and minimize them with. Karakuri Kaizen. The results of the Process Activity ...
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Proven Strategies for Minimizing Variability in Manufacturing
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ISO 9001 Flowchart Basics - 9000 Store
Enter the purpose (start/stop/decision/etc.) of each symbol within the shape and connect them with arrows to show the direction of the flow.
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Analyzing the logical structure of data flow diagrams in software ...
A data flow diagram (DFD) represents the functional dependencies within a system: it shows how output values in a computation are derived from input values.
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Formal Representations of the Data Flow Diagram: A Survey
This paper surveys techniques for formally representing data flow diagrams (DFD) to remove ambiguity and improve understanding of requirements and design.
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Control flow and data structure documentation: two experiments
Two experiments were carried out to assess the utility of external documentation aids such as macro flowcharts, pseudocode, data structure diagrams, ...
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Therefore this paper proposes a few small changes to the UML metamodel that will integrate activity diagrams into an object-oriented scheme, focusing on three ...
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About the Business Process Model And Notation Specification ...
Business Process Model and Notation has become the de-facto standard for business processes diagrams. It is intended to be used directly by the stakeholders.
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What is a Flowchart? Process Flow Diagrams & Maps | ASQ
### Summary: Flowcharts in Six Sigma Process Mapping
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What Is Order-to-Cash (O2C)? The Order-to-Cash Process Explained
May 1, 2025 · This diagram outlines the nine steps of the order-to-cash process, from purchasing to reporting, illustrating the flow of a customer order ...What Is the Order-to-Cash... · Order-to-Cash Best Practices
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Jan 31, 2025 · ISO 31000 is a risk management standard with two main components: a Framework and a multi-step Process for identifying and analyzing risks.
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COSO developed the framework in response to senior executives' need for effective ways to better control their enterprises and to help ensure that ...
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6 Key Phases of an ERP Implementation Plan - NetSuite
Sep 8, 2025 · A flowchart of the six phases of an ERP implementation, including discovery and planning, design, development, support, deployment, and testing.
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Feb 18, 2021 · The pandemic accelerated existing trends in remote work, e-commerce, and automation, with up to 25 percent more workers than previously estimated potentially ...
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None
Below is a merged summary of the manual/hand-drawn methods for flow diagrams, process flows, or engineering drawings, combining all the information from the provided segments into a concise yet comprehensive response. To maximize detail and clarity, I’ve organized the information into a table format (CSV-style) for key sections, followed by additional narrative details where appropriate. This ensures all specifics are retained while maintaining readability.
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[PDF] Engineering Sketching for Design and Communication - PDH Online
Lead engineers can use sketches to communicate each revision to the client for preliminary approval. 3.1 Flow Diagram Example. These are the instructions given ...<|control11|><|separator|>
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The 8 best flowchart software and diagram tools · Lucidchart for advanced functionality · Microsoft Visio for Microsoft 365 and Windows users · Zapier Canvas for ...
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https://www.drawio.com/
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Lucid Software - Crunchbase Company Profile & Funding
Legal Name Lucid Software, Inc. ; Also Known As Lucid, Lucidchart, Lucidspark ; Operating Status Active ; Company Type For Profit ; Founders Ben Dilts, Karl Sun.
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draw.io
Example diagram. Powerful features. Collaborate with shared cursors in real-time. draw.io has everything you expect from a professional diagramming tool.Example draw.io diagrams · Integrations · About draw.io · Blog
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P&ID Software | AutoCAD Plant 3D - Autodesk
Learn more about P&ID software and the Plant 3D toolset included with AutoCAD. Easily create piping and instrumentation diagrams for processes and 3D models ...
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Microsoft Visio: Diagramming & Flowcharts | Microsoft 365
Try Microsoft Visio, the best diagramming software for flowcharts, data visualization, and integrated workflows. Boost team collaboration and productivity.
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Microsoft Visio is software for drawing a variety of diagrams. These include flowcharts, org charts, building plans, floor plans, data flow diagrams, process ...<|control11|><|separator|>
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Business Process Modeling - BPMN - Bizagi
Build business process models to identify process improvement opportunities and increase efficiency and agility across your organization.The Bpmn Process Modeling... · Top 5 Business Process... · You May Also Be Interested...
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Draw.io VS Code Integration - Visual Studio Marketplace
This unofficial extension integrates Draw.io (also known as diagrams.net) into VS Code. Mentioned in the official diagrams.net blog.<|separator|>