ARENAB-UM001H-EN-P_Ttlepage 11/30/07 3:48 PM Page 1 Arena® Basic USER’S GUIDE PUBLICATION ARENAB-UM001H-EN-P–November 2007 Supersedes Publication ARENAB-UM001G-EN-P
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Contents 1 • Welcome to Arena Basic Edition What is Arena Basic Edition? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intended audience. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Where can I go for help? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference the user’s guides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
• • • • • ARENA BASIC EDITION USER’S GUIDE How do I use Rulers and Guides? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot the number of applications in-process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What is a model thumbnail? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rerun the simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Next steps . . . . . . . . . . . . . .
Distribute the Process Simulation add-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Publish process maps on a Web page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 A • Statistical Distributions Beta(b, a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discrete . .
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Welcome to Arena Basic Edition What is Arena Basic Edition? Arena Basic Edition software lets you bring the power of modeling and simulation to business process improvement. It is designed primarily for newcomers to simulation and serves as an introductory product and foundation to the rest of the Arena product family. Typically, any process that can be described by means of a flowchart can be simulated with Arena Basic Edition.
• • • • • ARENA BASIC EDITION USER’S GUIDE Where can I go for help? Our commitment to your success starts with the suite of learning aids and assistance we provide for Arena. Whether you’re new to simulation or a seasoned veteran putting a new tool to use, you’ll quickly feel at home with the Arena Basic Edition.
• • • • • 1 • WELCOME TO ARENA BASIC EDITION Access the Arena Symbol Factory Get phone support Rockwell Automation provides full support for the entire Arena family of products. Questions concerning installation, how modules work, the use of the model editor, and the use of the software are handled by technical support.
• • • • • ARENA BASIC EDITION USER’S GUIDE download page where you can check for possible software updates (patches). If you can’t find the answer you need, contact your local representative or Arena technical support. Get training Do you need training? Rockwell Automation offers a standard training course comprised of lecture and hands-on workshops designed to introduce you to the fundamental concepts of modeling with Arena. We also offer customized training courses designed to meet your specific needs.
2 Getting Started Introduction While you may not realize it quite yet, you now have the power to transform your business. Whenever you and others in your organization are wondering “what if…?,” you can look into the future to find the answer. With Arena, you can: Model your processes to define, document, and communicate. Simulate the future performance of your system to understand complex relationships and identify opportunities for improvement.
• • • • • ARENA BASIC EDITION USER’S GUIDE The Arena modeling environment If Arena is not already running, start it from the Windows Start menu and navigate to Programs > Rockwell Software > Arena. The Arena modeling environment will open with a new model window, as shown below. Model window flowchart view Project Bar Model window spreadsheet view To model your process in Arena, you’ll work in three main regions of the application window.
• • • • • 2 • GETTING STARTED In the model window, there are two main regions. The flowchart view will contain all of your model graphics, including the process flowchart, animation, and other drawing elements. The lower, spreadsheet view displays model data, such as times, costs, and other parameters. As we model the mortgage application process, we’ll work in all three of these regions of Arena.
• • • • • ARENA BASIC EDITION USER’S GUIDE Every process flow starts with a Create module. When you simulate the flowchart, individual entities will be created according to timing information you supply in the Create module properties. After it’s created, each entity moves from the Create module to the next shape in the process flow.
• • • • • 2 • GETTING STARTED 2 • Getting Started Note: If no connection appears between Create and Process, click the Object > Connect menu item or the Connect toolbar button to draw a connection. Your cursor will change to a cross hair. Start the connection by clicking the exit point ( ) of the Create module, then click the entry point ( ) of the Process module to complete the connection.
• • • • • ARENA BASIC EDITION USER’S GUIDE Decide whether applications are complete After the Process, we have a Decide module which determines whether the mortgage application is complete. 1. If you’re using the Auto-Connect feature (i.e., it’s checked on the Object > AutoConnect menu), be sure that the Process module is selected so that the Decide module will be connected to it. 2. Drag a Decide module to the right of the Process module.
Entity flow always begins with a Create module and terminates with a Dispose module. You may have as many of each of these modules as you need to generate entities into the model and to remove them when their processing is complete. • • • • • 2 • GETTING STARTED 2. Drag a Dispose module to the right of the Decide module. Arena will connect it to the primary (True) exit point of the Decide module. (We won’t include a graphic display since you’re now familiar with the drag-and-drop sequence.) 3.
• • • • • ARENA BASIC EDITION USER’S GUIDE Define model data Now that we’ve drawn the basic flowchart for our mortgage application process, let’s define the data associated with the modules, including the name of the module and information that will be used when we simulate the process. Initiate mortgage application (Create module) First, let’s visit the Create module, which will be named Initiate Mortgage Application.
• • • • • 2 • GETTING STARTED What are entities? Entities are the items—customers, documents, parts—that are being served, produced, or otherwise acted on by your process. In business processes, they often are documents or electronic records (checks, contracts, applications, purchase orders). In service systems, entities usually are people (the customers being served in a restaurant, hospital, airport, etc.).
• • • • • ARENA BASIC EDITION USER’S GUIDE For our Review Application process, we’ll use a minimum time of 1 hour, most likely value of 1.75 hours, and a maximum of 3 hours. We will assign a resource, the Mortgage Review Clerk, to perform this process. If more than one resource is required for a process to be performed, add as many as are necessary in the Process dialog’s Resources list. An entity won’t commence its process delay until all listed resources are available. 1.
• • • • • 2 • GETTING STARTED 5. In the Resource Name field of the Resource dialog box, type Mortgage Review Clerk. 6. Click OK to close the Resource dialog box. 8. Click OK to close the dialog box. For now, we’ll leave the default values for the other Process module properties. Feel free to explore their purposes through online help or the Modeling Concepts and Resources models in the SMARTs library.
• • • • • ARENA BASIC EDITION USER’S GUIDE 3. For the Percent True field, type 88 to define the percent of entities that will be treated with a “True” decision (i.e., will depart through the exit point at the right of the Decide module). 4. Click OK to close the dialog box. Accepted, Returned (Dispose module) In our simple process for reviewing mortgage applications, all the work that we’re interested in is done.
• • • • • 2 • GETTING STARTED 4. Click OK to close the dialog box. 2 • Getting Started Mortgage review clerk (Resource module) Along with our flowchart, we also can define parameters associated with other elements of our model, such as resources, entities, queues, etc. For the mortgage process, we’ll simply define the cost rate for the Mortgage Review Clerk so that our simulation results will report the cost associated with performing this process. The clerk’s costs are fixed at $12 per hour.
• • • • • ARENA BASIC EDITION USER’S GUIDE Prepare for the simulation To make the model ready for simulation, we’ll specify general project information and the duration of the simulation run. Since we’re just testing our first-cut model, we’ll perform a short, 20-day run. 1. Open the Project Parameters dialog box by using the Run > Setup menu item and clicking the Project Parameters tab.
If Arena displays an error message, you can use the Find button in the error window to locate the source of the problem. You can change between the error and model windows by selecting them from the Window menu. • • • • • 2 • GETTING STARTED As the simulation progresses, you’ll see small entity pictures resembling pages moving among the flowchart shapes. Also, a variety of variables change values as entities are created and processed, as illustrated below.
• • • • • ARENA BASIC EDITION USER’S GUIDE You also can step through the simulation one event at a time. Pause the simulation, then click the Step button or press the F10 key. Each time you step the simulation, an entity is moved through the flowchart. Usually, you’ll see animation of the entity’s movement, though sometimes no visual change will take place (e.g., when the next event is creating a new entity). When this occurs, just step again to move forward to the next event.
• • • • • 2 • GETTING STARTED By clicking on the entries inside the category sections, you can view various types of results from the simulation run. The following table illustrates some of the questions you could answer from the Category Overview Report on our simple mortgage application process simulation. Report Section Answer On average, how long did mortgage applications spend in the modeled process? Total Time (Entity), Average column 16.
• • • • • ARENA BASIC EDITION USER’S GUIDE Note: You can toggle between the split view (flowchart and spreadsheet) and a full-screen view of either area by clicking the Split Screen toolbar button or selecting the View > Split Screen menu item. When in full-screen view, clicking the icons on the Basic Process panel displays the appropriate view (flowchart for flowchart modules and spreadsheet for data-only modules).
• • • • • 2 • GETTING STARTED Animate the mortgage review clerk resource During the simulation run, our Mortgage Review Clerk resource can be in one of two states. If no mortgage application entity is in-process, then the resource is idle. We’ll use a picture of a person sitting at a desk to depict idleness. When an entity seizes the resource, the Mortgage Review Clerk’s state is changed to busy, in which case our picture will show the person reviewing a document. 1.
• • • • • ARENA BASIC EDITION USER’S GUIDE 8. If you’d like to have the clerk appear a bit larger, select the picture and use the resize handles to enlarge it. How do I use Rulers and Guides? Rulers Guides Glue to Guides Selecting the Rulers command on the View menu toggles horizontal and vertical rulers at the top and left edges of each drawing window. The ruler labels display the (+/-) distance from the origin in Arena world units.
• • • • • 2 • GETTING STARTED Plot the number of applications in-process Our second animation enhancement is a plot of how many mortgage applications are under review as the simulation progresses. This will give us a sense of the dynamics of the workload, which can vary quite a bit when the random nature of processes is incorporated into a simulated model. 1. Click the Plot button on the Animate toolbar.
• • • • • ARENA BASIC EDITION USER’S GUIDE With the edits complete, you may want to save them by clicking Save or pressing Ctrl+S. What is a model thumbnail? The Navigate panel on the Project Bar provides a model navigation tree for maneuvering through the different named views and hierarchical levels defined in the model. Included as part of the Navigate panel is a model thumbnail that helps users orient and change the current view within the active drawing window.
• • • • • 2 • GETTING STARTED Next steps You’ve succeeded in modeling, simulating, visualizing, and analyzing a simple mortgage application process. To further explore Arena’s capabilities, try solving a few of these extensions to the process. 1. Add a screening process before the application is reviewed. 2. Return some applications to the mortgage applicants after the screening process. On completion of the screening, 8% of the applications are returned.
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3 The Basic Process Panel This chapter describes the flowchart and data modules that you’ll use to model your process. Additionally, this chapter includes example uses of each module. Flowchart modules Flowchart modules are the set of objects that are placed in the model window to describe the simulation process. Create module DESCRIPTION This module is intended as the starting point for entities in a simulation model. Entities are created using a schedule or based on a time between arrivals.
• • • • • ARENA BASIC EDITION USER’S GUIDE Prompt Description Expression Any distribution or value specifying the time between arrivals. Applies only when Type is Expression. Units Time units used for interarrival and first creation times. Does not apply when Type is Schedule. Entities per Arrival Number of entities that will enter the system at a given time with each arrival. Max Arrivals Maximum number of entities that this module will generate.
• • • • • 3 • THE BASIC PROCESS PANEL Process module DESCRIPTION Indicator of a submodel process This module is intended as the main processing method in the simulation. Options for seizing and releasing resource constraints are available. Additionally, there is the option to use a “submodel” and specify hierarchical user-defined logic. The process time is allocated to the entity and may be considered to be value added, non-value added, transfer, wait, or other.
• • • • • ARENA BASIC EDITION USER’S GUIDE 32 Prompt Description Delay Type Type of distribution or method of specifying the delay parameters. Constant and Expression require single values, while Normal, Uniform, and Triangular require several parameters. Units Time units for delay parameters. Allocation Determines how the processing time and process costs will be allocated to the entity.
• • • • • 3 • THE BASIC PROCESS PANEL Process module — Resource dialog PROMPTS Description Type Specification of a particular resource, or selecting from a pool of resources (i.e., a resource set). Resource Name Name of the resource that will be seized and/or released. Applies only when Type is Resource. Set Name Name of the resource set from which a member will be seized and/or released.
• • • • • ARENA BASIC EDITION USER’S GUIDE Decide module DESCRIPTION Number of entities that have taken the True branch Number of entities that have taken the False branch This module allows for decision-making processes in the system. It includes options to make decisions based on one or more conditions (e.g., if entity type is Gold Card) or based on one or more probabilities (e.g., 75%, true; 25%, false). Conditions can be based on attribute values (e.g., Priority), variable values (e.g.
Prompt Description Named Specifies either the name of the variable, attribute, orentity type that will be evaluated when an entity enters the module. Does not apply when Type is Expression. Is Evaluator for the condition. Applies only to Attribute and Variable conditions. Row Specifies the row index for a variable array. Applies only when Type is N-way by Condition or 2-way by Condition and Variable is Array 1-D or Array 2-D. Column Specifies the column index for a variable array.
• • • • • ARENA BASIC EDITION USER’S GUIDE PROMPTS Prompt Description Name Unique module identifier displayed on the module shape. Type Method of batching entities together. Batch Size Number of entities to be batched. Save Criterion Method for assigning representative entity’s user-defined attribute values. Rule Determines how incoming entities will be batched. Any Entity will take the first “Batch Size” number of entities and put them together.
• • • • • 3 • THE BASIC PROCESS PANEL PROMPTS Description Name Unique module identifier displayed on the module shape. Type Method of separating the incoming entity. Duplicate Original will simply take the original entity and make some number of identical duplicates. Split Existing Batch requires that the incoming entity be a temporarily batched entity using the Batch module. The original entities from the batch will be split.
• • • • • ARENA BASIC EDITION USER’S GUIDE PROMPTS Prompt Description Name Unique module identifier displayed on the module shape. Assignments Specifies the one or more assignments that will be made when an entity executes the module. Type Type of assignment to be made. Other can include system variables, such as resource capacity or simulation end time. Variable Name Name of the variable that will be assigned a new value when an entity enters the module.
• • • • • 3 • THE BASIC PROCESS PANEL PROMPTS Description Name Unique module identifier displayed on the module shape. Type Type of observational (tally) or count statistic to be generated. Count will increase or decrease the value of the named statistic by the specified value. Entity Statistics will generate general entity statistics, such as time and costing/duration information. Time Interval will calculate and record the difference between a specified attribute’s value and current simulation time.
• • • • • ARENA BASIC EDITION USER’S GUIDE Data modules Data modules are the set of objects in the spreadsheet view of the model that define the characteristics of various process elements, such as resources and queues. Entity module DESCRIPTION This data module defines the various entity types and their initial picture values in a simulation. Initial costing information and holding costs are also defined for the entity.
Prompt Description Initial Other Cost Initial cost value that will be assigned to the other cost attribute of the entity. This attribute accrues the costs incurred when an entity is spending time in an other activity. Report Statistics Specifies whether or not statistics will be collected automatically and stored in the report database for this entity type.
• • • • • ARENA BASIC EDITION USER’S GUIDE Resource module DESCRIPTION This data module defines the resources in the simulation system, including costing information and resource availability. Resources may have a fixed capacity that does not vary over the simulation run or may operate based on a schedule. Resource failures and states can also be specified in this module.
Prompt Description Per Use Cost of a resource on a usage basis, regardless of the time for which it is used. Each time the resource is allocated to an entity, it will incur a peruse cost. StateSet Name Name of states that the resource may be assigned during the simulation run. Initial State Initial state of a resource. If specified, the name must be defined within the repeat group of state names. This field is shown only when a StateSet Name is defined.
• • • • • ARENA BASIC EDITION USER’S GUIDE TYPICAL USES Number of documents processed per hour Serial number to assign to parts for unique identification Space available in a facility PROMPTS Prompt Description Name The unique name of the variable being defined. Rows Number of rows in a dimensional variable. Columns Number of columns in a dimensional variable. Data Type The data type of the values stored in the variable. Valid types are Real and String. The default type is Real.
• • • • • 3 • THE BASIC PROCESS PANEL Patterns. (For more details, refer to the section entitled “Calendar schedule information.”) TYPICAL USES Work schedule for staff, including breaks Breakdown patterns for equipment Volume of customers arriving at a store Learning-curve factors for new workers PROMPTS Description Name The name of the schedule being defined. This name must be unique. Format Type Format of schedule being defined.
• • • • • ARENA BASIC EDITION USER’S GUIDE Set module DESCRIPTION This data module defines various types of sets, including resource, counter, tally, entity type, and entity picture. Resource sets can be used in the Process modules. Counter and Tally sets can be used in the Record module.
• • • • • 3 • THE BASIC PROCESS PANEL Calendar schedule information Time Pattern DESCRIPTION A Time Pattern defines a series of values that change over time. For example, a worker might be on duty during a standard work shift from Monday through Friday. The availability of the worker could be represented as a value of 1 when he’s on duty, 0 when he’s off duty. The time pattern that defines this availability schedule would list the changes from on duty to off duty over the week.
• • • • • ARENA BASIC EDITION USER’S GUIDE 48 Prompt Description Duration The length of this time pattern, which establishes the period in which the time pattern will repeat. For example, a time pattern of Duration equal to 1 day will repeat every 24 hours. This field is read-only, displaying the settings chosen in the Duration Edit dialog box for this time pattern. Base Date The beginning calendar date of this time pattern. Applies only when the time pattern type is Custom.
• • • • • 3 • THE BASIC PROCESS PANEL Calendar Exceptions DESCRIPTION An Exception defines a value that is to be applied for a resource over some fixed period of time. The exception value overrides the base value defined for the resource. For example, if a machine’s capacity was scheduled to be available (value of 1) during second shift according to its base time pattern, you could add an exception to change it to unavailable for second shift on a particular day (e.g., December 30, 2005).
• • • • • ARENA BASIC EDITION USER’S GUIDE Calendar States DESCRIPTION A Calendar State defines a name that can be used in place of a numeric value when defining time patterns and exceptions. This can be useful if a particular value (e.g., the number of workers in a pool of labor) needs to be entered in multiple places, but may need to be modified.
4 Using Visio and Arena Introduction Since the mid-1980s, Business Process Improvement (BPI) and simulation have become leading methodologies to allow corporations to deliver high-quality products and services through business process modeling. Businesses are seeking not simply to automate existing operations, but to improve and redesign business processes to meet and exceed customers’ expectations for the delivery of products and services.
• • • • • ARENA BASIC EDITION USER’S GUIDE Start a drawing Before opening the Visio stencil, it is necessary to have an administrator on the machine set the Visio macro security options to Low so that macros will be enabled. To begin a drawing, browse to the Process Simulation template, which the Process Simulator installs in the Program Files\Rockwell Software\Arena\Visio folder.
• • • • • 4 • USING VISIO AND ARENA Place and connect shapes You can change the Visio page layout or size via the File > Page Setup menu. For many process maps, a Standard page size and Landscape orientation work well. To define the process flow portion of your model, drag and drop flowchart shapes (e.g., Create, Process, Dispose) from the Process Simulation stencil into your drawing, just as you would with other standard Visio stencils.
• • • • • ARENA BASIC EDITION USER’S GUIDE Enter custom properties When you place shapes from the Process Simulation stencil, default names appear (e.g., Create 1, Process 1) to identify the steps in the process flow. Typically, you’ll replace these names with descriptions of the process steps. To do so, simply select the shape and type the new name, as with other standard Visio shapes.
• • • • • 4 • USING VISIO AND ARENA The property values that you define via the custom dialog boxes are stored with the individual shapes. When you transfer the process map to Arena, these parameters are used for simulation. Add data shapes To define the data modules (e.g., Entity, Resource) for the model of your process, you place shapes directly in the drawing for each of the elements you want to define.
• • • • • ARENA BASIC EDITION USER’S GUIDE If multiple problems are detected, each will be listed with a description and, in the case of invalid or missing properties, the field and value that are improper are listed. To correct the errors in your drawing, you can use the buttons at the bottom of the dialog box. For errors in shape properties, click the Edit Properties button, which displays the shape’s dialog box, to correct the data.
• • • • • 4 • USING VISIO AND ARENA translates your Visio process map into an Arena simulation model. When the process is complete, you have an Arena model containing modules from the Basic Process panel that mirror the shapes you used from the Visio Process Simulation stencil, including the properties and connections you specified in Visio. In Arena, you can set the simulation run length on the Run > Setup page.
• • • • • ARENA BASIC EDITION USER’S GUIDE throughout your organization so that everyone who has an interest in the process definition can access it directly through Visio. With this approach, process maps can be created and shared throughout the organization on any desktop with a Visio license. When simulation and animation are needed to visualize and analyze the behavior of the process, the drawings can be transferred to systems with the Arena Basic Edition.
A Statistical Distributions Arena contains a set of built-in functions for generating random numbers from the commonly used probability distributions. These distributions appear on pull-down menus in many Arena modules where they’re likely to be used. They also match the distributions in the Arena Input Analyzer. This appendix describes all of the Arena distributions. Each of the distributions in Arena has one or more parameter values associated with it.
• • • • • ARENA BASIC EDITION USER’S GUIDE To enter a distribution in an Arena field, you type the name of the distribution (or its fourletter abbreviation) followed by its parameters enclosed in parentheses. You may use spaces around punctuation to help read the distribution. A few examples appear below. UNIF( 3.5, 6 ) Uniform distribution with a minimum value of 3.5, a maximum value of 6 NORMAL(83, 12.8) Normal distribution with a mean of 83, a standard deviation of 12.8 DISCRETE(0.3,50,0.75,80, 1.
• • • • • A • STATISTICAL DISTRIBUTIONS Beta(β, α)BETA(Beta, Alpha) β–1 f(x) = Probability Density Function 0 Range Mean Variance Applications otherwise where β is the complete beta function given by B ( β, α ) = Parameters α–1 x-------------------------------------(1 – x) for 0 < x < 1 B (β,α) 1 β–1 ∫0 t (1 – t) α–1 dt Shape parameters Beta (β) and Alpha (α) specified as positive real numbers.
• • • • • ARENA BASIC EDITION USER’S GUIDE ContinuousCONTINUOUS(CumP1, Val1, . . ., CumPn, Valn) (c1, x1,. . ., cn,xn) Probability Density Function Cumulative Distribution Function f(x) = Parameters c1 if x = x1 (a mass of probability c1 at x1) cj – cj-1 if xj-1 ≤ x < xj, for j = 2, 3, . . ., n 0 if x < x1 or x ≥ xn The CONTINUOUS function in Arena returns a sample from a user-defined distribution. Pairs of cumulative probabilities cj (= CumPj) and associated values xj (= Valj) are specified.
• • • • • A • STATISTICAL DISTRIBUTIONS (xj–1, xj] with probability cj – cj–1; given that it is in this interval, it will be distributed uniformly over it. You must take care to specify c1 and x1 to get the effect you want at the left edge of the distribution. The CONTINUOUS function will return (exactly) the value x1 with probability c1.
• • • • • ARENA BASIC EDITION USER’S GUIDE DiscreteDISCRETE(CumP1, Val1, . . ., CumPn, Valn) (c1, x1, . . ., cn, xn) Probability Mass Function p(xj) = cj – cj-1 where c0 = 0 Cumulative Distribution Function Parameters Range Applications 64 The DISCRETE function in Arena returns a sample from a user-defined discrete probability distribution. The distribution is defined by the set of n possible discrete values (denoted by x1, x2, . . .
• • • • • A • STATISTICAL DISTRIBUTIONS Erlang(β, k)ERLANG(ExpMean, k) or ERLA(ExpMean, k) Probability Density Function –k k – 1 –x ⁄ β f(x) = β x e --------------------------------( k – 1 )! 0 Parameters Range Mean Variance Applications for x > 0 otherwise If X1, X2, . . . , Xk are independent, identically distributed exponential random variables, then the sum of these k samples has an Erlang-k distribution.
• • • • • ARENA BASIC EDITION USER’S GUIDE Exponential(β)EXPONENTIAL(Mean) or EXPO(Mean) Probability Density Function f(x) = --1- e –x ⁄ β β 0 Parameters Range Mean Variance Applications for x > 0 otherwise The mean (β) specified as a positive real number. [0, + ∞ ) β β2 This distribution is often used to model inter-event times in random arrival and breakdown processes, but it is generally inappropriate for modeling process delay times.
• • • • • A • STATISTICAL DISTRIBUTIONS Gamma(β, α)GAMMA(Beta, Alpha) or GAMM(Beta, Alpha) Probability Density Function f(x) = –α xα – 1 e–x ⁄ β β ---------------------------------Γ(α ) 0 for x > 0 otherwise where Γ is the complete gamma function given by Γ(α ) = Parameters Range Mean Variance Applications ∞ α – 1 –1 e dt ∫0 t Shape parameter (α) and scale parameter (β) specified as positive real values.
• • • • • ARENA BASIC EDITION USER’S GUIDE JohnsonJOHNSON(Gamma, Delta, Lambda, Xi) or JOHN(Gamma, Delta, Lambda, Xi) Probability Density Function Unbounded Family Parameters Range Applications 68 Bounded Family Gamma shape parameter (γ), Delta shape parameter (δ > 0), Lambda scale parameter (λ), and Xi location parameter (ξ). (− ∞, + ∞ ) Unbounded Family [ξ, ξ + λ] Bounded Family The flexibility of the Johnson distribution allows it to fit many data sets.
• • • • • A • STATISTICAL DISTRIBUTIONS Lognormal(μ, σ)LOGNORMAL(LogMean, LogStd) or LOGN(LogMean, LogStd) Denote the user-specified input parameters as LogMean = μl and LogStd = σl .
• • • • • ARENA BASIC EDITION USER’S GUIDE lognormal random variable X, but rather the mean and standard deviation of the normal random variable lnX.
• • • • • A • STATISTICAL DISTRIBUTIONS Normal(μ, σ)NORMAL(Mean, StdDev) or NORM(Mean, StdDev) Probability Density Function Parameters Range Mean Variance Applications f ( x) = 1 σ 2π e −( x − μ ) 2 /( 2σ 2 ) for all real x The mean (μ) specified as a real number and standard deviation (σ) specified as a positive real number. (− ∞, + ∞ ) μ σ2 The normal distribution is used in situations in which the central limit theorem applies; i.e., quantities that are sums of other quantities.
• • • • • ARENA BASIC EDITION USER’S GUIDE Poisson(λ)POISSON(Mean) or POIS(Mean) Probability Mass Function –λ x p(x)= e------------λ for xε {0, 1, ...} x! 0 Parameters Range 72 The mean (λ) specified as a positive real number. {0, 1, . . .} Mean λ Variance λ Applications otherwise The Poisson distribution is a discrete distribution that is often used to model the number of random events occurring in a fixed interval of time.
• • • • • A • STATISTICAL DISTRIBUTIONS Triangular(a, m, b)TRIANGULAR(Min, Mode, Max) or TRIA(Min, Mode, Max) Probability Density Function f(x) 0 x a m b 2( x – a) ---------------------------------(m – a)(b – a) f(x) = 2(b – x) ---------------------------------(b – m )( b – a ) 0 Parameters Range Mean Variance for m ≤ x ≤ b otherwise The minimum (a), mode (m), and maximum (b) values for the distribution specified as real numbers with a < m < b.
• • • • • ARENA BASIC EDITION USER’S GUIDE Uniform(a, b)UNIFORM(Min, Max) or UNIF(Min, Max) Probability Density Function f(x) 1 b-a 0 f(x) = 1 ----------b–a 0 Parameters Range Mean Variance Applications 74 b a x for a ≤ x ≤ b otherwise The minimum (a) and maximum (b) values for the distribution specified as real numbers with a < b. [a, b] (a + b)/2 (b – a)2/12 The uniform distribution is used when all values over a finite range are considered to be equally likely.
• • • • • A • STATISTICAL DISTRIBUTIONS Weibull(β, α)WEIBULL(Beta, Alpha) or WEIB(Beta, Alpha) Probability Density Function f(x) a=1/2 a=1 a=2 a=3 x 0 f(x) = aβ – a x a – 1 e – ( x ⁄ β ) 0 Parameters for x > 0 otherwise Shape parameter (α) and scale parameter (β) specified as positive real values. Range [0, + ∞ ) Mean β --- Γ ⎛ 1--- ⎞ a ⎝ a⎠ , where Γ is the complete gamma function (see gamma distribution).
• • • • • ARENA BASIC EDITION USER’S GUIDE Applications 76 The Weibull distribution is widely used in reliability models to represent the lifetime of a device. If a system consists of a large number of parts that fail independently, and if the system fails when any single part fails, then the time between successive failures can be approximated by the Weibull distribution. This distribution is also used to represent nonnegative task times that are skewed to the left.
Library Shapes and Symbols Arena .plb picture files Arena’s picture libraries (*.plb files) contain images that you may use for entity, resource, and global pictures. You can use the images in these libraries for any of these three types of picture animation. You also can copy these pictures into your own libraries, draw new pictures in Arena’s picture editor, or add pictures from the Arena Symbol Factory to any .plb file.
• • • • • ARENA BASIC EDITION USER’S GUIDE Arena .plb libraries The list of standard Arena picture libraries includes: Buldings.plb Equipment.plb Faces.plb Factory.plb General.plb Machines.plb Medical.plb Objects.plb Office.plb Office Equipment.plb People.plb Symbols.plb Vehicles.plb Workers.
• • • • • B • LIBRARY SHAPES AND SYMBOLS B • Shapes and Symbols The basic operation of Symbol Factory simply requires you to select an object from a category list, click Edit > Copy, and then paste the symbol into your picture editor window or the Arena application window (for static shapes). Details on the Arena Symbol Factory can be found in the extensive online help embedded in the application. You must have suitable license activation to use the full Symbol Factory capabilities.
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Index Numerics 2-way chance 34 2-way condition 34 A 59, 62 Index ActiveX support 51 adding plots to the model 25 animating resources 23 animation 7, 19 enhancing the graphics 21 animation scale factor 19 Arena Basic Edition 1 Arena Symbol Factory 3, 78 adding shapes to Arena 78 Assign module 37 Auto-Connect menu 8 collecting statistics 38 contact information 4 Continuous 62 Continuous empirical distribution counter sets 46 Create module 7, 29 creation of entities
• • • • • ARENA BASIC EDITION USER’S GUIDE disposing 30 duplicating 36 what are they? 13 Entity module 40 entity picture sets 46 entity type sets 46 Erlang distribution 59, 65, 67 Exponential distribution 59, 66 F flowchart modules 11, 29 flowchart objects 11 flowchart view 7 G Gamma distribution 59, 67 Glue to Guides 24 grid 9 grouping within the model 35 guides 24 J Johnson distribution 59, 68 pause the simulation 20 picture libraries 77 BasicProcess.
S Triangular distribution sample models 2 saving your model 18 Schedule module 44 Separate module 36 Set module 46 sets definition 46 simulating your process 18 simulation run length 57 SMARTs library 2, 12, 15 snap 9 split view 22 splitting batches 36 spreadsheet view 7 stepping through the simulation U tally sets 46 technical support 3 thumbnail 26 time delay 13 Time Pattern 47 time patterns 47 training courses 4 59, 73 59, 74 V 20 Variable module 4
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