Integral solutions
Double-triangular Distribution is the combination of two triangles, each with an area of 0.5. The mode is also the median.
The variance is:
Note: the variance is the same as for the triangular distribution.
The probability density is:
And the cumulative distribution function:
The double-triangular is quite unnatural. It is highly unlikely to be a proper representation of uncertainty. Moreover, estimating the median is, in my view, more difficult than the estimating the most likely value (mode).
The three-point estimation technique is used in management and information systems applications for the construction of an approximate probability distribution representing the outcome of future events, based on very limited information. While the distribution used for the approximation might be a normal distribution, this is not always so and, for example a triangular distribution might be used, depending on the application.,[1]
In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses:
These are then combined to yield either a full probability distribution, for later combination with distributions obtained similarly for other variables, or summary descriptors of the distribution, such as the mean, standard deviation or percentage points of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the 3 initial points, and there are clear dangers in using an assumed form for an underlying distribution that itself has little basis.
Based on the assumption (possibly unwarranted) that a double–triangular distribution governs the data, several estimates are possible. These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where:
E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate. In Project Evaluation and Review Techniques (PERT) the three values are used to fit a Beta distribution for Monte Carlo simulations.
The triangular distribution is also commonly used. It differs from the double-triangular by its simple triangular shape and the mode does not have to coincide with the median. The mean (expectation) is then:
In some applications,[1] the triangular distribution is used directly as an estimated probability distribution, rather than for the derivation of estimated statistics.
The expression “pay it forward” is used to describe the concept of asking the beneficiary of a good deed to repay it to others instead of to the original benefactor. The concept is old, but the phrase may have been coined by Lily Hardy Hammond in her 1916 book In the Garden of Delight.[1]
“Pay it forward” is implemented in contract law of loans in the concept of third party beneficiaries. Specifically, the creditor offers the debtor the option of “paying” the debt forward by lending it to athird person instead of paying it back to the original creditor. Debt and payments can be monetary or by good deeds. A related type of transaction, which starts with a gift instead of a loan, isalternative giving.
he first step in creating a responsibility assignment matrix is to decompose your projectand create a work
breakdown structure. Once you have completed this important first step, you will know what the project deliverables will be. If you compose an organizational breakdown structure – breaking the project down into a hierarchy of departments, it will facilitate the process of assigning deliverables to responsible parties. Creating this second chart is an option that is highly recommended.
Once you have the list of deliverables, open an Excel file. Down the left-hand side list each deliverable. If there were intermediate deliverables discovered in the process of creating the work breakdown structure, list those as well.
After listing each deliverable down the side, list each resource across the top of the table.
Now, you will assign deliverables to resources using the following code for roles:
R: Responsible – this is the resource that owns the work. Each deliverable should have at least one person responsible for it.
A: Accountable – this is the person who approves the work. There is only one accountable resource.
C: Consulted – this is the person who delivers information required to complete the work.
I: Informed: This is the person who is informed of the progress of the deliverable.
S: Supportive: This is the person who provides work in addition to the responsible party.
V: Verifies: This is the person who ensures that the work meets standards.
F: Final Authority: This person gives the final stamp on the completed work.
In assigning roles, you will use at least the first four listed above RACI. Assign each deliverable to at least one responsible party. Assign each deliverable exactly one accountable party. Continue until everything has been assigned. Distribute the responsibility assignment matrix monist the staff and make explicit your expectations for each of them.
Earned value management (EVM), or Earned value project/performance management (EVPM) is a project management technique for measuring project performance and progress in an objective manner.
Earned value management is a project management technique for measuring project performance and progress. It has the ability to combine measurements of the project management triangle:
In a single integrated system, Earned Value Management is able to provide accurate forecasts of project performance problems, which is an important contribution for project management.
Early EVM research showed that the areas of planning and control are significantly impacted by its use; and similarly, using the methodology improves both scope definition as well as the analysis of overall project performance. More recent research studies have shown that the principles of EVM are positive predictors of project success.[1] Popularity of EVM has grown in recent years beyond government contracting, in which sector its importance continues to rise[2] (e.g., recent new DFARS rules[3]), in part because EVM can also surface in and help substantiate contract disputes.[4]
Essential features of any EVM implementation include
EVM implementations for large or complex projects include many more features, such as indicators and forecasts of cost performance (over budget or under budget) and schedule performance (behind schedule or ahead of schedule). However, the most basic requirement of an EVM system is that it quantifies progress using PV and EV.
There is a measurement limitation for how precisely EVM can be used, stemming from classic conflict between accuracy and precision, as the mathematics can calculate deceptively far beyond the precision of the measurements of data and the approximation that is the plan estimation. The limitation on estimation is commonly understood (such as the ninety-ninety rule in software) but is not visible in any margin of error. The limitations on measurement are largely a form of digitization error as EVM measurements ultimately can be no finer than by item, which may be the Work Breakdown Structure terminal element size, to the scale of reporting period, typically end summary of a month, and by the means of delivery measure. (The delivery measure may be actual deliveries, may include estimates of partial work done at the end of month subject to estimation limits, and typically does not include QC check or risk offsets.)
A Guide to the Project Management Body of Knowledge (PMBOK Guide) is a book which presents a set of standard terminology and guidelines for project management. The Fifth Edition (2013) is the document resulting from work overseen by the Project Management Institute (PMI). Earlier versions were recognized as standards by the American National Standards Institute (ANSI) which assigns standards in the United States (ANSI/PMI 99-001-2008) and the Institute of Electrical and Electronics Engineers (IEEE 1490-2011).[
he PMBOK Guide is process-based, meaning it describes work as being accomplished by processes. This approach is consistent with other management standards such as ISO 9000 and the CMMI Institute‘s CMMI. Processes overlap and interact throughout a project or its various phases. Processes are described in terms of:
A Guide to the Project Management Body of Knowledge — Fifth Edition provides guidelines for managing individual projects and defines project management related concepts. It also describes the project management life cycle and its related processes, as well as the project life cycle.[3]
The Guide recognizes 47 processes that fall into five basic process groups and ten knowledge areas that are typical of most projects, most of the time.
Each of the ten knowledge areas contains the processes that need to be accomplished within its discipline in order to achieve effective project management. Each of these processes also falls into one of the five process groups, creating a matrix structure such that every process can be related to one knowledge area and one process group.
The PMBOK Guide is meant to offer a general guide to manage most projects most of the time. There are currently two extensions to the PMBOK Guide: the Construction Extension to the PMBOK Guide applies to construction projects, while the Government Extension to the PMBOK Guide applies to government projects. The PMBOK Guide is also used as a support to prepare the Project Management Institute (PMI) certifications, such as the CAPM and PMP.
Strictly speaking matrix management is the practice of managing individuals with more than one reporting line (in a matrix organization structure), but it is also commonly used to describe managing cross functional, cross business group and other forms of working that cross the traditional vertical business units – often silos – of function and geography.
A lot of the early literature on the matrix comes from the field of cross functional project management where matrices are described as strong, medium or weak depending on the level of power of the project manager.
Some organizations fall somewhere between the fully functional and the pure matrix. These organizations are defined in A Guide to the Project Management Body of Knowledge[1] as ’composite’. For example, even a fundamentally functional organization may create a special project team to handle a critical project.
However, today, matrix management is much more common and exists at some level, in most large complex organizations, particularly those that have multiple business units and international operations.
Key advantages that organizations seek when introducing a matrix include:
Key disadvantages of matrix organizations include:
The advantages of a matrix for project management can include:
The disadvantages for project management can include:
Representing matrix organizations visually has challenged managers ever since the matrix management structure was invented. Most organizations use dotted lines to represent secondary relationships between people, and charting software such as Visio and OrgPlus supports this approach. Until recently, Enterprise resource planning (ERP) and Human resource management systems (HRMS) software did not support matrix reporting. Late releases of SAP software support matrix reporting, and Oracle eBusiness Suite can also be customized to store matrix information.
The work breakdown structure approach allows us to visually see the work that is needed in order to complete a project.
According to the Project Management Body of Knowledge (PMBOK®), and the Practice Standard for Work Breakdown Structures – Second Edition from the Project Management Institute (PMI), the work breakdown structure can be used to effectively decompose the project scope, to improve estimating, to better control the project execution and to more accurately verify project completion. In addition, using a work breakdown structure approach summarizes project information to improve the opportunity for use of historical information, which, can aid in both speed and accuracy of future projects. The work breakdown structure is a repeatable process that can be used as a template for future projects.
the PMBOK® describes the work breakdown structure as “a deliverable-oriented hierarchical decomposition of the work to be executed by the team”. This is a way of describing the work so that the team knows exactly what work is needed in order to meet the goals of the project. In many cases, a work breakdown structure is the first transition of organizational goals into real work that people can actually perform. It helps to provide clarity of the scope for the project and “breaks down” the scope into whole work units.
A work breakdown structure is deliverable-oriented. So what is a deliverable? In a word, it can best be described as a noun.
A work breakdown structure is a hierarchy. That means that deliverables can be further decomposed into parent and child relationships.
The work breakdown structure technique is described in the Project Scope Management section of the PMBOK and further elaborated in the Practice Standard for Work Breakdown Structures – Second Edition. A scope definition is necessary to decide what all should and should not be covered with in the project. When complete, the work breakdown structure lowest level components called “work packages” can be delegated to teams for further development and estimating and a work breakdown structure dictionary can be developed. In this way, project responsibilities can easily be distributed and committed to. This information can then be placed into a scheduling tool. In addition, the work packages can be used to create a project baseline that assures all the work can be evaluated for completeness.
A work breakdown structure is typically presented in the form of an organization chart-like structure. It can be presented as a list, idea map or outline form as well. The key is to put it in a form that can most easily be used by both the team members and organizational leaders with the tools that your company uses most easily.
