three-point estimation

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:

  • a = the best-case estimate
  • m = the most likely estimate
  • b = the worst-case estimate.

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 doubletriangular 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 = (a + 4m + b) / 6
SD = (b − a) / 6

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:

E = (a + m + b) / 3.

In some applications,[1] the triangular distribution is used directly as an estimated probability distribution, rather than for the derivation of estimated statistics.

pay it forward

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.

Earned value management

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:

  • Scope
  • Schedule, and
  • Costs

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

  1. a project plan that identifies work to be accomplished,
  2. a valuation of planned work, called Planned Value (PV) or Budgeted Cost of Work Scheduled (BCWS), and
  3. pre-defined “earning rules” (also called metrics) to quantify the accomplishment of work, called Earned Value (EV) or Budgeted Cost of Work Performed (BCWP).

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:

  • Inputs (documents, plans, designs, etc.)
  • Tools and Techniques (mechanisms applied to inputs)
  • Outputs (documents, plans, designs, etc.)

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.

  • The five process groups are:
  1. Initiating : Those processes performed to define a new project or a new phase of an existing project by obtaining authorization to start the project or phase.
  2. Planning : Those processes required to establish the scope of the project, refine the objectives, and define the course of action required to attain the objectives that the project was undertaken to achieve.
  3. Executing : Those processes performed to complete the work defined in the project management plan to satisfy the project specifications
  4. Monitoring and Controlling : Those processes required to track, review, and regulate the progress and performance of the project; identify any areas in which changes to the plan are required; and initiate the corresponding changes.
  5. Closing : Those processes performed to finalize all activities across all Process Groups to formally close the project or phase.
  • The ten knowledge areas are:
  1. Project Integration Management : Project Integration Management includes the processes and activities needed to identify, define, combine, unify, and coordinate the various processes and project management activities within the Project Management Process Groups.
  2. Project Scope Management : Project Scope Management includes the processes required to ensure that the project includes all the work required, and only the work required, to complete the project successfully.
  3. Project Time Management : Project Time Management includes the processes required to manage the timely completion of the project.
  4. Project Cost Management : Project Cost Management includes the processes involved in planning, estimating, budgeting, financing, funding, managing, and controlling costs so that the project can be completed within the approved budget.
  5. Project Quality Management : Project Quality Management includes the processes and activities of the performing organization that determine quality policies, objectives, and responsibilities so that the project will satisfy the needs for which it was undertaken.
  6. Project Human Resource Management : Project Human Resource Management includes the processes that organize, manage, and lead the project team.
  7. Project Communications Management : Project Communications Management includes the processes that are required to ensure timely and appropriate planning, collection, creation, distribution, storage, retrieval, management, control, monitoring, and the ultimate disposition of project information.
  8. Project Risk Management : Project Risk Management includes the processes of conducting risk management planning, identification, analysis, response planning, and controlling risk on a project.
  9. Project Procurement Management : Project Procurement Management includes the processes necessary to purchase or acquire products, services, or results needed from outside the project team
  10. Project Stakeholders Management : Project Stakeholder Management includes the processes required to identify all people or organizations impacted by the project, analyzing stakeholder expectations and impact on the project, and developing appropriate management strategies for effectively engaging stakeholders in project decisions and execution.

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.

Hindsight bias

Hindsight bias, also known as the knew-it-all-along effect or creeping determinism, is the inclination, after an event has occurred, to see the event as having been predictable, despite there having been little or no objective basis for predicting it, prior to its occurrence.[1][2] It is a multifaceted phenomenon that can affect different stages of designs, processes, contexts, and situations.[3] Hindsight bias may cause memory distortion, where the recollection and reconstruction of content can lead to false theoretical outcomes. It has been suggested that the effect can cause extreme methodological problems while trying to analyze, understand, and interpret results in experimental studies. A basic example of the hindsight bias is when, after viewing the outcome of a potentially unforeseeable event, a person believes he or she “knew it all along”. Such examples are present in the writings of historians describing outcomes of battles, physicians recalling clinical trials, and in judicial systems trying to attribute responsibility and predictability of accidents.

Power and dominance

Non verbal expressions of power and dominance are gestures or motions that assert one´s authority over another.


The colors one wears affect other´s perceptions of one´s authority:

purple: people of high status adorn their clothing with purple to distinguish themselves as noble or wealthy

people attribute greater authority to others wearing red

It is human to strive for power and dominance in social settings

simple gestures establish authority

A firmer handshake
Better posture
Causing slight interruptions in conversation

can rise authority in group situations

many peers view Non verbal expressions of power and dominance as manipulation for self gain

Their abuse can be disastrous

Men and women have different perceptions of Non verbal expressions of power and dominance

Nodding is misinterpreted in cross gender communication

women interpret a nod as a signal of understanding

men interpret a nod as a signal of agreement

small miscommunications and misinterpretations lead to disagreement and confrontation

Russel (as cited in Dunbar & Burgoon, 2005) describes, “the fundamental concept in social science is power, in the same way that energy is the fundamental concept in physics“. Power and dominance-submission are two key concepts in relationships, especially close relationships where individuals rely on one another to achieve their goals (Dunbar & Burgoon, 2005) and as such it is important to be able to identify indicators of dominance.

Power and dominance are different concepts yet share similarities. Power is the ability to influence behavior (Bachrach & Lawler; Berger; Burgoon et al.; Foa & Foa; French & Raven; Gray-Little & Burks; Henley; Olson & Cromwell; Rollins & Bahr, as cited in Dunbar & Burgoon, 2005) and may or may not be fully evident until challenged by an equal force (Huston, as cited in Dunbar & Burgoon, 2005). Unlike power, that may be latent, dominance is manifest reflecting individual (Komter, as cited in Dunbar & Burgoon, 2005), situational and relationship patterns where control attempts are either accepted or rejected (Rogers-Millar & Millar,as cited in Dunbar & Burgoon, 2005). Moskowitz, Suh, and Desaulniers (1994) mention two similar ways that people can relate to the world in interpersonal relationships: agency and communion. Agency includes status and is a continuum from assertiveness-dominance to passive-submissiveness – it can be measured by subtracting submissiveness from dominance. Communion is a second way to interact with others and includes love with a continuum from warm-agreeable to cold-hostile-quarrelsomeness. Power and dominance relate together in such a way that those with the greatest and least power typically do not assert dominance while those with more equal relationships make more control attempts Dunbar & Burgoon, 2005).

As one can see, power and dominance are important, intertwined, concepts that greatly impact relationships. In order to understand how dominance captures relationships one must understand the influence of gender and social roles while watching for verbal and nonverbal indicators of dominance.

wagon-wheel effect

The wagon-wheel effect (alternatively, stagecoach-wheel effectstroboscopic effect) is an optical illusion in which a spoked wheelappears to rotate differently from its true rotation. The wheel can appear to rotate more slowly than the true rotation, it can appear stationary, or it can appear to rotate in the opposite direction from the true rotation. This last form of the effect is sometimes called thereverse rotation effect.

The wagon-wheel effect is most often seen in film or television depictions of stagecoaches or wagons in Western movies, although recordings of any regularly spoked wheel will show it, such as helicopter rotors and aircraft propellers. In these recorded media, the effect is a result of temporal aliasing.[1] It can also commonly be seen when a rotating wheel is illuminated by flickering light. These forms of the effect are known as stroboscopic effects: the original smooth rotation of the wheel is visible only intermittently. A version of the wagon-wheel effect can also be seen under continuous illumination.

Rushton (1967[5]) observed the wagon-wheel effect under continuous illumination while humming. The humming vibrates the eyes in their sockets, effectively creating stroboscopic conditions within the eye. By humming at a frequency of a multiple of the rotation frequency, he was able to stop the rotation. By humming at slightly higher and lower frequencies, he was able to make the rotation reverse slowly and to make the rotation go slowly in the direction of rotation. A similar stroboscopic effect is now commonly observed by people eating crunchy foods, such as carrots, while watching TV: the image appears to shimmer.[6] The crunching vibrates the eyes at a multiple of the frame rate of the TV. Besides vibrations of the eyes, the effect can be produced by observing wheels via a vibrating mirror. Rear-view mirrors in vibrating cars can produce the effect.

Truly continuous illumination

The first to observe the wagon-wheel effect under truly continuous illumination (such as from the sun) was Schouten (1967[7]). He distinguished three forms of subjective stroboscopy which he called alpha, beta, and gamma: Alpha stroboscopy occurs at 8–12 cycles per second; the wheel appears to become stationary, although “some sectors [spokes] look as though they are performing a hurdle race over the standing ones” (p. 48). Beta stroboscopy occurs at 30–35 cycles per second: “The distinctness of the pattern has all but disappeared. At times a definite counterrotation is seen of a grayish striped pattern” (pp. 48–49). Gamma stroboscopy occurs at 40–100 cycles per second: “The disk appears almost uniform except that at all sector frequencies a standing grayish pattern is seen … in a quivery sort of standstill” (pp. 49–50). Schouten interpreted beta stroboscopy, reversed rotation, as consistent with there being Reichardt detectors in the human visual system for encoding motion. Because the spoked wheel patterns he used (radial gratings) are regular, they can strongly stimulate detectors for the true rotation, but also weakly stimulate detectors for the reverse rotation.

There are two broad theories for the wagon-wheel effect under truly continuous illumination. The first is that human visual perception takes a series of still frames of the visual scene and that movement is perceived much like a movie. The second is Schouten’s theory: that moving images are processed by visual detectors sensitive to the true motion and also by detectors sensitive to opposite motion from temporal aliasing. There is evidence for both theories, but the weight of evidence favours the latter.

Discrete frames theory

Purves, Paydarfar, and Andrews (1996[8]) proposed the discrete-frames theory. One piece of evidence for this theory comes from Dubois and VanRullen (2011[9]). They reviewed experiences of users of LSD who often report that under the influence of the drug a moving object is seen trailing a series of still images behind it. They asked such users to match their drug experiences with movies simulating such trailing images viewed when not under the drug. They found that users selected movies around 15–20 Hz. This is between Schouten’s alpha and beta rates.

Other evidence for the theory is reviewed next.

Temporal aliasing theory

Kline, Holcombe, and Eagleman (2004[10]) confirmed the observation of reversed rotation with regularly spaced dots on a rotating drum. They called this “illusory motion reversal”. They showed that these occurred only after a long time of viewing the rotating display (from about 30 seconds to as long as 10 minutes for some observers). They also showed that the incidences of reversed rotation were independent in different parts of the visual field. This is inconsistent with discrete frames covering the entire visual scene. Kline, Holcombe, and Eagleman (2006[11]) also showed that reversed rotation of a radial grating in one part of the visual field was independent of superimposed orthogonal motion in the same part of the visual field. The orthogonal motion was of a circular grating contracting so as to have the same temporal frequency as the radial grating. This is inconsistent with discrete frames covering local parts of visual scene. Kline et al. concluded that the reverse rotations were consistent with Reichardt detectors for the reverse direction of rotation becoming sufficiently active to dominate perception of the true rotation in a form of rivalry. The long time required to see the reverse rotation suggests that neural adaptation of the detectors responding to the true rotation has to occur before the weakly stimulated reverse-rotation detectors can contribute to perception.

Some small doubts about the results of Kline et al. (2004) sustain adherents of the discrete-frame theory. These doubts include Kline et al.’s finding in some observers more instances of simultaneous reversals from different parts of the visual field than would be expected by chance, and finding in some observers differences in the distribution of the durations of reversals from that expected by a pure rivalry process (Rojas, Carmona-Fontaine, López-Calderón, & Aboitiz, 2006[12]).

In 2008, Kline and Eagleman demonstrated that illusory reversals of two spatially overlapping motions could be perceived separately, providing further evidence that illusory motion reversal is not caused by temporal sampling.[13] They also showed that illusory motion reversal occurs with non-uniform and non-periodic stimuli (for example, a spinning belt of sandpaper), which also cannot be compatible with discrete sampling. Kline and Eagleman proposed instead that the effect results from a “motion during-effect”, meaning that a motion after-effect becomes superimposed on the real motion.


Because of the illusion this can give to moving machinery, it is advised that single-phase lighting be avoided in workshops and factories. For example, a factory that is lit from a single-phase supply with basic fluorescent lighting will have a flicker of twice the mains frequency, either at 100 or 120 Hz (depending on country); thus, any machinery rotating at multiples of this frequency may appear to not be turning. Seeing that the most common types of AC motors are locked to the mains frequency, this can pose a considerable hazard to operators of lathes and other rotating equipment. Solutions include deploying the lighting over a full 3-phase supply, or by using high-frequency controllers that drive the lights at safer frequencies.[14] Traditional incandescent light bulbs, which employ filaments that glow continuously, offer another option as well, albeit at the expense of increased power consumption. Smaller incandescent lights can be used as task lighting on equipment to help combat this effect to avoid the cost of operating larger quantities of incandescent lighting in a workshop environment.