Published here March 2004.


Musings Index

Those Sexy Triangles Again

Our December 2003 Musings, Triangles, Sex and Simplicity, generated some interesting discussion, so we thought we would visit the subject again but with some illustrative graphics. At issue is the relationship between scope, time and cost, or performance, or resources (take your pick) and where does quality fit in? I have argued that the there are four core project management parameters and that they are scope, quality, time and cost arranged in a square and not a triangle. In fact, one of my earliest models was a four-cornered star, rather than a square, published by PMI in 1987.[1] The important part of the illustration is shown in Figure 1.

Figure 1: The core of project management
Figure 1: The core of project management

The associated text said in part:

The star points to the four key constraints of scope, cost, time and quality. As every project manager knows, these restraints are inextricably intertwined. Scope-quality represents performance, scope-cost represents viability, cost-time represent viability, cost-time represents effort, and quality-time represents competitiveness.

The complete original diagram had a lot more to say, but that's enough for now. Although seemingly self evident, few academics appear to have picked up on the significance of pairing the core constraints idea.

By 1991, I was trying to demonstrate how the balancing of these four constraints, or objectives if you are the project's sponsor, vary with different project products. This is shown in Figure 2.[2] Of this diagram, I said:

More particularly, some projects may lean more towards one constraint than another. Therefore, the project manager and his team, in the course of managing the project process, must choose options and make decisions according to such priorities. This may be viewed graphically as the Tetrad Trade-off, as shown in [the Figure].

In this diagram, four projects are shown, one in each of the four quadrants of the tetrad. The projects have "handles" which are intended to represent vectors signifying the extent and bias of (or pull on) the particular project as a consequence of the four constraints. Thus, project P1 is in the scope emphasis quadrant and its priority leans towards defining the project scope (rather than developing a defined scope). Good examples include research and development (R & D) and defense projects. Such projects consequently tend to be very uncertain in terms of quality, time and cost.
Figure 2: The Tetrad Tradeoff
Figure 2: The Tetrad Tradeoff
More often, the scope is reasonably well defined, but the emphasis may be on quality, as represented by P2. Examples include new high-end-market automobiles, high-end residential or commercial office construction, or heavy-duty public infrastructure projects, where durability and public safety are key concerns. Conversely, P3 is in the time emphasis quadrant, as in the case of meeting the opening day deadline of a national exposition, or the opening night of a theater production. Or the emphasis may be on a balance between scope and cost, P4, such as in the case of market research projects, or in some government studies.

The inexperienced project manager should be cautioned that the priority emphasis for a project may well shift during its life cycle. For example: a scope and quality oriented project at the outset may well shift towards cost and schedule towards the end of its life cycle. An illustration of this might be a project which, having experienced cost overruns, is running out of financing. Conversely, a cost-schedule oriented project may have a tendency to move towards scope and quality towards its end. An illustration of this might be a product launch which needs to be moved "up-market" as a result of new market competition. However, this latter shift is difficult to achieve retroactively, and emphasizes the importance of sound early project planning and development.

Managing the Tetrad Trade-off with skill and understanding is a very important part of managing a project. Rarely does a project manager have the luxury of a project which has equally balanced constraints, such that the achievement of all four is entirely feasible!

But at least by 2002, Microsoft has recognized the relationship that quality has with scope, time and cost. In their Microsoft Office Online web site Assistance for Microsoft Project 2000, they illustrate "The Quality Triangle" as shown in Figure 3.[3] (Thanks to Dylan Wan for bringing this to our attention.[4]

Figure 3: Microsoft's quality angle
Figure 3: Microsoft's quality angle

As Microsoft explains it:

Quality, a fourth element, is at the center of the project triangle. Changes you make to any of the three sides of the triangle are likely to affect quality. Quality is not a side of the triangle; it is a result of what you do with time, money, and scope.

For example, if you find you have additional time in your schedule, you might be able to increase scope by adding tasks and duration. With this extra time and scope, you can build a higher level of quality into the project and its deliverables.

Or, if you need to cut costs to meet your budget, you might have to decrease scope by cutting tasks or reducing task durations. With decreased scope, there might be fewer opportunities to achieve a certain level of quality, so lower quality may result from the need to cut costs.

We don't quite agree with that, but it is a step in the right direction. However, Derrick Davis has an even better idea.[5] He proposes a tetrahedron which I have drawn in Figure 4.

Figure 4: Davis's project management tetrahedron
Figure 4: Davis's project management tetrahedron

Now, that's really innovative thinking. It not only facilitates the display of the scope-time (need) and quality-cost (value) pairs, but it preserves the triangle and all it's sexiness as well!

1. Wideman, R. M., Project management Body of Knowledge (PMBOK), Project Management Institute, PA, 1987, Figure 3, p1-5
2. Wideman, R. M., A Framework for Project and Program Management Integration, Project Management Institute, PA, 1991, Figure V.2, pV-6
3. The Quality Angle displayed in Microsoft Office Online >Assistance > Office 2000 > Project 2000 at, 2003.
4. Wan, D., by Email, 12/9/03
5. Davis, D., by Email 12/10/03
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