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My projects generally have 6 areas (Engineering, Fabrication, Assembly etc). Each area has been allotted a budget for a particular project (dollars and hours).

Every week, I get a report on how much we spent (in dollars and hours) in each area on that particular project.

I am trying to incorporate some kind of health check tool in addition to this info. For eg- Engineering had 40 hrs and $1600 allotted. Say they have used used up 30 hours and are only 50% complete, what formula can I use to show the health of this?

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To be honest I just use Word or Excel in conjunction with pre-defined parameters to assess and report project health on a regular basis to my sponsors, project board and key stakeholders. Establishing those parameters is the challenging part, and they will likely change from one project to the next. You may want to investigate Earned Value Management techniques, applying concepts like Schedule Performance and Cost Performance indices to your decision making if your projects are sufficiently costly and complex to warrant the overhead.

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I second the Earned Value technique as a valuable tool for indicating status and forecasting.

You might start simple by also asking for an Expected to Complete (ETC) in hours: how much time will they need to finish the other 50%? Is it again 30 hours or will it be the original 20?

By adding the ETC to the actuals, you can calculate the total expected cost. The variance between original budget and expected cost will give you your health check.

Make sure the "50% complete" is validated by tangible (measurable) evidence and not a guess.

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There are multiple metrics that would indicate the health, but since you mentioned costs and hours, Earned Value is the method you want to deploy. It is very involved to execute this method properly and is expensive to operate. Typically, it is used on more complex and expensive projects.

While Earned Value monitors hours, it is a tool that measures dollars. Hours can overrun while dollars underrun, and vice versa. So, once you "dollarize" the work, hours become less relevant.

That said, most people think in hours--obviously--when they are estimating work so you need to use both. But your ETCs and EACs are in dollars.

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TL;DR

A useful information dashboard shows whether your project is on-track or at-risk. There is no single formula for determining that, especially when a project has fallen prey to the "80% of stuff is 50% done" anti-pattern.

Define Your Metrics

The problem with "health checks" is that they must be intrinsically meaningful to both your project and your organization. When you say:

Engineering had 40 hrs and $1600 allotted...they have used used up 30 hours and are only 50% complete[.]

there's no obvious context or action item. For example, is the point to say that you have to do the remaining 50% of the work in 10 man-hours, or that you only have $400 left in the budget? Is 50% the amount of value you've received from work on the current feature, or the level of effort remaining to complete it?

As you can see, there are too many ways to interpret this data. It may also be the wrong data anyway, because...

Fixed Budgets Aren't Level-of-Effort Estimates

Your question does not define how these schedules and budgets are arrived at. Are they based on fixed labor costs, or are they based on level-of-effort estimates for a particular milestone?

Based on the limited information provided in your question, the only valid conclusion one can draw from the data is that your current estimates are off by 25-50%. If this is a routine shortfall, then to my way of thinking you have a fundamental problem with your estimating or budgeting processes.

This may be a real problem (e.g. your delivery dates are slipping) or it may simply be a transient issue (e.g. schedule or budget will be made up somewhere else). Nevertheless, the point is that the project is not meeting someone's expectations, and that information should be disseminated and the process re-evaluated in light of your empirical results.

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