In effect a set of work units called Milestones is arriving over time to a team trying to resolve them.

Staff loading needs to be calibrated by the number of effort hours they have available per week. Suppose staff has 25% of their 40 effort hour week available to you and each works just as hard as the others. So each staff has 10 effort hours available per week.

Utilization = Effort hours/wk / 10 effort hours/wk

For quick estimates, consider the MM1 Queue that assumes a signal to noise ratio for staff effort and work load arrival near 1 to 1.

Te = the time needed to execute for each arriving item of piece work.

Ta = the average rate piece work is arriving on schedule.

M = Number of parallel staff working on the task

U = (Te/(M*Ta)) = Effort hours worked/Effort hours Available per staff. U <1 or project time explodes.

Average Time waiting in Queue = Te * U/(1-U)

Sigma Time waiting in Queue = Te *sqrt(U/(1-U))

Average Time for full project = Te / (1-U)

Sigma Time for full project = Te * sqrt(U/(1-U)^2 + 1)

Method of computing confidence intervals assuming core project Te, Ta can float tends to lead to Poisson Estimates that the project will not be more than expected.

Odds of project completion time above X

1-exp(-Time/Planed_Project_Time)

The following update on project sampling data is recommended if the source of the data are human experts that are using intuition rather than hard measured facts.

1) Humans really want the average to be half way between the extremes and tend to either fudge the extremes or average to make this wish come true. Do not collect both average and extreme data at the same time or from the same team.

2) Humans under estimate statistical extremes the following adjustment to the Beta Model is offered.

18.5% Extreme High

18.5% Extreme Low

63% Typical

The same approach applies:

Average = .185*Low + .185*High + .63*Typical

Sigma = sqrt(.185*(Low-Average)^2+.185*(High-Average)^2+.63*(Typical-Average)^2)

To compute better confidence intervals using Poisson Statistics – a close relative of Beta Statistics – the following is helpful

Average = Step * L

Sigma = Step * sqrt(L)

L = (Average/Sigma)^2

Step = Sigma^2/Average

Full odds for every case add up to 100%. All cases start at 0 and go to infinity… but odds fall off very fast. Suppose Sigma turn out to be 40 effort hours for a 200 effort hour project.

L = (200/40)^2 = 25 Steps to the peak odds.

Step = 40^2/200 = 8 Effort hours

Average Effort Hours = 8 Effort Hours * 25 Steps = 200 effort hours

Sigma Effort Hours = 8 Effort Hours * sqrt(25 steps) = 40 Effort hours

Individual step odds for (Value/Step = x_steps) = L^x/fact(x) * exp(-L)

Spreadsheet ready version of Poisson Statistics

Odds no step happens = exp(-L)

1 step = L*exp(-L)

2 steps = L^2/2 *exp(-L)

N steps = L^N/fact(N)*exp(-L)

N+1 Steps = Odds N Steps * L / (N+1)

Peak odds occurs near N ~= L

Peak odds is approximately 1/sqrt(2*PI*L)

Sum Odds between steps to produce confidence interval information.

Odds for N or less steps is the sum of step N to step 0 of the odds.

Use the fact the odds add up to 100% to compute N or larger odds.

1 – sum odds Less than N to step 0 is the odds of N or more.

As Poisson Statistics is a close relative of Beta Statistics, this tends to give good completion time odds for projects.