Re: Project Management

[Jean-Marie Gogue <jmegogue@wanadoo.fr>]

Rudi,

In your post dated 30 Jul 2000, you explained your problem again, and you
asked two questions concerning two different domains.

1. Domain of Statistics

>When the distribution is normal the sum of the squares of task variances is
>equal to the variance of the projects completion time. This means that the
>standard deviation of the project is much smaller than the sum of the
>standard
>deviations of the tasks!
>
>What is the situation when the distribution is skewed? Does the the same hold
>true? Is the standard deviation of the project still much smaller than the
>sum of
>the std deviations of the tasks? Is the project even safer because of the
>skew or
>is it less safe (vs a situation where there is no skew?)

2. Domain of Operations

>Clearly the above is an idealised situation. However, why is it not real?
>Why,
>if projects have so much safety in them, are so many late? (By the way a
>study by the Standish group (of 8000 projects)  shows that only 16% of
>projects were able to meet their goal in terms of time, budget and quality!)

Statisticians often confuse statistical concepts and psychological
concepts. In his book "Statistical Method from the Viewpoint of Quality
Control" (also available in French) Walter A. Shewhart wrote that data can
be communicated in two languages: (1) scientific, (2) subjective. With a
good sense of humour, he showed that sometimes the statistician's language
is subjective, but that we are not fully aware of this subjectiveness.

IMHO the confusion between both languages makes that many people have a
superstitious belief in Statistics.

Let me add my 2 cents contribution to your first question.

The variance of the sum of normal and independent variables is equal to the
sum of the variances. You know this theorem. There is no equivalent theorem
applicable to any random variables. Therefore it's useless to look for a
calculation giving the variance of the sum of random variables in general.

You can however calculate the probability for a sum of random variables to
be above a given limit, or between given limits. In a recent post, Rip
Stauffer gave a bit of the solution. He wrote:

>From a pure, probabilistic statistical standpoint, if you have a number of
>sequential tasks that operate at 90% reliability, your reliability goes
>down by
>a factor of .9 with each task. Say you have five such tasks, the chance of
>them
>all meeting the goal goes down to .9 * .9 * .9 * .9 * .9 = .59.

This is a basic probability theorem (but remember that the random variables
must be independent). In addition, the 90% (or any %) reliability limit for
each random variable is given by the _Tchebychev_Theorem_ :

Given a random variable X (average = m, std-deviation = s)
           Pr [ m - ts < X < m + ts ] > 1 - 1/t square

Numerical data:
           2 sigma double-sided probability = 75%
           3 sigma double-sided probability = 89%

That's not guess work, that's pure mathematics.

Best wishes,

Jean-Marie Gogue
President
The French Deming Association
jmegogue@wanadoo.fr

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