Hello,




Read again, i correct about more of my philosophy about Six Sigma and more..

I am a white arab, and i think i am smart since i have also
invented many scalable algorithms and algorithms..


I think i am really smart, and now i will talk more about Six Sigma
since i have just talked about SPC(Statistical quality control), so
you have to know that Six Sigma needs to fulfill the following steps:

1- Define the project goals and customer (external and internal)
deliverables.

2- Control future performance so improved process doesn't degrade.

3- Measure the process so that to determine current performance and
quantify the problem.

4- Analyze and determine the root cause(s) of the defects.

5- Improve the process by eliminating the defects.


And you have to know that those steps are also important steps toward
attaining ISO 9000 certification, and notice that you can use
SPC(Statistical process control) and the control charts on step [4] and
step [5] above.

Other than that i have just read the following interesting important
paper about SPC(Statistical process control) that explains all the
process of SPC(Statistical process control), so i invite you to read it carefully:

https://owic.oregonstate.edu/sites/default/files/pubs/EM8733.pdf

So as you notice in the above paper that the central limit theorem
in mathematics is so important, but notice carefully that the necessary
and important condition so that the central limit theorem works is that
you have to use independent and random variables, and notice in the
above paper that you have to do two things and it's that you have to
reduce or eliminate the defects and you have to control the
"variability" of the defects, and this is why the paper is talking about
how to construct a control chart. Other than that the central limit
theorem is not only related to SPC(Statistical process control), but it
is also related to PERT and my PERT++ software project below, and notice
that in my software project below that is called PERT++, i have provided
you with two ways of how to estimate the critical path, first, by the
way of CPM(Critical Path Method) that shows all the arcs of the estimate
of the critical path, and the second way is by the way of the central
limit theorem by using the inverse normal distribution function, and you
have to provide my software project that is called PERT++ with three
types of estimates that are the following:

Optimistic time - generally the shortest time in which the activity
can be completed. It is common practice to specify optimistic times
to be three standard deviations from the mean so that there is
approximately a 1% chance that the activity will be completed within
the optimistic time.

Most likely time - the completion time having the highest
probability. Note that this time is different from the expected time.

Pessimistic time - the longest time that an activity might require.
Three standard deviations from the mean is commonly used for the
pessimistic time.


And you can download my PERT++ from reading my following below thoughts:

More of my philosophy about the central limit theorem and about my
PERT++ and more..

The central limit theorem states that the sampling distribution of the
mean of any independent, random variable will be normal or nearly
normal, if the sample size is large enough.

How large is "large enough"?

In practice, some statisticians say that a sample size of 30 is large
enough when the population distribution is roughly bell-shaped. Others recommend a sample size of at least 40. But if the original population
is distinctly not normal (e.g., is badly skewed, has multiple peaks,
and/or has outliers), researchers like the sample size to be even
larger. So i invite you to read my following thoughts about my software
project that is called PERT++, and notice that the PERT networks are
referred to by some researchers as "probabilistic activity networks"
(PAN) because the duration of some or all of the arcs are independent
random variables with known probability distribution functions, and have
finite ranges. So PERT uses the central limit theorem (CLT) to find the expected project duration.

And as you are noticing this Central Limit Theorem is also so important
for quality control, read the following to notice it(I also understood Statistical Process Control (SPC)):

An Introduction to Statistical Process Control (SPC)

https://www.engineering.com/AdvancedManufacturing/ArticleID/19494/An-Introduction-to-Statistical-Process-Control-SPC.aspx

Also PERT networks are referred to by some researchers as "probabilistic activity networks" (PAN) because the duration of some or all of the arcs
are independent random variables with known probability distribution
functions, and have finite ranges. So PERT uses the central limit
theorem (CLT) to find the expected project duration.

So, i have designed and implemented my PERT++ that that is important for quality, please read about it and download it from my website here:

https://sites.google.com/site/scalable68/pert-an-enhanced-edition-of-the-program-or-project-evaluation-and-review-technique-that-includes-statistical-pert-in-delphi-and-freepascal

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So I have provided you in my PERT++ with the following functions:


function NormalDistA (const Mean, StdDev, AVal, BVal: Extended): Single;

function NormalDistP (const Mean, StdDev, AVal: Extended): Single;

function InvNormalDist(const Mean, StdDev, PVal: Extended; const Less: Boolean): Extended;

For NormalDistA() or NormalDistP(), you pass the best estimate of
completion time to Mean, and you pass the critical path standard
deviation to StdDev, and you will get the probability of the value Aval
or the probability between the values of Aval and Bval.

For InvNormalDist(), you pass the best estimate of completion time to
Mean, and you pass the critical path standard deviation to StdDev, and
you will get the length of the critical path of the probability PVal,
and when Less is TRUE, you will obtain a cumulative distribution.


So as you are noticing from my above thoughts that since PERT networks
are referred to by some researchers as "probabilistic activity networks"
(PAN) b