# Probability/ Stats Puzzles – 2 & 3 (Solutions)

If you’ve not seen/ attempted the puzzles, the links are here: puzzle-2 and puzzle-3. These were presented in earlier posts.

Both these puzzles are adopted from a delightful little book by John Allen Paulos titled A Mathematician Reads the Newspaper.

I will provide more details about the book next week. For now, here are the solutions to the two puzzles.

## Puzzle-2

You need to call the throw of a dice a 1000 times. Like all dices, in each throw, this dice also gives you a number between 1 and 6. You are also told that the dice is slightly distorted / damaged – the probability of getting the six results is as follows: 1- 20%; 2- 10%; 3- 25%; 4-15%; 5-15%; 6-15%.

What strategy would you use to call the answers for the 1000 throws? Your objective is to get the right answer for a maximum of the throws.

Solution:

Call 3, 3, 3, 3…. all the 1000 times. This will get you aprroximately 250 right calls.

Or better still, tell the dice roller that your call is 3 all the thousand times, go for a coffee, or do something useful, come back after some time.

## Puzzle-3

Two contestants are to decide on the winner of 10 mn by flipping a coin. The winner will be the one who reaches six (6) correct calls first.

After 8 flips, contestant A has 5 correct calls, and contestant B has 3 correct calls. At this stage they agree NOT to continue with the flipping of the coin. Here are some proposals on how the money should be shared:

1. Contestant A says that since he is leading, he should get the 10mn.
2. Contestant B says that since the flipping was called off before the final result, the 10mn should be shared equally.
3. The show-host says that TV quiz program sponsors should retain the 10mn, since both the contestants agreed to call off the contest.
4. Someone from the audience suggests that the prize money be split in the 5:3 ratio (5 for A and 3 for B), in line with the number of right calls
5. A mathematician calls in to suggest that the money be split A7:B1 (try and guess the logic here, it is related to the probability of winning from this point, if the flipping had continued)

Solution:

The question on how the money is to be shared is not a mathematical /statistical problem at all! It is a matter of fairness and justice, and each solution proposed (and some yet to be proposed) has its own merit.

However, if you have not yet worked out the logic of why the mathematician proposed option # 5 above, here it is:

For contestant B to win 6 calls in a row, he/ she needs to call ALL of the next three calls correctly (even if he / she calls one incorrectly, A will reach 6 right calls. So the probability of B winning is (0.5) x (0.5) x (0.5) = 0.125; which means A has a probability of 0.875 – that is 7:1.

Next week, I will cover the source of these puzzles, a book titled A Mathematician Reads the Newspaper by John Allen Paulos.

You may also forward the link to this post to your friends, colleagues, and anyone else who may be interested.

Notes:

Nothing Official About It! – The views presented above are in no manner reflective of the official views of any organization, community, group, institute, country, government, or association. They may not even be the official views of the author of this post :-).

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Probability/ Stats Puzzle – 3

I encountered another problem in the same book (I will disclose the name of the book in a later post along with the answer). Here is the problem:

Two contestants have reached the last round of a TV quiz contest and one of them is hoping to be the winner of a prize of 10 mn (currency deliberately left vague) via a tie-breaker. Even after the tie-breaker, neither of them has beaten the other.

The show-host offers to break the tie with a coin (my guess is that the show host did not have any more questions left :-)). However, to maintain the suspense and gain more TRP, he proposes that the winner will be one who reaches six (6) correct calls first.

After 8 flips, contestant A has 5 correct calls, and contestant B has 3 correct calls. At this stage both the contestants agree NOT to continue with the flipping of the coin (maybe the coin is lost or it breaks or falls into something disgusting – use your imagination). They have to decide on the winner based on result of the 8 flips.

Here are some proposals:

1. Contestant A says that since he is leading, he should get the 10mn.
2. Contestant B says that since the flipping was called off before the final result, the 10mn should be shared equally.
3. The show-host says that TV quiz program sponsors should retain the 10mn, since both the contestants agreed to call off the contest.
4. Someone from the audience suggests that the prize money be split in the 5:3 ratio (5 for A and 3 for B), in line with the number of right calls
5. A mathematician calls in to suggest that the money be split A7:B1 (try and guess the logic here, it is related to the probability of winning from this point, if the flipping had continued)
6. Any other…

It is interesting to note so many options to a simple situation.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Probability/ Stats Puzzle – 2

I encountered this simple problem in a book (I will disclose the name of the book in a later post along with the answer).

Here is the problem:

You need to call the throw of a dice a 1000 times. Like all dices, in each throw, this dice also gives you a number between 1 and 6. You are also told that the dice is slightly distorted / damaged – the probability of getting the six results is as follows: 1- 20%; 2- 10%; 3- 25%; 4-15%; 5-15%; 6-15%.

What strategy would you use to call the answers for the 1000 throws? Your objective is to get the right answer for a maximum of the throws.

Here are some answers that I have heard:

1. Call the number ‘3’ all the 1000 times – this is the most common answer I have heard.
2. Call the numbers in the same pattern as the probability: 1- 200 times; 2- 100 times; 3- 250 times; 4-150 times; 5-150 times; 6-150 times.
3. Call the numbers randomly, ignoring the distortion in the dice.
4. A variation of 2 above is to call the numbers in the same pattern, but also taking into account the answers to the past throws, so that we try and keep the probabilities similar to the expected patterns. So if in the first 100 throws, 1 has already rolled more than 20% and 2 has been rolled less than 10%, then in the 101st throw, call 2 instead of 1, and so on.
5. There are other possible answers too – and the right one may not be listed above (this is not a mutiple choice question 🙂 )

Work out the reasons for your choice, not just make a choice. The reasons are more important.

This is a simple question, and you should get the right answer.

The answer will be posted later.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Probability/ Stats Puzzle – 1 (Solution)

If you have not tried to solve the puzzle, click here for the problem. The problem was discussed in an earlier post.

This is a famous puzzle, called the “Monty Hall Problem”. Monty Hall was a host in the early episodes of the game show Let’s Make a Deal.

The common version of the the puzzle used three doors (instead of 3 boxes) and a car and two goats (instead of gold and garbage).

The problem was originally posed by Steve Selvin and became famous when it was quoted by Marilyn vos Savant in Parade magazine in 1990.

The answer: You increase the probability of winning the gold if you change your choice of the box to open. The probability of winning the gold is only 1/3 if you continue with your original choice and 2/3 if you change your choice.

Here is a brief explanation of why:

When you initially selected a box, you had a 1/3 probability of being right. The host knowingly opened a box with garbage in it, so that eliminated one of the wrong choices.  You still have a 1/3 probability that you initially chose the right box; this means that the other unopened box has a 2/3 probability of containing the gold.

Amit Bhattacharjee, Satish K Mariyappagoudar, and Patrick OToole got it right.

Or you can watch the youtube video.

You can also search the internet for the keywords “Monty Hall Problem” – you will get lots of hits.

You may also forward the link to this post to your friends, colleagues, and anyone else who may be interested.

Notes:

Nothing Official About It! – The views presented above are in no manner reflective of the official views of any organization, community, group, institute, country, government, or association. They may not even be the official views of the author of this post :-).

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Probability/ Stats Puzzle – 1

This problem was presented to me by Swapna (my wife) on last Friday – I could not work out the right answer even after considerable struggle.

You are participating in a TV show contest. You have reached the last round. If you win this round, you get take home a pure gold brick of 5 KG (5KG = 11.02 lbs); if you lose you have to take away an equivalent quantity of stinking garbage.

Here is the problem in the last round:

There are 3 closed boxes (let us say B1, B2, B3). Inside two of the boxes is garbage. Inside one of the boxes is the gold. You have to open one box and take home whatever is in that box. You decide to open B1. The show-host/ quiz-master asks you to stop, and as a hint opens one of the other two boxes, and inside that box there is garbage. The show-host gives you the option of changing your choice. Would you still go for your original choice or switch to the other unopened box?

Here are some relevant assumptions/ hints/ guidances:

1. Most important: you would prefer to take home the gold instead of the garbage :-).
2. You will not be able to smell the garbage or gold without opening the boxes, or in any way be able to “know” what is inside the unopened boxes.
3. You do not know the show host’s motivation. The show-host may be trying to help you or trick you, or trying to increase hir (his/her) popularity rating, or just following a script. So, do not consider the show host’s motivation in trying to solve the problem (when Swapna presented me the problem, I went on the motivation track, and could not approach it as a problem of probability, even after she told me to ignore the show host’s motivation 🙁 ).
4. There is no “trick” in the problem or the solution – so, approach it as a problem of probability/ statistics.
5. Do not be lazy and search the internet to find a solution. That is cheating. I have changed some things in the problem so that is not easy to search. However, this is not a test of how quickly and ingeniously you can search the internet.
6. You will have to work out the reasons for your choice, not just make a choice. The reasons are more important.

Don’t feel bad if you don’t get the answer right, many renowned statisticians have got it wrong.

The answer is available in another post here.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Time and Material Business Model is Injurious to Process Improvement

An incident in a large software development organization:

Here is a part of a conversation between a Sig Sigma Expert (SSE) and the Delivery Head (DH) in a software development/ maintenance organization where most projects were run on a T & M or Headcount based billing for their customers.

SSE: “Initial analysis shows that with minor changes in the processes and the use of some spreadsheet macros, we can eliminate some non-value add steps. This can reduce the effort required by 25% for the current mix and volume of work.”

DH: “But that will reduce my head-count and billing by 25%! My target this year for improving efficiency/ productivity is only 5%. Maybe we can implement the changes a bit every year, and not all at once. If I implement all these change right now, I will miss my revenue and headcount targets – these have the highest weight in my performance objectives.”

Another incident in a different organization:

A Project Manager’s project end bonus was slashed because she delivered her project at a much lower cost than what was estimated (the estimate was done by someone else). She was informed that her lower bonus was because the project total billing was much lower than the project estimate.

Both these incidents occured in situations where the projects were being run in a T & M (Time and Material) mode by a software service vendor organization.

The T & M mode of engagement basically shifts the cost related risks and benefits (cost overruns, cost efficiencies) to the customer, while the vendor organization has a steady return, and cannot make large profits or losses. The T & M mode is suitable in many situations – e.g., when requirements are unclear and likely to change, when the customer wants to work closely with the vendor team, when the customer wants more micro control (sometimes interference), or when the customer-vendor organizations are in the initial phase of establishing a relationship. A variation of this is Committed Head Count, where the customer and vendor agree on a fixed number of staff assigned to the customer’s work over a period, independent of the actual quantum of work. Another variation is the dedicated ODC (Offshore Development Center).

As against this, there is the Fixed Price (FP) mode, where the billing amounts and billing timelines are fixed based on an agreed value and agreed deliverables. The FP contract may have penalties and incentives built in (for delivery dates and/or  quality). Effort overruns are the problem of the vendor, and effort savings are additional profits made by the vendor. Variations of the FP model include billing by volume, quality and timeliness of work done. In such cases the vendor is usually free to utilize the staff in an optimal way (maybe on multiple projects).

Many engagements between customers and vendor organizations start off as T & M, for good reasons. However, they continue in the T & M mode, even when the FP mode would serve everyone better. This could be because of inertia, because no one wants to rock the boat, or because no one has examined the issue for that engagement.

Structurally, the T & M model does not create incentives for the vendor to initiate and pursue improvements that will reduce the effort and headcount. The software industry has got addicted to T & M model to such an extent that head count growth, and billable person-days have become stated performance objectives for senior executives in many software services organizations.

Maybe the title of this post should have been “T&M model kills process improvement”, like the changed statutory warnings on tobacco products. Or is that overstating the case?

Notes:

Nothing Official About It! – The views presented above are in no manner reflective of the official views of any organization, community, group, institute, or association.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Book Review – “Fooled by Randomness” by Nassim Nicholas Taleb

I picked up Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, by Nassim Nicholas Taleb, on the recommendation of a mathematician (Vipul Naik, my son). I was expecting a heavy treatise on economics and statistics. It was however a very engrossing book written in a lucid and conversational style, with historical events and everyday situations used freely to provide insights.

Here is the book summary/ key insights (that I picked up from the book):

1)      Human beings are wired in a way that they are unable to intuitively handle randomness and chance.

2)      We are adept at explaining everything through a cause-effect; because we just can’t handle uncertainty. And a statistical correlation does not necessarily mean one causes the other.

3)      Ignoring rare events (outliers) in building prediction models is fooling ourselves – rare events are a part of the process and environment, and their impact is rarely understood or considered by people.

4)      We try to explain extraordinary successes as the result of brilliant strategy or business model or formula or leadership skills or intelligence; while it is often just dumb luck. This is more so of domains like stock trading, marketing, and running a business. We try to learn from and emulate the “winners”, without much success ourselves (by trying to implement the so-called strategies of successful people). Basically, according to the book, many of the winners are just lucky fools :-).

5)      Nice symmetrical probability distributions cannot be expected of any human endeavor (symmetrical distributions may be used to understand controlled situations like gambling – toss of a coin, or rolling of a dice). When we simplify probability distributions and approximate them to neat curves, the results that we get are unreliable.

6)      Though Monte Carlo simulations are looked down upon (“that is cheating, it is not statistics!”) by purists, it is still be the best way to model complex, real situations and understand the potential randomness of the outcomes, and can be used for informed decision making.

7)      Past performance cannot be blindly used to predict future performance. Hence, we should not overestimate the accuracy of our beliefs just because we have been successful in the past, we should reexamine our beliefs based on logic, and always have a backup plan.

One of issues with the book is that it lacks structure and tends to jump from topic to topic. The tone is also snobbish and contemptuous at places, and it may make some people (who are secretly think that their success may be attributable to luck :-)) annoyed or even angry.

The author Nassim Nicholas Taleb is Distinguished Professor of Risk Engineering at New York University’s Polytechnic Institute. He has been a mathematical trader, essayist, philosopher, and researcher. He specializes in understanding uncertainty, luck, probability, knowledge, and decision making. Taleb has been described as a dissident thinker, maverick, irreverent, iconoclastic, and unconventional.

Another book by Taleb in a similar vein is The Black Swan – this is an earlier book, and again very interesting to read. Taleb has also authored AntiFragile, The Bed of Procrustes and Dynamic Hedging.

I recommend this book very highly for anyone involved in high maturity implementation of the CMMI®/ People CMM® models.

For people who are looking for quick-fix templates and control chart macros, this book is not for you (as if high maturity practices can be implemented using quick-fix solutions :-).

Here are some details of the book, in case you want to get your hands on it:

## By the way, you DON’T need a Kindle device to read a Kindle ebook.

Title: Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

Author: Nassim Nicholas Taleb

Publishing Date: First Version Around 2001

Publisher: Random House/ Penguin

Available at: Amazon.com, Amazon.in, and Flipkart

## By the way, you DON’T need a Kindle device to read a Kindle ebook.

Notes:

Nothing Official About It! – The views presented above are in no manner reflective of the official views of any organization, community, group, institute, or association.

Other book reviews uploaded on the same blog:

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Book Review – “The Checklist Manifesto: How to Get Things Right” by Atul Gawande

I had earlier read two engrossing books by Atul Gawande – Complications and Better. So when I saw The Checklist Manifesto while browsing in the neighborhood library, I decided to pick it up looking forward to an interesting read (some reviewers had strongly recommended it). The title also indicated that it may a good book to review for this weblog.

Well, I was partially right – it was suitable to post a review on this blog. So, here goes…

The main theme of the book/ book summary is as follows:

• Over the years, many activities have become extremely complex.
• Even experts struggle to master and remember all the tasks they have to perform.
• Use of checklists can minimize human errors of oversight. In many cases this it can improve the performance significantly.
• Use of checklists can also help the experts focus on the difficult, tricky parts of a situation, rather than worry about the mundane activities.
• There is need to create better checklists, organize them for easy use and ensure that they are used.

The author uses examples from multiple industries and situations. The best ones are from hospitals and medical emergencies (Dr Gawande is a surgeon :-)). There are other examples from the airline industry (where pilots use checklists for normal as well as abnormal situations), construction industry, retail, and restaurants.

There is a whole chapter dedicated to research where the impact of the use of checklists in hospitals was studied. The research showed that there was a significant reduction in deaths (47% reduction) and major complications (36% reduction) for surgical patients. One interesting finding was that though only 80% of the hospital staff found the checklists useful, 93% of them said they would want a checklist to be used if they were themselves getting operated!

The book sometimes extends the concept of “checklist” beyond its normal usage. Here are a few examples of things that are treated under the concept of checklist in the book (though I believe they are different concepts, with their own place in “how to get things right”):

• Preparing detailed project plans, dependencies, action items, schedules and list of deliverables (example of a building construction project)
• Use of collaboration meetings (of experts) to handle non-routine situations (e.g., a building floor developing unforeseen problems)
• Empowerment for doing something extraordinary (how Wal-Mart employees went beyond their formal authority to help people affected by Hurricane Katrina)
• Use of focus, expertise and wits (how a pilot saved lives by crash landing on Hudson river in 2009 – by focusing on flying the plane, not on using a checklist!)

In trying to bring everything under the umbrella of “checklists”, the author dilutes the concept and utility of checklists as well as other equally important concepts of detailed planning, collaboration, empowerment, dedication, competence and focus. Maybe the title “The Process Manifesto” would have been more apt.

For people who are already convinced about the use of checklists, procedures, plans, collaboration meetings, etc., this book can provide you with interesting examples to relate to process skeptics in your organization. It can also provide process trainers with interesting case studies to relate to the class. You may also consider gifting this book to colleagues who resist the use of formal processes – the book is an easy read and is able to hold the reader’s attention reasonably well.

If you are looking for readymade checklists that will help you reach some level in CMMI®/ People CMM®, then this book is not for you :-).

Those who have read Gawande’s earlier books – Complications and Better may find The Checklist Manifesto a bit disappointing – it is not as engrossing as the earlier two. This is possibly because the earlier books focused primarily on hospitals, medicine and healthcare based scenarios, where Gawande has accumulated loads of experience. And in Checklist, he provides examples from other industries (aircraft manufacture, real estate, retail stores, restaurants, and so on) where he may not have had the same level of familiarity and insight.

Here are some details of the book, in case you want to get your hands on it:

## By the way, you DON’T need a Kindle device to read a Kindle ebook.

Book Title: The Checklist Manifesto: How to Get Things Right

Author: Atul Gawande

ISBN-10: 1846683130

ISBN-13: 978-1846683138

Publishing Date: Jan 2010

Publisher: Profile Books

Available at: Amazon.com, Amazon.in, and Flipkart

## By the way, you DON’T need a Kindle device to read a Kindle ebook.

Other book reviews uploaded on the same blog:

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Size Does Matter! (for baselines and sub-process control) -Continued

Let us take the example of  examination/ test centers, that run an exam throughout the year, every day. Past one-year data shows – 30% of the candidates pass the exam and 70% fail the exam, all over India.

The Bangalore test center handles around 1000 candidates per month, whereas the Mysore center handles around 100 per month. Over the last one year, both centers have shown the same 30 pass: 70 fail ratio.

For the month of June 2010, one center has reported 38% pass and another has reported 29% pass. Which center (Bangalore or Mysore) is more likely (has a higher probability) to have reported 38%?

Well, Mysore is more likely to have the higher deviation from the average (+8%) than Bangalore (-1%), because Mysore, handling lesser candidates, has a lesser number of opportunities to “average out”. An easy way to figure this out is to take the case of a center that handles only 1 candidate. This center can have either 0% or 100%  pass percentage; a -30% to +70% deviation from the average.

Let us now get back to the process performance baselines that we create and the way we do sub-process control. Here are some things that we need to keep in mind while creating, publishing and using baselines:

1) Baseline (mean and standard deviation) for a sub-process parameter (like coding productivity) will be different depending on whether we consider each the coding phase of each project as a data point, or we consider each program coded in each project as a data point. The standard deviation in the first case (large base) is likely to be smaller than the second case (small base).

2) When we publish performance baseline data, we need to qualify it with the level of detail at which it applies.

3) When we use the baseline data to do sub-process control, it needs to be applied to the same level of detail. So, to do sub-process control on program level coding productivity, we need to use the baseline that was created using programs as data points (not each project as a data point).

4) Baselines need to be created using similar situations of the base data. For example, we cannot combine the coding productivity on large programs with the productivity on small programs. Even if the average/ mean remains the same, the standard deviation will be higher when we take data from a smaller base as against a larger base.

The above points are not just “nits” but have an impact of the usefulness of baselines and sub-process control. Incorrect usage of baselines leads to incorrect displays of process instability / stability.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.

# Size Does Matter! (for baselines and sub-process control)

Here is a small brain-teaser.

Let us take the example of a examination/ test centers, that run an exam throughout the year, every day of the year. Analysis of the past one-year data shows that 30% of the candidates pass the exam and 70% fail the exam, all over India.

The Bangalore test center handles around 1000 candidates per month, whereas the Mysore center handles around 100 per month. Over the last one year, both centers have shown the same 30 pass: 70 fail ratio.

For the month of June 2010, one center has reported 38% pass and another has reported 29% pass. Which center (Bangalore or Mysore) is more likely (has a higher probability) to have reported 38%? Why do you think so?

See my post dated August 3, 2010 for the answer and implications.

I am Rajesh Naik. I am an author, management consultant and trainer, helping IT and other tech companies improve their processes and performance. I also specialize in CMMI® (DEV and SVC), People CMM® and Balanced Scorecard. I am a CMMI Institute certified/ authorized Instructor and Lead Appraiser for CMMI® and People CMM®. I am available on LinkedIn and I will be glad to accept your invite. For more information please click here.