Vishwadeep Khatri

You can also learn these basics using on-line resource by clicking here

Level 3 can help you learn more. However, it is not necessary for everyone to follow Level 3. Try the following question - If you ask 23 random people their birth dates, what are the chances that at least two will match?If you ask 40 random people their birth dates, what are the chances that at least two will match?If you ask 60 random people their birth dates, what are the chances that at least two will match?Surprisingly, with only 23 people, the probability of at least one match is about 0.5073. With 40 people, the probability is about 0.8912, and with 60 people, the probability is about 0.9941 Why? How? Have a look by clicking here

1. Conditional Probability Learning - Example The probability of A is 7.5%. The probability of B is 20%. Move the events A and B around and study all event probabilities on the right side. Use the diagram by clicking here. Want to play around with more flexibility? Try this link here. 2. Probability of success in an event that requires multiple stages to be correct. Please try this link by clicking here Use all three probabilities as 80%. They seem good individually. Try rocket launches 20 times. How many were successful? Why? What happens if you keep all three probabilities as 50%.

The word 'statistics' appears to have been derived from the Latin word 'status' meaning 'a (political) state'. In its origin, statistics was simply the collection of data on different aspects of the life of people, useful to the State. Over the period of time, however, its scope broadened and statistics began to concern itself not only with the collection and presentation of data but also with the interpretation and drawing of inferences from the data. Statistics deals with collection, organisation, analysis and interpretation of data. To refersh your basics on statistics of grouped data, have a look at this material statistics-level 1 To refresh your basics on statistics of ungrouped data have a look at this material statistics-level 2

Many problems are solved with the use of mathematical models. To get an introduction to the creation of mathematical models, you may study the following: Mathematical Modelling-1 Mathematical Modelling-2

It is remarkable that a science, which began with the consideration of games of chance, should be elevated to the rank of the most important subject of human knowledge. -Pierre Simon Laplace Where a mathematical reasoning can be had, it is as great a folly to make use of any other, as to grope for a thing in the dark, when you have a candle in your hand. - JOHN ARBUTHNOT If you study Six Sigma, you work with probabilities very often. Examples of basic questions - What is the probability of defects in process A or in process B or in Process C if the probabilities in A, B and C are 0.2, 0.3, 0.1 respectively? What is the probability of defects in this process? If someone says that probability is 0.35, is it a small chance or a worrisome probability? To refresh such concepts, you can go through some content on probability. Probability-1 Probability-2 Probability-3

Do you know how to convert ratios into percentages? How would you convert 2:3:5 into percentages? To refresh such concepts please go through Ratios and Percentages.

Do you know why the equation of a line is in the format y = mx + c? To refresh your concepts about equations please go through the following chapters: Equations-1 Equations-2 Equations-3

Do you find ratios difficult to work with? What is three fourth of four fifth of hundred? If you wish to refresh your concepts please go through the following material - Ratio and Proportion-1Ratio and Proportion-2Rational Numbers-1Rational Numbers-2

During Six Sigma training, I come across participants unfamiliar with terms like 3 multiplied by ten to the power of minus 6. You may need to refresh the concepts of powers by moving through this chapter. Use the following link http://forum.benchmarksixsigma.com/index.php?/files/file/13-powers/

One needs to be familiar with basics of Data Handling. Pictographs, Bar Charts - Data Handling-1Measures of central tendency and why they are needed - Mean, Median, Mode. Data Handling-2Grouped frequency distribution, histogram, pie chart, events and probabilities. Data Handling-3 If you are familiar and comfortable with these terms, you can skip this section.

You need to know basics of Algebra shown in chapter named Algebra-1 Also useful are Algebraic expressions from chapter named Algebra-2. If you can comfortably create equations, write algebraic expressions using letters as variables, combine them and solve them, you are through with this section.

It is said that algebra as a branch of Mathematics began about 1550 BC, i.e. more than 3500 years ago, when people in Egypt started using symbols to denote unknown numbers. Around 300 BC, use of letters to denote unknowns and forming expressions from them was quite common in India. Many great Indian mathematicians, Aryabhatt (born 476AD), Brahmagupta (born 598AD), Mahavira (who lived around 850AD) and Bhaskara II (born 1114AD) and others, contributed a lot to the study of algebra. They gave names such as Beeja, Varna etc. to unknowns and used first letters of colour names [e.g., ka from kala (black), nee from neela (blue)] to denote them. The Indian name for algebra, Beejaganit, dates back to these ancient Indian mathematicians. The word ‘algebra' is derived from the title of the book, ‘Aljebarw'al almugabalah', written about 825AD by an Arab mathematician, Mohammed Ibn Al Khowarizmi of Baghdad.

Why study Algebra - A common feature in Algebra is the use of unknown variables with x,y,z. This has special relevance in Six Sigma for the following reasons. Use of letters will allow us to write rules and formulas for elements that can vary. This helps in developing relationship between variables (like relation between cost and quality)Commonly letters denote unknown quantities. By learning methods of determining unknowns, we develop powerful tools for solving puzzles and addressing many process problems.Since letters stand for numbers, operations can be performed on them as on numbers. This leads to the study of algebraic expressions and their properties. This has application in many Six Sigma tools. Examples are regression analysis, design and analysis of experiments.

Sigma denotes the standard deviation. Shows extent of variation in a data set. Does not depend on mean or specification limit. Z value denotes the sigma level for the process. It is a measure of process capability and depends on three elements for continuous data - the standard deviation, the mean and the specification limit.

Dear All, Good to see so many responses to this subject. I plan to start uploading content soon. You can expect the first set of uploads within this week. Regards, VK

I suppose everyone agrees that if one is not good with numbers, career growth is likely to face a serious roadblock at one stage or the other. I have noticed several people who fear mathematics and this leads to certain problems in learning or applying Six Sigma. Many have already given up hope assuming that they can never cover up. Good news, however is that this weakness can be addressed by most people. It definitely needs a persistent effort to capture Mathematics concepts that are really important. Some of these are Algebra, Data Handling, Decimals, Equations, Exponents and powers, Fractions, Graphs, Integers, Mathematical modelling, Mathematical Reasoning, Probability, Proportions, Ratios, Rational Numbers and Statistics. If you are one of those who felt this way and wish to improve your math, I can provide you a step by step approach which shall broadly follow the sequence below. Plan study time for these topicsUse the uploaded materialStudy identified topics and answer questions provided in the text. Check your answers with answer key provided.Conquer your weakness and face the Six Sigma world more confidently.In case good number of people see value in such a sequence, I shall be putting in extra effort and make the content and sequence available to you free of cost. I have written this post just to know whether there are many people out there who really wish to use such content and approach. Reply to this post showing your interest so that I can view the count. Best Wishes, VK

An important twist in this question - We have come across senior professionals making statements of the following types. Although I have not undergone Green Belt training (or for that matter, any formal Six Sigma training), I should be allowed to directly attend Black Belt training. Seniority should be made criteria for direct entry into Black Belt. I have been in the industry for more than 10 years. If someone needs a Black Belt without undergoing Green Belt, he/she should consider ten days black belt training (PLUS 2-4 days of pre-course and mid course self-study and practice exercises). This ten days Black Belt training can be obtained by enrolling into our 4 days Green Belt followed by 6 days Black Belt (both having pre-course and mid course self-study and exercises). What I mean is quite obvious - there are no short cuts. It is important to complete graduation before considering post graduation.

Dear Velusamy, If the solution is known (soft skills training), there is no need to carry out a Six Sigma project. Regards, VK

Kindly note the following - Six Sigma is not just a process. Rather it is a management approach, a management methodology. A word of caution - Outsiders may not be able provide you inputs on how a Six Sigma application can give you wonderful results in your campaign management/ automation process (unless they study your process well). To be able to apply Six Sigma, let us first need understand a few basic elements. A Six Sigma project is undertaken to address a pain area within your company. This could relate to a customer's pain or business pain area. Six Sigma learning provides you tried and tested management techniques that work practically everywhere. In many situations, what you may apply is a specific Six Sigma concept or technique (and there is no need to carry out a complete DMAIC project) A DMAIC project is needed only if the causes and soutions for a problem are unknown (and cannot be found by common sense methods) Six Sigma application is extremely situation specific. A Six Sigma project carried out in one research organisation at one time cannot be replicated at another research organisation. Some of the successful projects that I have seen in your area had the following objectives - Improving data integrity by 70% (DMAIC project) Enhancing lead generation through campaigns. (DMAIC project) Increasing percentage of qualified leads. (DMAIC project) Designing a new promotional process that maximizes qualified lead generation. (DMADV project) Designing a social media strategy (DMADV project) Hope this helps. Best Regards, VK

Yes Anish,as recommended by others, continuous datais better as it can be analyzed in several ways. Also, continuous data can always be converted into discrete if need be. Discrete data, however cannot be converted into continuous. Best Regards, VK

Dear Vijay Vittal Rao, Thanks for your response. I am sorry to mention that your point is unclear to me. Can you please reword it for my understanding. Best Regards, VK

Dear Pradeep, Look for pain areas where you need to do deep diving for cause and solution analysis. Your pain areas (or those based on VoC of your customers) are best known to you. If you need help please type in the pain areas based on VoB and VoC, and we can jointly explore if some of them are worth Six Sigma rigour. Best Regards, VK

Trained - Attended training Certified - By either of the following two methods. Certified on basis of project submission. Certified on basis of examination Many companies (especially for nominated candidates) prefer the second one as they do not wish to provide a certified status unless candidates complete a project. However, some training organizations do provide certified status on basis of practice projects and examination. In all cases, it is recommended that a person should carry out a live project and earn a project completion certificate. Hope this clarifies. Best Regards, VK

You can do Six Sigma project for a pain area that has unknown cause and an unknown solution. You need to find out within the company what is the pain area that key people are experiencing. Every single recruitment function challenge is a potential pain area. You need to sit with a key recruitment SME (subject matter expert) to know his pain area. Regards, VK