Black Belt in Lean Six Sigma

Thiago has a degree in Production Engineering, a graduate course in statistics and a degree in administration from the Federal University of Juiz de Fora (UFJF). Black Belt in Lean Six Sigma, worked with methodologies for cost reduction and process optimization at Votorantim Metais, subsequently joining MRS Logística as a trainee, where he held positions of manager and specialist in continuous improvement. With Microsoft Office Specialist (MOS) certification and ISO 9001 Auditor Lead Advisor, attended several companies in consulting projects, in addition to training and lectures related to Lean Six Sigma, Career Entrepreneurship in nationally renowned congresses such as ENEGEP (National Meeting of Production Engineering) and international as International Six Sigma Brazil congress. In the academic environment, he works as a professor of undergraduate and graduate courses in the areas of management and entrepreneurship. Thiago had the opportunity to participate in projects of several segments. Founder of the Voitto Group, he was selected in the Promessas Endeavor Program, having the opportunity to receive valuable mentoring to accelerate his business. He is currently a business mentor and dedicates himself to the executive front of Voitto, carrying with his team the vision of being the best online school of management in Brazil.

Founder of Voitto Group, currently a business mentor and dedicated to the executive front of Voitto, carrying with his team the vision of being the best online business school in Brazil.

Learn what it is and how to calculate the probability of a binomial distribution.

Binomial distribution: what it is and how to do it

It is quite common for scholars to attempt to describe a particular phenomenon by studying the probability of occurrence of an event associated with it.After all, this is exactly what happens when a Six Sigma project studies a process and attempts to estimate the likelihood of a particular type of defect occurring.That is, the binomial distribution is a type of statistical distribution. But do you know what a statistical distribution is? Do you know the difference between a continuous distribution and a discrete distribution?If you answered &quot;no&quot; to any of these questions, continue reading this article and find out the answers.<h2>What is a binomial distribution?</h2>Theoretically, the binomial distribution is the distribution of probability of the number of successes resulting from a certain sequence of attempts, which follow the following characteristics:<ul><li>Finite sample space</li><li>Only two possible outcomes (success or failure) for each attempt</li><li>All elements must have equal possibilities of occurrence</li><li>Events must be independent of each other.</li></ul><h2>When to use binomial distribution?</h2>When starting a Six Sigma project, the Green or Black Belt should check what type of data (continuous or discrete) he&amp;rsquos dealing with at the exit of the process. This will determine which tools will be used in project development.It is up to this professional to define which of the numerous statistical distributions is the one that best represents the process being studied. The statistical distributions can be divided into two large groups:<ul><li>Discrete Distribution (Attributes)</li><li>Continuous Distribution (Variable).</li></ul>Discrete distributions must be used to model situations where the output of interest can only assume integer values (discrete) such as a number of faces or crowns, 0 or 1 for failure or success, or 0,1,2, 3, ... as the number of occurrences of a particular event of interest for example.The discrete distribution can still be divided into two families:<ul><li>Binomial Distribution</li><li>Poisson distribution.</li></ul>In this post, we will address the binomial distributions. This should be used to model situations where for a given output of interest the probability of occurrences of a &#39;p&#39; success and a &#39;q&#39; failure is always constant.This condition works well when batch sizes are large or in continuous productions for example.Are you tired of missing out on incredible career opportunities because you don&#39;t know about the main Excel tools?So you are in the right place! In the<a target="_blank" rel="nofollow" href="https://thinkleansixsigma.thinkific.com/courses/excel-for-beginners"> Excel for Beginners</a> course, you will learn to work with data in an agile way.In addition, the course is available for FREE, just click on the banner button below and embark on this journey of knowledge!<a target="_blank" rel="nofollow" href="https://thinkleansixsigma.thinkific.com/courses/excel-for-beginners"> <Image quality="95" src="https://images.prismic.io/voitto-blog/45fd4463-eb50-470d-a2e2-1a98155e7fdc_Bot%C3%A3o++Banner+-+Cursos+TLSS+%282%29.png" width="980" height="180" alt="Excel for Beginners" title="Excel for Beginners"/></a><h2>How to calculate the binomial distribution?</h2>The probability of having k successes in an event following the binomial distribution is calculated by the following equation: <Image quality="95" width="164" height="34" src="https://images.prismic.io/voitto-blog/NmE2NWE5NjUtOGYzYi00ZjEzLTg2YjMtYThlMzU4NDk1OWEz_ykat1y293hknyzr5yjlqbcjnevjye-r9n6cyldmqtnrfjmb98-_9-i-gdugjgr4ebvlu5foskyku0mzwevpqbkvyebtkm3iu4mocl2xkow9j0in0hluuqpkpwrcj_mqomafmf9lg" alt="" title="" /> Where the probability of success is given by &#39;P&#39;, and that of failure is given by &#39;Q&#39;, satisfying the relation Q = 1 - P. &#39;x&#39; is the number of successes in a sample, &#39;n&#39; is the total number of trials.It is worth remembering that is the combination of n values taken from k to k. <Image quality="95" width="122" height="46" src="https://images.prismic.io/voitto-blog/NjA5YzczYTQtMDRhMi00Mjg0LWE3MTYtN2FiY2UwNGJhNjA2_3d9cyvp4hyr2amqeszp3w7kf2cdgamfoscyvcccb3ycsqhzuu_4o-h5dn7wk2hs-1wlnveisc-_uyczipqqtotytdvmls5-mkroggw7swiycum_2sa05eqnz022zeere0uqkjhmk" alt="" title="" /><h2>Binomial distribution: example</h2>Suppose that incandescent lamps are manufactured in a production line. And they are packaged so that each package contains 10 units of bulbs.A Green Belt knows that the probability of a lamp having a defect after leaving the production line is 5%. And he wants to calculate the probability that the same package contains 3 units of defective bulbs.To help this professional, you, as a probability and statistical expert, will apply the following equation. <Image quality="95" width="164" height="34" src="https://images.prismic.io/voitto-blog/NWEzYjEwOWMtM2E5Ni00OTUwLTlhNTctY2Q0YmNhNjljZGEx_21x0hi2bf9m89uom7d7vrr8qhhqsees1catcbfgxp8_5c8bzutoxtgbck_yptjco40otsyuy1d4uxmx1kzsgmps0bwaplsvc2dqgsl6wgdd-p-ovetokplew6qjl9oz-ynszjwd-" alt="" title="" /> With the presented data we can identify that: k = 3n = 10P = 0.05Q = 1 - P = 0.95 It is very important to note that we use the probability of success at &#39;P&#39;, and this should not be confused with the likelihood that the lamp will not be defective. But rather the probability of the event we are focused on. That is, it is the probability of a defect occurring.Applying these values and concepts in the presented equation, we have: <Image quality="95" width="373" height="45" src="https://images.prismic.io/voitto-blog/N2E1NDM4NDUtNmFkOC00NGZhLTk4MmUtYzdlMzQzZWY1NWYy_nhusd25jebafztlvun1hupnzjfihelvnn4ingg4_1waudv_-xth-z5t9yqzzskysx2brqp8tdynjwchkjm6ha7zujuw_5ctkbm_seboqaapcjjrbbp-s5sbaqxe5mlg-b_8k2xj1" alt="" title="" /> The Green Belt could then conclude that the probability of a box with 3 defective bulbs is 1.05%.<h2>Master the Lean Six Sigma methodology!</h2>Looking for development in your professional career?What do you think of becoming a reference professional in the market through one of the most used methodologies in the world?Our Black Belt training in Lean Six Sigma is the next step towards your growth and recognition!With our Black Belt certification, you will learn how to manage projects, increase results, lead teams, and the main Lean Six Sigma tools for solving highly complex corporate problems in search of strategic competitiveness.Don&#39;t waste time! Develop the knowledge and skills that will make you a reference professional in the market! <a target="_blank" rel="nofollow" href="https://thinkleansixsigma.thinkific.com/courses/lean-six-sigma-black-belt-upgrade"> <Image quality="95" src="https://images.prismic.io/voitto-blog/f6f988e8-00b9-43bb-ab52-27b100ce660a_Black+Belt+-+Bot%C3%A3o+Banner.png" width="1026" height="206" alt="Black Belt in Lean Six Sigma" title="Black Belt in Lean Six Sigma"/></a>