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Sigma-concepts.com a Website for excellent reading with figures & diagrams
Dr. Amrendra Kumar Roy
QbD Head, Jubilant Generics, NOIDA
A Six-sigma and QbD professional
We would like to share our ~13 yrs of practical experience in the field of product development using statistical tools. But first, what compelled us to pursue six-sigma. Most of us started our career as a process chemist after completing PhD and it was during those initial days we realized the importance of “first time right” during commercialization. This enabled not only first mover advantage but also ensured timely and un-interrupted supply of our products into the market. Another aspect of the process development is its robustness, which ensures sustainable margins in whatever products we manufacture. Above achievement was possible only because of the six-sigma tools that we learned and applied at R&D stage. Latter we shifted our focus to the legacy products running in the plants, which we again studied using six-sigma tools to beat the eroding margins and this was possible because of few chemical engineers with six-sigma black belt joined the team.
As a chemist we were never trained on statistical tools hence, it was really a Herculean task for us to understand it. Another problem we faced was the statistical software, we would like to confess that we were never comfortable using these software as we were aware of “garbage in and garbage out” concept very well. We were never confident of the calculations thrown by software because we were not acquainted with the statistics. To site some examples
We were using regression analysis on five variables and found that we were getting an R Sq. of ~0.99 by including all five variables. We were happy about the results but we failed to realize that Adj. R Sq. has decreased while we added 4th and 5th variable, ending with a regression equation with un-necessary terms in it. As a result, we un-necessarily proposed control strategies for those insignificant variables which involved investment.
Another mistake we often made is to ignore the outliers during the Design of Experiments (DOE)! But we always wonder why we were ignoring these outliers? Just because we wanted to have a good regression equation? Are we not doubting our own experimental data? Later on we learned that if we keep ignoring the outliers just to have a good model, we would ultimately be modeling the system noise rather than modeling the effect. It is better to investigate the cause of outlier rather than ignoring it.
Above examples made us realize that having theoretical knowledge of six-sigma is not enough, it is the practical experience that really matters. Real challenge is the correct analysis of the experiments data so that the product could be scaled up without any problem. Learning to do the correct statistical analysis using any software was the mantra of the game. We should be confident that whatever output we are getting from the software is correct and this is possible only if we have good understanding of the statistical concepts. We are not saying that we should master the statistics but we must have clear understanding of the concepts before we use any software. It took us too long to understand these fundamentals aspects of applied statistics, main reason being the absence of statistical guru with adequate industrial experience. But major hurdle was to find a good tutor or at least a good book which can explain the concepts without involving too much of the statistics. We started looking for applied statistics courses and we found some solace in the “research methodology” module of MBA courses. Having gone through it, it gave us the confidence that six sigma tools can be learned without having in-depth knowledge of statistics.
During last 7-8 years we developed our own way of learning applied statistics with the help of diagrams and figures. During this journey we also found that each statistical topic have some connections with other topics and we can’t study any topic in isolation.
How normal distribution and hypothesis testing is working behind the scene in ANOVA, DoE, regression analysis and control charts.
Having gone through these hardship, I decided to share the experience with all those who like to understand the six sigma tools but are reluctant in doing so because of the statistics involved. Our website would help all six-sigma aspirants to understand the statistical concepts with the help of figures and diagrams. We would also be helping you in understanding the relationship between two unrelated topics like hypothesis testing and control charts.
Another feature that will help you is the solved example from the industry. Hence this would be an ideal website if you wish to appear for green/black belt exam from a reputed institute. We are saying this because we ourselves are ASQ certified six-sigma black belt and we want to share one important thing about the exam that we experienced, you can’t clear the exam unless you have understood the statistical concepts behind every six sigma tools. When we are saying understanding the statistical concepts, it doesn’t means learning pure statistics but only the concepts behind any tool, their advantages and limitations. This becomes important as ASQ never asks direct questions but questions are applied in nature. For example
A bulb production process found to follow normal distribution. A sample of 100 bulbs were drawn from a batch of 1000000 at random and found to have a mean life time of 1525 hrs. Historical mean life time was found to be 1548 hrs. with a standard deviation of 200 hrs. What is the percentage of bulbs having a life span of exactly 1548 hrs. from the current batch?
A manufacturing process was under optimization in a plant and a sample to 10 bags were selected at random from each batch. There were 5 batches in total and the mean weight (in Kgs) of the samples (10 bags) withdrawn are 100.5, 101.1, 99.8, 100.2 and 99.95. The range (in Kg) for these consecutive 5 batches were found to be 0.7, 0.9, 0.8, 0.9 and 1 Kg. Calculate the control limits for the chart.
Problem looks simple, in first case just calculate the z-value to tell the percentage and in the second case appears to be a direct question where we can easily calculate the control limits. But there is a catch, in first case probability for z = any number is zero! it is always about finding the probability between two numbers for a continuous probability distribution. In second case, if you missed the opening statement “under optimization” you are wasting your time in calculating the control limits, as control charts are always calculated for the stable process. In either of the question if you start the calculation, we can ensure that you won’t be finishing the exam in time!
Another major issue during applying six-sigma is the “use of right tool at the right place”. Hence our focus would not only to understand the concepts behind any statistical tools but also about selecting an appropriate tool for a given situation.
This website will start posting the six sigma topics (mainly statistical portion) from first week of January, 2017. Hence get registered on this course as soon as possible. The way we are planning to run the course is by posting one topic every week so that we can understand it well before taking subsequent topic. We are doing it in a slow pace because once we are on some advanced topic say “normal distribution” then at that time we should not be struggling with topics like variance, mean, z-transformation etc. Each topic will be followed by real life examples so that one can understand not only the concepts but also the use of appropriate tools. At the end of each topic we will also be demonstrating the use of excel sheet in resolving statistical problems. We are emphasizing on excel sheet as it is available to all. This would be our main USP during the course.