Suresh Jayaram

Six Sigma is all about reducing variation, reducing defects, and improving customer satisfaction. All businesses are made of processes - hiring process, ordering process, inventory management process, etc. All processes have variation - it is not possible to have a single process with no variation in it. There is bound to be some variation - however small. The key question is - is this variation bigger than what your customers and/or business stakeholders can tolerate? So, identify the key processes, identify the amount of variation you currently see in these processes, indentify the amount of variation your customers can tolerance. Once you have this data, you will be able to point to projects that could benefit from Six Sigma. There are other threads in this group that talk about initiating projects - please do a search: One such search is found below: http://forum.benchmarksixsigma.com/forum/63-improvement-assignment-support/

Hi Shalini, Don't worry - these are advanced topics that are covered in MBB training. Most of the questions here refer to Multiple Linear Regression which is not covered in BB training - only Simple Linear Regression is covered. You should be able to answer 1 and 4 based on BB training. Best Regards, SJ

Dear Shalini, This concept is very similar to Acceptance Sampling. Please refer to the following article: http://www.itl.nist.gov/div898/handbook/pmc/section2/pmc2.htm Best Regards, SJ.

Dear Kiran, Ideal state refers to perfection. For example, if the current Work in Process (WIP) = 1000, the ideal WIP = 0. However, we cannot get to the ideal state within a short period of time. So, people plan for an interim future state usually six months or one year from now. This is called the future state. For this example, maybe the future state could show that we want to reduce WIP from 1000 to 500. After the end of one year, the future state becomes the new current state and we plan for another future state at that point with the goal of getting to the ideal state in the long run. Hope this helps, SJ

Dear Kiran/Shalini, Both of you are right. If both are known, then we usually work with the defects and if we drive the defects down the zero, then defective also goes down to zero. However, if we are working with only defectives, some people assume defects = defectives. As Kiran points out, technically, they are different. Please note that there are some practitioners who believe that we should only be working with defectives and not defects because we may artificially claim a good process sigma level if we inflate the number of possible defects in a product/service. Best Regards, SJ

Hi Kiran, If you look at the confidence interval of Cp/Cpk (process capability index), you will find that the confidence interval is pretty wide when the sample size is small. For example, the confidence interval is around +/- 0.4 when the sample size is 30. If you calculate the process capability index as 1.0, it could be as low as 0.6 or as high as 1.4. If you use a smaller number of samples as recommended by the Sequential Test Method, say 15, then the confidence interval would be a lot higher. This would mean that the error in analysis could be a lot higher. A process that is shown to be capable may in fact be not capable. So, I would recommend to use this method with caution. Best Regards, SJ

Dear Kiran, We need to differentiate between continuous and discrete variables. Let's first look at the discrete case. For example, if we are talking about tossing a coin. The probability of getting a head is 0.5 and the probability of getting a tail is 0.5. The value 0.5 can be referred to as the probability mass function. For continuous variables, the probability mass function is referred to as the probability density function. However, the value of the probability density function does not equal the probability of getting a value in the continuous case. In fact, the probability of exactly getting a value for a continuous distribution is always 0. The area under the probability density function gives the probability in the continuous case. For example, if we have normally distributed data with mean = 20 and standard deviation = 5, then the probability of getting say 20, P(20) = 0. We can however, calculate the probability of getting values between 19 and 21, represented as P(19 < X < 21). If we look at the probability of getting all values less than 21, i.e. P(X < 21), this function is called the cumulative distribution function. It is the area to the left of that value under the probability density function. This can also be represented as CDF(21). Note: P(19 < X < 21) = CDF(21) - CDF(19). The area between 19 and 21 is equal to the total area to the left of 21 minus the total area to the left of 19. In most cases, for continuous distributions, we usually work with areas, so CDF values are more important than PDF. However, when we plot the distribution functions, we usually plot the PDF as their shapes are easier to recognize compared to CDF. It is hard to explain this without a figure. Hope this helps. SJ.

Hi, I am not sure I could comment on the temporary vs. permanent solution with this exercise. You can only state whether there is or is not a statistical difference between the two proportions. For example, proportion of licenses with reconciliation is statistically similar to the proportion of licenses without reconciliation. Statistically, there is a difference between license policy of 60 days vs. 90 days. You will have to determine if the change you detected is practically important and how you can establish a good control plan so that the process will work over the long term. Best Regards, SJ.

Dear Adhiraj, You can calculate incremental costs and claim these as benefits for your project. Cost A: Cost that would impact your organization assuming you did not do this project. Cost B: Cost that would impact your organization assuming you did this project. The difference between A and B would be your project benefits. For example - If you did not do the project, the revenue would increase by 2% and cost by 1% If you did the project, the revenue would increase by 5% and cost by 3%. Cost A: 1% increase in margin Cost B: 2% increase in margin So, you can claim 1% as a result of your project. Hope this helps! SJ.

Dear Satheesh, Regression model is nothing but a relationship between your input(s) and your output. It is primarily used when your input(s) and output are continuous. Typically, we build a linear model between the input(s) and output. If you have one input and one output, we use simple regression of the form Y = m*X + c. Where, X is your input and Y is your output. For your question, if I understand it correctly, you have three inputs, X1, X2, X3, in which case, we would use multiple regression where the model would be: Y = m1*X1 + m2*X2 + m3*X3 + c Once you build a regression model and check that you have a decent model between your inputs and output, then you can use this for prediction or optimization. Make sure you check the adjusted R^2 values, the appropriate P-values, and also make sure that you check the model assumptions are satisfied. One of the most important requirements is that X1, X2, and X3 should not be co-linear. Once you have a model, you can then use it for optimization by adding additional constraints on X1, X2, and X3 (if appropriate). This optimization can be done using Linear Programming (LP) - a reference to LP is shown below. Reference: http://en.wikipedia.org/wiki/Linear_programming. Hope this helps, SJ

Dear Shanka, If you look at the right hand top corner of this website, you will find a search feature. If you search for Lean Six Sigma as the keywords, you will find several articles on this topic. Best Regards, SJ

Dear Shiva, Just wanted to understand why you indicate that a 2-proportion test is not relevant here. Could you not do a 2-proportion test with the first case (90-day policy) and determine how many licenses would be freed (events) vs. total number of licenses (trials). Similarly, you can calculate for the second case (60-day policy) how many licenses would be freed (events) vs. total number of licenses (trials). Using this information, you should be able to use the 2-proportion test and get an appropriate value of P based on the discrete distribution (in this case a Fisher's test). As an approximation, you could use the 2-sample t test if the proportions you calculated above are not close to 0 or 1. SJ

Dear Anish, There are several approaches to solve any problem. You will have to pick the most appropriate one depending on your situation. Box-Cox transformation is a group of transformations that help with transformation of the data from Non-normal to Normal. This transformation includes, among others, taking the reciprocal of the data set, or taking the square of the data set, or taking the logarithm of the data etc. in order to make it Normal. Box-Cox tries different combinations and then picks the transformation that best makes the data Normal. There is NO guarantee that if you apply the Box-Cox transformation, your data will become Normal. One application of Box-Cox transformation is in Control Charts for Individuals (example I-MR Chart). In order to use I-MR charts, data has to be Normal. If it is not Normal, then you may try using a Box-Cox to make it Normal before using the I-MR chart. When you are doing Hypothesis testing and say comparing two populations, it may be preferable to use Non-parametric distributions rather than apply Box-Cox transformations (please see one of my earlier posts on this topic). Hope this helps. SJ.

Dear LR, It is okay to take action when points go beyond the control limits (especially when there is a special cause which causes the points to fall out of the control limits). In order to compute process capability, we compare the process performance to specification limits. The control limits are an indication of process performance. When we talk about specification limits, we implicitly use LSL or USL or both. However, when we calculate DPMO or Sigma level using this approach, we assume any parts that fall outside LSL/USL as defects - which causes some problems as you have correctly identified. It may be better to use Taguchi loss function to characterize quality / cost rather than use specification limits. SJ

Dear SK, These are two different tools within Six Sigma with totally different objectives – even though they do have some similarities. QFD (Quality Function Deployment) is a tool that is used to translate Voice of the Customer (VOC) into design requirements. It basically translates what the customers desire into specific measurable metrics with well defined targets. QFD is one of the primary tools in Design for Six Sigma (DFSS) projects. FDM (Function Deployment Matrix) is a tool that is also called the Cause and Effect Matrix (C&E Matrix) or the XY matrix. This tool can be used to map which X’s have a big impact on the output Y (usually based on team perception). So, if you have a large number of X’s, you can use the FDM tool to narrow down the list of X’s that may be important to investigate further. The similarity between QFD and FDM is that one of the houses of QFD (the central house) that determines which design specifications are important uses a relationship matrix that is very similar to the FDM methodology usually using a 1-3-9 scale. QFD does a lot more than what an FDM does – for example, it can be used to evaluate competitor’s products, conflict between design requirements etc. In addition, there are second and third level QFDs which can further translate the design requirements into the next level – such as manufacturing tolerances etc. Hope this helps, SJ.

Hi Vineet, Since you are working with a primary metric that is discrete, you don't have to really worry about normality analysis or tests - unless you want to assume that the data is "roughly" continuous and this is a relatively good approximation for the discrete data that you have. If you have a large enough data set and many possible values of Y, this assumption may be okay. If you choose this route, and the data is not normal, I would recommend that you use the appropriate non-parametric tools like (moods median, mann-whitney etc). If you choose to work with Y as discrete, and your X is also discrete, you would use a 1-proportion, 2-proportion, or a Chi-Square test. If your X is continuous, then you would potentially have to do a logistic regression. SJ

Dear Fowzieh, Abhijit, Right. When you do a current state Value Stream Map (VSM), you can identify the potential improvement areas (called Bombs) on the VSM using a Kaizen burst image. Some of these improvement opportunities can be done right away (JDI - Just Do It), some of them require some cross-functional team input and some basic analysis (these would be ideal for a Kaizen team), and still others may be chronic issues which may not go away without some serious analysis. The last category would be ideal for Six Sigma projects. When you perform a VSM analysis, you would need to figure out these improvement areas and then focus your efforts on the appropriate opportunities. Hope this helps, SJ.

Dear Fowzieh, What do you mean by a Lean event? If you are referring to some Lean deployment, you can start off with deploying basic Lean tools that deal with Stability and Standardization first - things like 5S, Standard Operating Procedures, Waste Elimination etc. The benefit of using Lean is that you can start getting quick benefits right away - then you can use Six Sigma for more tougher problems. You will have a good foundation with some preliminary data collection in place that can be used to identify Six Sigma projects. Secondly, you could use Lean tools within Six Sigma in DMAIC as a Lean Six Sigma project. For example, use of 5 Why's in the Analyze Phase to identify root causes. Best Regards, SJ.

Dear Prashant, Are you asking about Normality test? If so, normality check can be done using Anderson-Darling statistic (within Minitab, go to Stat->Basic Statistics -> Normality Test) SJ

Dear Amit, I would look in Naukri, Monsterindia, LinkedIn. If you use the keyword "Black Belt", there are roughly 330, 165, and 161 jobs listed on these sites today. SJ

Dear Prashant, I am not sure how your productivity is calculated - but I am presuming that this data is continuous. You will need to review sufficient historical data (say couple of years) to see if there are any trends or seasonality in the data. This along with the amount of variation you see in your data will determine how much historical and future data you would need to collect for this project. Establishing a target of QnQ increase will necessitate a longer control period as you may need to collect data for several quarters to ensure that your process is in control. If permissible, I would recommend you to consider a shorter timeframe - like weeks or months. You can perform a check on normality of the data to see if the data is normally distributed in which case you can work with the averages, if not, you may have to work with the medians. Based on this, you can establish a baseline level of mean and standard deviation if the data is normal, or median and IQR if the data is non-normal. If you also have any specification limits, then you will be able to establish a process capability index, DPMO, and Sigma Levels for the baseline. Best Regards, SJ.

When one or more populations are not-normal, the first thing to do is to check the cause of non-normality. Sometimes, normal data appears non-normal if we make errors in typing in the data points, if we have significant measurement systems error etc. Let's say we rule out these obvious issues and the data is still not normal, what can we do? In this case, we should not be using the 2-sample t test as it relies on the normality of the data points. If there are minor departures from normality, it may still be okay to use a 2-sample t test as these tests are relatively robust. One option is to use a non-parametric test such as the Mann-Whitney test to do this analysis. This approach will work but it has the limitation of loss of information. For example instead of working with the raw data, we will be working with ranks. Secondly, these tests are not very sensitive and will usually report that the null hypothesis is true. They will only report that alternate hypothesis is true (there is a difference between populations) when there are marked differences between the populations. A second option is to transform the data. You could try the Box-Cox transformation, using the different distributions (Log-normal, etc), Johnson transformation etc. The problem with the transformations is that we are no longer working with the original data but with transformed data. For example, if we take the square root of one data set to make it normal and the other data set is already normal, then we will be comparing the means of one population with the mean of the square root of the other population. Which is usually hard to interpret/understand. It is not possible to make a data set normal by collecting more data points. Of course, if you collect more points, the averages of the samples will be normal not the individual data points themselves. SJ

Dear Shiva Kumar, The count data would probably be a Poisson distribution. It may be better if you take a square root transformation in order to make this data normal. Also, since the numbers are fairly high, it may be okay to assume that the data is continuous rather than discrete. The sample size of 4 seems too small. What parameters for difference to detect, power, standard deviation did you use to estimate it? With just 4 data points, it would be hard to detect deviations from normality using the normality test - most likely you will accept the null hypothesis indicating that the data is normal. You would be making more type II (beta) error with fewer samples. You could work with daily or weekly data rather than monthly data to increase your number of data points. Best Regards, SJ

Dear Shiva Kumar, Since this is discrete data, we usually work with proportions. Is it possible to determine the maximum number of possible ticket counts (trials) and then work with ratios rather than the count of the tickets? When you are working with proportions (1-Prop test), you will find that you will get similar answers if you make a normal approximation when the number of trials is very large. SJ.

Dear Biswajit, Use Stat->Basic Statistics -> 1-Sample t (Make sure you use Summarized data to feed in your values). This should give you the required 2-sided confidence intervals in the session window. SJ.