Afzal Wadood

Similar to histogram , Rootogram is a graphical tool to visually depict the distribution of the variable data. One of the limitation of histogram is that it is difficult to can be difficult because small frequencies are dominated by the larger frequencies and it is hard to understand the pattern of histogram bars when compared with the distribution. Comparison can become easier by ‘hanging’ the observed results from the theoretical curve, and that way the discrepancies are seen by comparison with the horizontal axis rather than a sloping curve. Here vertical axis is scaled to the square-root of the frequencies so as to draw attention to discrepancies in the tails of the distribution. Reference: https://datavizproject.com/data-type/rootogram/

In many situations , we have to compare central tendencies(generally mean is compared) of multiple samples. For 2 sample, t test is widely used. We can use Z test for large sample size. ANOVA (Analysis of variance) is used in cases when we have to compare more than 2 means. Though we can use multiple t test but it will be time consuming and less efficient. ANOVA is a parametric test and requires various assumption for the populations samples to be compared. This includes assumption of Normality, Independence and approximately equal variance. ANOVA is not used in the Nominal data . Below are the steps to perform the ANOVA: Calculate the mean of all the samples Define the null and alternate hypothesis (e.g.: Ho= All samples have equal mean, Ha= All Sample means are not equal) Perform calculation to get the Sum of squares and mean squares based on degrees of freedom for within and between samples differences. Calculate the F statistic. Look up statistical Table , Compare the F statistic with the tabular values and conclude on the results. ANOVA is a parametric test and hence can not be used in all situations. We can use Kruskal Wallis test which is the non parametric alternative to the One Way ANOVA. It compares the sum of ranks in the samples instead of mean.

Yamazumi chart is kind of stacked bar chart and it graphically represent the processes for optimization purpose. “Yamazumi” is a Japanese word and can be translated as stack up. To create Yamazumi chart, we have to select a process and calculate the time taken by value added, non- value added and necessary activities in the identified process. Yamazumi chart then shows these activities in a form of stacked bar. This can also be compared with Takt time. If the bar height is more than the Takt time (target value), the process steps can be rearranged , improved or deleted to optimize the process. The chart helps in business process improvement by visually showing how the processes are overloaded (stacked bar height more than the Takt time) or underutilized. This way teams can perform line balancing analysis and identify areas to do Kaizen.

There are multiple statistical test are available to compare the variance of different populations. Below are some of the test: F test: This is suitable in case the populations are normally distributed or near to that. This is a parametric test and used for comparing 2 populations variance. Bartlett's test : Like F test , this is also used if the populations are normally distributed or near to that. This is also a parametric test and can be used for comparing more than 2 populations variance. Levene’s Test: This is again a test for variance comparison and can be used for both normal and non-normal data. This can be used for two or more than two population samples. These test are often used as part of mean comparison test wherever we have assumed equal variance for the population samples. For multiple comparisons in these test , we have individual and Simultaneous Confidence interval. Individual confidence level will show percentage of confidence that the true population parameter for that population will lie in the Confidence interval. Simultaneous Confidence interval is derived from the individual confidence intervals of multiple populations. It can be interpreted as % of confidence that the entire set of confidence intervals includes the true population standard deviations for all groups.

Outliers are the data points which looks different and far from the rest of the data. Outliers can influence estimates such as mean , variance ,etc. and reduces the power of statistical test. It is important to handle the outliers carefully before working on any estimates. Outliers can be detected though tools like boxplot, scatterplot, Z score, etc. Below are some of the the approaches to handle the outliers: Identify the outliers in the data using some of tools mentioned above. Check whether outliers are the results of measurement or data entry error. We can discuss the same with the data provider and correct the entry if possible. In case , we know that it is a data entry error but we don’t know the actual data value we can simply replace the value using various imputation techniques (Example: replacing it with mean or median values). We can also use some filters to cap the outliers values. For example , any value above the 95th percentile can be replaced with 95th percentile value. Similar approach can be taken for low outliers. If we think that outlier is because of mixing of another population then we can simply remove them so that our sample becomes more representative. In this case, we should document the removed data values along with the reasons for the data removal. Finally deciding on the best way to handle outliers requires detailed evaluation on the problem under study, data distribution, research methodology, etc.

Multi voting is a decision making method, to gain consensus in a group having a large list of choices to select and priorities. It helps to select the choice which is favored by most in the individuals in a group. It involves following steps: Brainstorm the list of ideas Discuss the idea with the group participants so that everyone understand it. All participants then vote for the ideas. Generally they rank the ideas by assigning a number for each idea. The votes are then counted (or rank are summed) and ideas having highest votes (or rank sum) are selected. Its benefits include team engagement and consensus and is especially useful for large teams and when we have a long list of ideas. However it is possible that no consensus is reached in the voting. We can then assign weights and repeat the voting process if required. For example. If we want to increase the sales of the company product, the possible ideas can be: giving more discounts, reduce the prices, better services , etc. To select the top 2 ideas, we can ask the group members to rank the ideas which are then summed. The ideas having highest sum will be picked to improve the sales.

Deming 14 steps: 1.Create a consistency of purpose toward improvement. 2.Adopt the new philosophy. 3.Cease dependence on inspections. 4.Use a single supplier for any one item instead awarding business on the basis of price tag. 5.Improve constantly and forever. 6.Institute training on the job. 7.Implement leadership. 8.Eliminate fear. 9.Break down barriers between departments. 10.Eliminate unclear slogans. 11.Eliminate management by objectives. 12.Remove barriers to pride of workmanship. 13.Implement education and self-improvement. 14.Put everyone in the transformation process. Crosby 14 steps: Management commitment Quality improvement team Quality measurement Cost of quality Quality awareness Corrective action Zero defects planning. Supervisor training Zero defects day Goal setting Error cause removal Recognition Quality councils Do it over again Similarity and Difference: From the above points we can say , Deming focuses more on process control and involvement of everyone in the quality improvement initiatives while Crosby focusses more on Motivation , zero defect and attitude change

Platform economy is a kind of business model where multiple independent framework (technological, social , etc.) are used to sell products/services. For example, we can use a business website or a mobile app or a social media application to purchase the product. In many cases , there is a single individual/organization which owns the platform and different producers use the platform to sell their products. Amazon.com, Alibaba, flipkart, etc are some of examples of platform economy model. These Organizations can apply six sigma in the some of the below area’s to improve profitability: Understanding and improving customer satisfaction ratings so that more and more people use the platform Improve the response time for customer queries coming through email, chat , helpdesk , etc. The product refund rates and how to minimize that. ROI of marketing campaigns

Chi Square test is a hypothesis test performed on the categorical data in various scenario’s. To perform the test, we first have to calculate the square of difference of observed and expected values and divide this by expected value. This is summed for all the distribution values which gives the calculated Chi Square values (X^2). Then we look for the tabulated chi square value for the applicable degrees of freedom. If Calculated X^2> Tabulated X^2 then we reject the null hypothesis(which means we accept alternate hypothesis). Below are the types of comparison where we can apply the chi square test. Test of Homogeneity : Homogeneity refers to how similar thing are. So if want to check that 2 distributions are similar , we can perform this test of homogeneity. For example, we can use the test to check whether male or female have same/similar preference for various subjects in graduation studies (math, humanities, Science, etc.). Test of goodness of fit: This is used to check how similar are the observed values to the values expected based on assumed distribution. For example , we have certain expectation for sales of our company product in different days of the week . This may be based on some sales distribution we have assumed. Then we check the observed sales for the week days. Now we can use the test to check whether observed sales distribution is similar to the expected sales distribution or whether the expected distribution is the right fit for the observed values. Test of Independence: This is used to test whether 2 variables are somewhat associated/related or they are independent. This is part of non- parametric tests. Suppose we want to check whether the education level and gender are related to each other. In other words whether gender of the person influences the education level of that person. Here we can use the Chi Square test of independence to check the relationship.

Change is difficult to implement even if we know that it is needed .In any organization, to implement change we need some defined approach or framework. Kotter’s 8 step is one of such change management framework. Since the LSS projects are also change projects, we can use this model steps in different stages of DMAIC for successful LSS project completion. Here are the change management steps: Kotter’s 8 steps : Establishing a Sense Of Urgency Building A Coalition That Can Make Change Happen Develop A Vision And Strategy Communicating The Change Vision Empower Broad Based Action Generating Short Term Wins Consolidating Gains and Producing More Change Anchoring New Approaches in the Culture These steps can be integrated in the below stage of LSS projects. Define : Here we select the most important opportunities for improvement and define the project scope. We also identity project team members (stakeholders) and project goals. So , Kotter’s step 1, 2 and 3 can be used here in define stage of the DMAIC. Measure: Here we establish baselines of current performance of the process we want to improve through the LSS project and communicate this to stakeholder. Here step 3 , 4 of the Kotter’s model will be relevant. Analyse & Improve: Here we analyze the underlining causes of the problems, from where improvement actions can be decided. Team identifies, communicate and implement the improvement actions needed. Kotter’s model step 5 and 6 are relevant here. Control : Work on maintaining the improved process under control for long term effectiveness. Once the process is changed and stabilized, look for further process improvement opportunities. Step 7 and 8 of Kotter’s model can be utilized in this stage.