Natwar Lal

4 Eyes Principle - it is a risk control method where a set of 4 eyes (or 2 people) must approve or check something before it could be done. The fact that no human being is perfect led to the use and popularity of method. The concept is simple - the odds of two different people making the same mistake at the same time are very very small and NOT ZERO. This is the reasons that there have been instances where some errors have happened even when 2 or more people have checked the same thing.
 
If implemented in the process, will it be value adding or non-value adding?
 
Ideally, it will be a non value adding activity. However there are instances where the customers are willing to pay for multiple people checking the same thing. In such scenarios, 4 or 6 or even 8 eye checks become value adding. Barring it, 4 eyes principle is a non-value adding activity usually made mandatory by the regulator for safety concerns and hence is classified as value enabling activity.
 
Examples where 4-Eyes principle is value adding
1. Authors usually want multiple reviews (copy edits, proof reads etc.) of their work before publishing and they are willing to pay for such reviews. 
 
2. Managed services (outsourcing work), clients sometime warrant dual data entry and pay for the same (imagine the cost arbitrage - cost of 2 outsourced FTEs is less than 1 onshore FTE) 
 
3.  Patients willingly take second opinions before major medical procedures.
 
In the above it is clear that the customer is willing to pay for the multiple reviews or checks.
 
Examples where 4-Eyes principle is non-value adding
1. Banking transactions need to be approved by 2 or more people depending on the ticket value (usually called as maker-checker process)
 
2. Presence of 2 pilots in the cockpit. Both should check and confirm the same thing before an action is taken
 
3. Closing of doors on the plane. 2 crew members should check and confirm it
 
4. Presence of team of doctors and nurses during surgeries. Doctors ask for the instrument by calling its name, the junior doctors or nurses hands over the instrument by calling its name again. Double confirmation that correct instrument is being used
 
5. Presence of two people for opening of bank safes and lockers
 
All these examples have a cost of failure and hence 4-Eyes principle is implemented so that the risk of failure is minimized. In such cases this becomes an example of a value enabler activity.
 
Example where 4-Eyes principle is a complete waste
1. Putting additional layers of audits in service industry because of customer complaints and escalations
 
 
 

Pseudo continuous data as the name suggests is pseudo continuous i.e. it is actually not continuous (or discrete) but it considered as continuous. 
 
Advantages
1. More powerful analytical tools can be used on the data
2. Continuous data tends to follow normal distribution and if it does, we could apply its properties
3. As a Lean Six Sigma practitioner, you need to remember less number of tools :)
 
Dis-advantages
1. Conversion of statistical solution to practical output have a chance of going wrong as the properties of discrete and continuous data are different
2. Misinterpretation and misuse of tools and techniques
 
Guidelines to consider discrete data as continuous
1. There are many (read as uncountable) possible values of discrete data. This is one reason why percentage is usually considered as pseudo continuous.
 
Considering discrete data as pseudo continuous is a powerful method that can be used aby LSS experts in data analysis. However discretion is required by the project leader in using this method.

Control Impact Matrix is a 2D tool which helps in comparing items against two parameters
1. Control that we have over the items
2. Impact (expected) that the item could have on solving the problem
 

 
In a DMAIC project, this tool is primarily used in Analyze phase for prioritizing the causes that can be focused on. Typically the priority order is as follows
1. Causes in High Control High Impact
2. Causes in High Control Low Impact
3. Causes in Low Control High Impact
4. Causes in Low Control Low Impact
 
There is debate on the order of points 2 and 3. However, I feel point 2 should have higher priority wrt to point 3.
 
It may also be used in Improve phase to prioritize for solutions however, there is another matrix tool that is more suitable for this purpose. We could use an Effort Impact Matrix for solution prioritization. Therefore, I feel that Control Impact matrix is better suited for Analyze phase.

In order to answer the question 'Why is the problem occurring?", below steps are done in Analyze phase
 
1. List all potential causes
2. Analyze potential causes
3. Identify critical causes
 
 
There are 2 approaches that can be deployed for analyzing potential causes. I have summarized both in the table below
 

 
P.S. the usage of tools is not exclusive i.e. tools can be used either for process or data door depending on the situation. The table only highlights the preferred or the most commonly used tools.
 
 

Let us consider two numbers a and b where a is greater than b. If the ratio of the sum of these numbers (i.e. a+b) to the larger number (i.e. a) is same as the ratio of the numbers (i.e a is to be), then these two numbers are said to be in a Golden Ratio.
 
Golden Ratio => (a+b) / a = a / b
 
This is denoted by Greek letter phi ( or ). This ratio comes to an irrational number = 1.618
 
Applicability of Golden Ratio is found in 
1. Nature - sunflower, position of leaves
2. Architecture
3. Art
4. Music
5. Technical Analysis of Stocks
6. Design Thinking - laptop screens, mobile screen size
7. Book layouts and publishing
8. Logo designs - Twitter and Apple
9. Computer algorithms
10. Mathematics - fibonacci series
11. Geometry - spiral shapes

Box-Cox Transformation is the most commonly used method to transform non normal data to normal data. It transforms the original data by applying a power to it (usually denoted by lambda). The value of lambda varies from -5 to 5.
 
Why will we need to transform the data?
Short answer to the long theory is because of following two reasons
1. Properties of normal distribution
2. Normality is a pre-requisite condition for parametric statistical analysis
 
If we expect the data to be normally distributed, but it is not, then before we apply the transformation, we should first check for data entry issues. But then most of the times the process data does not tend to follow normal distribution and hence the transformations come in handy.
 
Analysis that can be performed after applying Box-Cox transformation
1. Stability Analysis - one of the pre-requisite for continuous data control charts is that the data should follow normal distribution
2. Capability analysis - the original data will get transformed, however the capability of the process is still usable. If one knows the underlying distribution of the data, then this transformation may not be required, however not everyone knows the multiple types of distributions
3. Regression analysis (or any of its variants) where the residuals are non normal due to heteroscedasticity (i.e. data does not have constant variance)
 
Analysis that should not be performed after applying Box-Cox transformation
1. Descriptive Statistics - there are measures that can handle non-normal data (Median and IQR)
2. Inferential Statistics -  there are non-parametric tests (median tests) that can be performed for non-normal data. These tests do not require one to understand the underlying distribution and are robust enough to handle non-normal data
 
 
 
 

As per Wikipedia, Ben Franklin effect is  - a person who has already performed a favor for another is more likely to do another favor for the other than if they had received a favor from that person.
 
This effect appears to be the result of cognitive dissonance, because if we have done a favor for someone, how can we possibly not like the person. Given that this phenomenon works, businesses or individuals could use it to their advantage in following ways
 
1. Good inter-personal relations
2. Good client vendor relations
3. Customer loyalty
4. Good supplier relations
5. Good team bonding
 
In all the above cases, the approach would be to first ask for a favor from the other party. One the other party obliges and fulfills the favor, they will inherently start liking you (as per the Ben Franklin effect) resulting in good relationships.

Excellent way of applying the teachings with the current affairs - using Time Series and Forecasting to forecast the number of new cases for Coronavirus.
 
Basis my research (and I am sure by now everyone knows), that pandemics follow an exponential growth. So, when governments say they want to flatten the curve, they basically mean that the exponential growth should be controlled.
 
Exponential growth happens when base grows not be addition or multiplication but by powers. A to the power of B is an example of exponential growth. E.g. let's assume 1.01 to the power of 2
Day 1 => 1.01 to power of 2 = 1.0201
Day 2 => 1.0201 to power of 2 = 1.04
Day 3 => 1.04 to power of 2 = 1.08
...
...
...
Day 10 => value becomes 26612.57
 
Initially the growth is relatively smaller, but as the time passes, the exponential growth results in very high numbers.
 
Regarding the forecasts for Coronavirus, I picked up the actuals data that was published. Picked up the data from 15th Mar as you are using that as the base value (as below)

After running the trend analysis in Minitab for Exponential Growth and using the same for forecasting, below are the results.
Growth Model for 26th March forecast

Using the above growth model, the forecasted value for 26th March = 60064
 
Doing the same analysis for 27th March, but this time added the actual figure for 26th March.
Growth model for 27th March

Using the above growth model, the forecasted value for 27th March = 69336
 

Confidence Interval is the interval in which the population mean is supposed to fall. Confidence Intervals are determined in all hypothesis tests as we infer something about the population from the sample.
 
Prediction Interval is the interval in which an individual value is supposed to fall. Prediction Intervals are determined when we use statistical tools for predictions.
 
Since Confidence Intervals are estimates for means, there are less chances of going wrong and hence it is smaller. On the contrary, since prediction intervals are point estimates, there are higher chances of going wrong and hence it is bigger than confidence interval.
 
Examples
1. Estimating the Sensex or Nifty level at the month end will be like determining Confidence Intervals, whereas, estimating the price of a particular stock at month end is like determining Prediction Intervals
2. Confidence Interval - estimating the overall sales for the product mix. Prediction Interval - estimating the sales for a specific product
 
Regression analysis when used for forecasting or predictions will yield both confident and prediction intervals. Usage of one over the other would depend on the output / variable that the organization is forecasting for. I would believe that most organizations work with confidence intervals, while prediction levels give them an indication of the best and the worst case scenarios.

Process Capability Assessment is the main step in Measure phase where the Baseline Metric is calculated. Following are the metrics that can be used for assessment
1. Sigma Level Long Term (Zlt or Zoverall) and Sigma Level Short Term (Zst or Zwithin)
2. Pp, Ppk (using overall standard devaition) and Cp,Cpk (using within standard deviation)
3. DPMO, DPU and Defective %
 
Zwithin uses the within standard deviation for calculation while Zoverall uses overall standard deviation for calculation. The difference between within and overall standard deviation is how you perceive the collected data. If the entire data set is (or the population data) is used, it results in Overall Standard Deviation. While if we divide the entire data into rational subgroups then we get Within Standard Deviation (which is also known as Pooled standard deviation)
 
Another common method to understand the difference
within overall standard deviation is when only common cause variation is considered
overall standard deviation is when both common cause and special cause variation is considered
 
Sub-grouping or Rational subgroups is the collection of data under similar process conditions thereby resulting in lesser variation leading to the following concept
within standard deviation < overall standard deviation
 
Following are few scenarios where sub-grouping is NOT preferred
1. Rational sub-groups do not make sense while working with discrete data. For e.g. if we do weekly sub-groups and are collecting data on defects. For a particular week, if there are no defects (though unlikely but still), then within standard deviation will be 0. Hence does not make much sense to use sub-grouping when dealing with discrete data. On the contrary, one should check for possibility of sub-grouping in case of continuous data
 
2. Consistent and standardized process that does not change very often. E.g. Temperature control for stem cells. Assuming that it is maintained at -4 Celsius, it is unlikely that it will show a lot of common cause variation. In such cases, even if we do sub-grouping, the variation within and overall will be more or less same (unless there was a presence of a special cause)
 
3. Project scope deals with a specific product or service being delivered to a specific client. E.g. delivery time of same kind of pizza by only one pizza outlet and to a specific corporate customer (assuming this corporate customer orders almost on a daily basis and orders the same pizza everytime from the same outlet)
 
4. All process inputs are well controlled. If all the process inputs are all well controlled, then there are less chances of variation in the process. In such a scenario, one could avoid doing rational sub-grouping. Closest example I can think of is the process of making a burger at McDonald's. All the process inputs are well controlled and hence we get the same taste of the burger. One could argue that it is not a perfect example. And I tend to agree because it is very difficult to find a process where all inputs could be controlled. There will always be fatigue, wear and tear etc. Like they say, there is no "perfect process"
 
Important thing to note here is that irrespective of whether you do sub-grouping or not, one should be consistent with the approach for doing a pre vs post project comparison. If baselined with Zwithin, then compare the improvement with Zwithin only.
 
P.S. - If all of this is too tedious, one could simply use the empirical formula Zwithin = Zoverall + 1.5 (however, one should remember that if the data is continuous, both these can be determined independently as well)

Genchi Genbutsu - "Go and See" to investigate the issue and truly understand the customer situation. It basically refers to go and observe the process where the actual value is being added. As the question suggests, it makes perfect sense to use in in manufacturing however it is a myth that it is only used in manufacturing. As a concept Genchi Genbutsu is domain and industry agnostic.
 
While preparing process maps, we usually tell the participants to create a map of "What the process is" and not "What it should be" or "what you think it is". One of the best means of understanding "What the process is" is to pick up a transaction and do a walkthrough of the process with it. This is Genchi Genbutsu for you as when you do a walkthrough of the process with the transaction you actually go to the process and see how it works. 
 
I am providing some examples below where the idea is same "Go and See".
 
1. Issue Resolution: when you raise an issue, the first thing that the agent / engineer will do is try to replicate the issue. They might do a screen share or take control of your computer and replicate the issue to understand where to attack and what to do
 
2. Software Testing: The first one happens when the code is compiled. The compiler does a walkthrough of the entire code and highlights the section of the codes that could not be compiled due to incorrect coding. Second happens during the multiple stages of testing - unit testing, integration testing and UAT. If a particular test case fails and the code is sent back to developer, the developer will first recreate the situation to see the failure (this is Genchi Genbutsu)
 
3. Medical conditions: Various invasive and non-invasive screening methods are used to first go to the specific location in the body and see the extent of the problem. E.g. X-ray, MRI, CT-scans, angiography etc.
 
4. Servicing of car: when you take your car for its regular service, the mechanic will first take a test drive of the car. What he is trying to do is to get a feel of how the car is driving so that he could pinpoint the issue which he will not be able to do unless he drives it himself.

Looking at the above differences, it becomes clear as to why Test of Equivalence is considered as opposite of Hypothesis testing.
 
Having laid down the differences, there are some similarities as well
 
1. Both work with samples and apply the concepts of Inferential Statistics (Significance Level, Confidence Intervals etc.)
2. Researcher is interested in Alternate Hypothesis in both (even though the alternate hypothesis are opposite in the two)
 
Choice between hypothesis testing and equivalence will depend on the purpose of the study. Equivalence tests are most commonly used in pharma industry to check if a generic drug (lower cost option) has the same efficacy as the patented drug. 
 
To summarize, equivalence tests could be used wherever we want to use substitutes to an original item without significantly impacting the final outcome. Some e.g. that I could think off
1. Construction - Substituting building materials without impacting the compressive strength
2. Chemical / oil / pharma - Substituting chemicals without impacting the reaction time
3. Medical devices - substituting the type of laser without impacting the burning efficiency and precision
4. Tyre industry - substituting the rubber components without affecting the grip or the life of the tyre

Sampling Errors are of two types (as already mentioned in the question) - Biased and Unbiased.
 
Biased Sampling Error - is one which results in a bias in the sample. The effect of this bias is that the result of the sample will not reflect the true nature of the population. There are three sources of such bias
1. Survey Bias: where the survey questionnaire or the process of collecting data is biased
2. Researcher Bias: bias introduced by the researcher of the study
3. Respondent Bias: bias in the responses if the respondent chooses not to give the correct answer
 
Unbiased Sampling Error - is one which is the resultant of chance. The sample will never reflect the population simply because the observations will vary from each other. 
 
Selecting a large sample size is one way in which both these biases could be avoided. However, since our analyst has decided to choose a smaller sample size, he should take care of the following things
 
1. Sampling method: choose the one which gives a random representative sample
2. If there is a questionnaire involved, then ensure that there are no leading questions or questions for which the respondents might have a tendency to not give the right response. Make the survey anonymous so that respondents could give correct responses
3. Determine which is more important - alpha or beta error? Since sample size is fixed, he could then determine either the significance level or Power of the Test that he is going to get and whether it is ok or not

One of the reasons for project failure is 'Lack of Planning' and this not only includes planning for what one is going to do in the project but it also involves planning on how to check that the project is on track. Doing effective tollgates is an excellent mechanism to check the progress and ensure that project is still on the right path.
 
For the tollgates to be effective, one basically has to seek answers to 5W and 1H (What, Why, Where, When, Who and How)
Let us look at each element in slightly more detail

1. WHAT - Determine the requirements. What is the purpose of the tollgate? What is the information / artifacts that are required? What questions have to be asked?
 
2. WHY - Determine the objectives of the tollgate. Why are we doing tollgate? Why is it important to do the tollgate? Is the purpose only to review or also to approve?
 
3. WHERE - Determine the logistics of the tollgate. Where are we doing the tollgate?
 
4. WHEN - Determine the frequency, duration of the tollgates. When should the tollgates be set up during the project lifecycle? 
 
5. WHO - Determine the participants in the tollgate. Who should be presenting the progress? Who should be audience during the tollgate? Who should be asking the questions? Who is going to take down the action items and meeting minutes?
 
6. HOW - Determine the decision criteria for acceptance / rejection of the tollgate. How are we going to judge the success of the tollgate? How many tollgates are required in the project lifecycle?
 
If the team has thought through the above indicative questions, the chances of having an effective tollgate increases manifold. An effective tollgate will have following benefits
1. Keep the project team honest and true to the project objective
2. Ensure that scope, cost and schedule creep DO not happen
3. Effective communication across various levels in the organization (as the sponsor and/or other stakeholders may not be too close to the project)
4. Any issues / challenges are brought to notice at the right time and to the right people so that solutions could be identified

Customer Satisfaction is a key metric for all organizations but more so for any marketing company. It is commonly known as CSAT score and is an average of ratings provided by customers who have used the organization's service / product. CSAT happens to be most common way of capturing Voice of Customer (VOC).
Business to Customer (B2C) company is where the product or service is offered directly to customer. E.g. Uber, Fast Food Joints, Netflix, FMCG companies, Airtel DTH etc. Sometimes the CSAT captured for such companies could be misleading. Below are the reasons and how best to tackle it
 
1. Intermediaries between the company and customer: Following a typical value chain, you will have Manufacturer --> Distributor --> Wholesaler --> Retailer --> Customer. Ideally speaking the immediate customer for Manufacturer is the Distributor, however it is a very narrow view by the organization and is not a good idea. In this value chain, the customer experience is influenced by a lot of other factors as well which may not be in direct control of the the manufacturer. However, it is only the manufacturer that captures the CSAT. 
2. Customer does not provide unbiased and specific CSAT score (even if there are not too many intermediaries between the provider and customer)
3. Average of scores is used to check for overall customer satisfaction. Even though average works in most cases, sometimes it ignores the extreme scores which might be of importance
4. Capturing of CSAT is outsourced to a third party which might not give it the due importance.  Even if it is done inhouse, one should be vary of the below
a. Customer segments or sample not selected appropriately: With B2C companies the customer base is very big and hence selecting the right sample sometimes becomes a challenge as the service offering could be different for say different regions
b. Questions in CSAT survey not designed effectively: CSAT could be done for multiple reasons. One of the most common drawback in a CSAT survey is that it usually focusses on the overall satisfaction of the customer. At times, the company might want to know about the additional features that they want to provide and if the survey does not capture these correctly in questions, then the effectiveness of the survey becomes a challenge
c. Inappropriate rating scale in the CSAT survey: Giving too many options to the customer might confuse them. Also it might possess a challenge in inferences
d. Too small a sample to make any meaningful inferences
e. Purpose of capturing CSAT is unclear
f. Data cleansing not performed. There are methods in which you could actually check if the customer feedback is consistent or not as one would ideally want to filter out those customers who have just filled the survey without giving due attention to it. Certain questions may not be answered etc. and these have to factored in during reporting
 
How to overcome the above:
1. Do not outsource the work that is core to the organization. E.g. You may purchase an Airtel DTH set from any electrical shop. However, it is only the Airtel servicemen who will come and install it
2. Ask the customer to be more specific when capturing feedback. E.g. If a less than 5 star rating is given in Uber, they ask customers to choose from multiple options for giving low rating. Some of the parameters are linked to driver while rest are for Uber
3. Increase the touch points with the customer i.e. the company should be easily accessible to the customers who want to give a feedback
4. If CSAT is a key performance indicator for the organization, do not outsource it and have competent team plan and execute on how CSAT has to be captured
5. Requesting customers to register the product. This could not be done for all B2C companies, however, it gives an opportunity to the organization to know about the customer
6. Value chain integration i.e. the manufacturer works with various partners in the value chain to inculcate the same values and attitude towards customer service. E.g. automobile companies
7. Keep the questionnaire relevant to the purpose of seeking the CSAT

Outlier – is a data point that is significantly different from the rest of the data point. Another definition of an outlier is a data point that significantly varies from the distribution of the data set. It is a common phenomenon to get outliers in any data one collects. There can be many reasons for outliers in a data set. Some of the more common reasons are as below
1. Experimental error
2. Measurement system error (either the gauge gave an incorrect reading or it was noted down incorrectly by the operator)
3. Data collected from 2 or more distributions
4. Special Cause occurrences or anomalies
5. Attempts of fraud
 
Outlier management may be a thesis topic in itself. However, I will try to keep it simple and practical here  
 
How to identify the outliers
1. Box Plot: It is the most common method to identify the outliers. An outlier will be marked in * in a box plot. These star marks are observations which are smaller or greater than 1.5 times IQR (Inter Quartile Range)
2. Control Charts: Any point outside the control limits is considered as an Outlier. Applying Nelson rules, one could also identify the unusual observations though these may not be significantly different from the rest of the data points
3. Modelling (like Regression Analysis, Probability distribution fitting etc.): whenever a model or a probability is fitted using historical data, it lets us know if there are any data points that do not fit the model. Usually such data points are outliers in the dataset which do not follow the fitted model
There are other statistical methods also to identify the outliers in any data set. The ones listed above are the basic ones.
 
What to do if you encounter an outlier?
First do not panic  And I write this because I have seen people panicking about outliers in their data sets. Getting outliers in a data set is not an outlier (it is very common)
Second, take a structured approach to resolve the Outliers
1. Find out the reason for the outlier. Best and the easiest method is to do a 5 Why analysis
2. Determine if the root cause is a part of the nature of the business or process (say a seasonal or cyclical effect etc). One will need common sense and business knowledge for this determination. If one does not have either   then it is advisable to work with an SME while doing this step. E.g. – the daily transactions during a month end show an unusual spike. However this spike is in the nature of banking business. Compare it with spike of transactions that happened due to demonetisation (Demonetisation is not the usual nature of business)
3. If the root cause is part of the nature of business, then the Outlier CANNOT be removed from the data set. Removing such an outlier would result in undesired data modification. If the outlier cannot be removed from the data set, then there are two possibilities
a. Outlier is beneficial for the process – in which case the root cause for the outlier should be replicated
b. Outlier is bad for the process – in which case the root cause for the outlier should be eliminated from the process (eliminating root cause is different from removing the data point. Elimination would ensure non recurrence of a bad outlier)
4. Alternatively, if the root cause if not part of the nature of business, then it may be EXCLUDED. It can be done in following two ways
a. Trimming i.e. deleting the outlier from the analysis
b. Winsorising i.e. replacing the outlier with the border case values (these border case values are not outliers)
 
If there is outlier or any data point that is excluded or winsorised, it should be clearly called out in the reporting
 

Kanabn Board is a tool that is used to depict the position of work in the process. As the question mentions itself, Kanban boards were primarily done for work allocation, monitoring the progress, decision making and reporting (at the end of the day). The most common usage of these boards were found in the daily huddles / daily team meetings / stand up meeting (what ever you might want to call it). It is mostly done on a white board where columns are created to track progress. These days there are multiple online versions of Kanban boards (but the joy of doing it is using post it notes or a marker pen on a white board - the good old way). 
 
The selection of manual or a systemic Kanban board is of lesser significance. What is more important is to track the progress. The simplest of Kanban board looks like
 

Source: Google Images (smartsheet.com)

Source: Google Images
 
The best feature about the Kanban board is how it has evolved across various industries and domains and how it is being utilized these days. The underlying feature of allocating work, tracking progress and decision making remain the same.
 
1. Kanban Board in Agile Software Development / Project Management

Source: Google Images search
 
2. Kanban Board in sales

Source: Google Images search
 
3. Kanban Board in Hiring

Source: Google Images search
 
4. Kanban Board in Incident Management

Source: Google Images search
 
5. Kanban Board in aviation (flight progress strips)

Source: Google Images search
Automated version of flight progress strips

Source: Google Images search
 
6. Kanban Board in Food Ordering

Source: Google Images search
 
You notice that there are multiple variations of Kanban board (manual or systemic) with all trying to help the business and/or customer know the progress of their product/service through the various process stages.
 
A more advanced or recent variation of Kanban board is a Swimlane Kanban Board where additional characteristics could also be tracked.

Source: Google Images search

Imagine you got to choose a solution from a list of probable solutions with the following conditions
1. all solutions will be evaluated one after the other
2. a solution if evaluated and rejected cannot be selected again
3. each solution has a different reward or benefit associated with it which you are unaware of. You will be aware of the rewards for only those solutions that have been evaluated
4. probable solutions are in no particular order
5. If you reject all solutions, by default the last solution will be selected even though it may no give you the best result
 
In such a scenario, the biggest challenge is to determine where to stop? Ideally you want the maximum reward or the best solution. However, you do not know if it is still to be evaluated or whether you have already rejecting it assuming that there is a better solution yet to be evaluated.
 
Optimal Stopping Problem provides a solution in such situations. It says that if you have to choose from 'n' solutions, always reject the first 'n/e' (where e = 2.71) solutions. Let us call this number as 'x'. Then select the next solution which is better than the 'x' solutions already evaluated. Working with this rule, you will select the best solution in about 37% of the cases (which as per Wikipedia is a very good success rate - i have not gone into the validation part of it yet). 'x' is basically a sample that is drawn from the population 'n'. And 'n/e' ensures that we have a sufficient sample size to consider.
 
E.g. picked from the classic 'Secretary Problem' associated with Optimal Stopping Problem (source: Wikipedia)
You have 100 applicants for the position of Secretary. All the above rules (points 1 through 5) apply here and you have to select the best candidate. As per the Optimal Stopping Problem, one should reject the first 100/2.71 ~ 37 candidates and then select the next candidate who is the best fit from among the candidates interviewed so far.
 
P.S. This will ideally not happen as the interviewer will always have the option to go back to any candidate. I do not have examples of any practical application of this this concept is new to me. Hoping someone shares practical examples here.

What are existing process controls?
Simply stated these are the measures taken in the process to ensure that defective items are not produced. 
 
What are the types of existing process controls?
There are two types 
1. Preventive
2. Detective
 
Preventive process controls have an effect on Occurrence ratings as they prevent the occurrence of the failure modes. 
Detective controls have an effect on Detection ratings as they help detect that a failure mode has occurred.
The same principle is applied when Mistake Proofing is done in the Control phase of a six sigma project. 
 
Let us take some examples
1. Production checklist that an agent uses is a preventive control as it ensures that processing is done correctly. If it is used, it will reduce the occurrence of defects. Audit checklist is a detective control as it checks if a defect has occurred or not
2. Using coding best practices is a preventive control as it reduces the number of bugs. Unit testing is a detective control as it checks for bugs present in the system
3. The spelling auto correction or highlighting of the word with red underline in MS word is a preventive control which reduces the number of spelling mistakes (while writing the article). However, a spell check in MS word is a detective control as it detects the incorrect spellings (after the article is written). By the way, in Excel there is only spell check and no auto correction
4. Preventive Maintenance is done in manufacturing. It reduces the occurrence of unplanned downtimes due to faults and hence impacts the occurrence rating
5. The "Caps Lock is on" warning is a preventive control in order to prevent instances of entering incorrect passwords and hence impacts the recurrence rating. The system not allowing to log in if an incorrect password is entered is a detective control which first checks for a valid password and hence impacts detection rating
6. In certain websites, one cannot enter alphabets if it is a numeric field. This is a preventive control which reduces the occurrence of incorrect entry in the field. The warning that some mandatory fields are left blank and system not allowed to go the next screen is the detective control where it checks for entries in all mandatory fields
7. Metal detectors and smoke detectors are examples of detective process controls. These will not impact the occurrence but will definitely have a bearing on the detection rating.
8. The seat belt not worn is a detective process control as it detects that the seat belt is not worn. In some advanced cars, the car will not start unless the seat belt is worn. This is a preventive control as it does not let the occurrence happen
 
In all the above examples, preventive controls impacts the occurrence rating while detective controls impact the detection rating.
 
To sum it up, while doing process FMEA, the below format is more useful where it clearly shows that preventive process controls impact Occurrence ratings and detective process controls impact Detection rating.
 

Source: APQP FMEA format sourced from Google images
 

Run Chart is a plot of the data points for a particular metric with respect to time. It is primarily used for following two purposes
 
1. Graphical representation of performance of the metric (without checking for any patterns in it). E.g. The scoring comparison in a cricket match. The runs are plotted on Y axis and X axis has overs (which is a substitute for time spent)

Source: The Telegraph
 
2. To check if the data from the process is random or if there is a particular pattern in it. These patterns could be one or more of the following
a. Clusters
b. Mixtures
c. Trends
d. Oscillations
 

Source: Minitab help section
 
Run chart if used for point number 2, performs following tests for randomness
- Test for number of runs about the median. This is used for checking Clusters and Mixtures.
Clusters are present if the actual number of runs about the median is less than the expected runs. This implies that there are data points in one part of the chart
Mixtures are present if the actual number of runs are more than expected runs. This implies that there are frequent crossings of the median line
- Test for number of runs up or down. This is used for checking Trends and Oscillations.
Trends are present if the actual number of runs is less than the expected runs. This implies that there is a sustainable drift in the process (either up or down)
Oscillations are present if the actual number of runs is more than the expected runs. This implies that the process is not steady
 
These are hypothetical cases with the below hypothesis
Ho - Data is random
Ha - Data is not random
p values are calculated for all the 4 patterns. A p value of less than 0.05 indicates acceptance of Ha implying that the particular pattern is present in the data set.
 
Absence of these patterns indicate that the process is random.
 
Advantages of Run chart over Control chart
Ideally control chart is a more advanced tool as compared to a run chart. However following situations warrant the use of run chart over a control chart
1. Run chart is preferred when we need a snapshot of the metric performance with time without taking into account the control limits or if the process is stable/unstable. E.g. like the scoring run rate comparison for cricket (refer the screenshot above)
2. One can start creating run chart without any prior data collection unlike in a control chart (where data is collected first to determine the control limits)
3. As a quick check to see if the process data is random or not. For doing such checks (clusters, mixtures, trends and oscillations) in a control chart, one would have to run all the Nelson tests (usually control charts are used with only one test i.e. any points outside 3 standard deviations and hence might not be able to detect such patterned data)
4. Apart from the above, it is easy to prepare and interpret a run chart in comparison to a control chart

Misuse of tools and techniques is a very common phenomenon. Misuse of a tool primarily happens because of two reasons
1. Intentional Misuse (it is better to call it as Misrepresentation)
2. Unintentional Misuse (due to lack of understanding of the concept)
 
Pareto analysis or the 80/20 rule is a prioritization tool that helps identify the VITAL FEW from TRIVIAL MANY. 80/20 implies that 80% of problems are due to 20% of the causes.
 
Intentional
Top 20% causes might not be the ones leading to bigger problems - usually it is observed that causes with smaller effects occur more often. Applying the Pareto principle will divert the focus of the team to the causes that have a smaller effect on the customer while the actual cause might be languishing in the trivial many Prioritization without keeping in mind the goal - Pareto will help if the significant contributors identified help us achieve the goal. However, it is seldom checked whether the VITAL FEW will help us achieve the goal or if there is a need to take a larger number of causes. As an example, if our goal is complete defect elimination, we will need to consider all causes. If our goal is elimination of 95% defects, we will need to cover more of the cause.  
Unintentional
Going strictly by the 80/20 rule - some people take the 80/20 principle in the literal sense. They will do a Pareto plot and blindly apply the 80/20 principle. What needs to be noted is that 80/20 is a rule of thumb and it is not necessary to always have 80/20 split. It could also be 70/30 or 90/10 Keeping the total to 100 = 80+20. This is one of the most common misunderstanding of the 80/20 rule where one beliefs that the sum should always be 100. It could be 80/15 or 75/25 as well Unclear about the purpose of using a Pareto Analysis. Pareto can be used while defining afocus area and also in Root Cause Analysis to identify significant contributors. In the former, data is for problems and their occurrence while in the later, it is causes and their occurrence. Due to lack of clarity of purpose, if problems and causes are clubbed together in the same Pareto, then meaningful inferences cannot be drawn. Treating Pareto as a non-living tool - Pareto is usually done once and the same result is treated as sacrosanct for a long period of time. Pareto chart only provides a time snapshot. Over a period of time, the defect categories or causes and their occurrence numbers might also change and hence if Pareto Analysis is done at different points of time, it might yield different results  
Some that could fit in both categories
Small data set - Pareto Analysis will help if you want to prioritize vital few from a big data set. Doing a Pareto analysis on 4-5 categories will seldom yield a good result Completely ignoring the trivial many - Pareto analysis helps identify the vital few but it does not say that one should ignore the trivial many. It simply states that first fix the vital and then move on to trivial. However, most people consider that if they fix the top 20%, they do not need to work on the remaining. Pareto can be used to continuously improve the process by repeatedly prioritizing the causes that you need to focus on Doing Pareto at a high level only - Like most of the tools in Root Cause Analysis, Pareto can also be used to drill down. E.g. Pareto can be done first to identify the top defect categories and then a second level Pareto can be done for the top defect categories (using the causes)

Process Mapping - is a diagrammatic representation of the flow of information and/or material in a process. It depicts all the process steps and the decisions taken in the process. Flowchart is the most common form of a process map. (as taken from Benchmark's Dictionary)
 
If you search the net, there are multiple levels of a process map that one would come across. Some content say there are 5 levels (level 0 through level 4) while some talk about 4 or 3 levels. It is all about the perspective and the level of detail that one captures in a process map. 
 
I am more comfortable working with 4 levels of Process Mapping which I am detailing below
 
Level 1 - SIPOC (high level view of the process or 30000 feet view of the process). At this level, the entire process is captured in about 3-5 very high level steps
Level 2 - Activity Level Process Map. At this level, all the various activities are covered. A particular high level step (as covered in SIPOC) might be broken down into 3-4 activity steps
Level 3 - Task Level Process Map. At this level, the tasks within the activities are captured and displayed
Level 4 - Key Stroke Level Process Map (more like an SOP). All the key stroke levels are displayed
 
Let us take an example of the process for planning and taking the flight for a vacation. 
 
Level 1 - SIPOC will look something like this

Level 2 - Activity Level Process Map. Expanding the step of 'Book the Ticket'. It will be broken into following activities

Level 3 - Task Level Process Map. Expanding the 'Payment' Activity

Level 4 - Key stroke level process map. Expanding the 'Enter Details on Website' task

 
The above is just for explanation sake. You will notice that at each subsequent level (or as we go deeper) more details are getting added.
 
Thumb rules for As-Is process mapping in a DMAIC project - 
1. It should never be done at SIPOC (Level 1) or Key Stroke Level (Level 4). SIPOC leaves out too many details while Key stroke will capture too many details
2. If a project is being done for the entire process, As-Is map should be prepared at an 'Activity' Level (Level 2)
3. If the project is being done at a sub-process level, one would prefer to prepare the 'Task' Level (Level 3) map
4. All decision points in the process should be captured in the As-Is process map (both Level 2 and Level 3 maps suffice this requirement)
5. The details in As-Is map should enable one to do the 'Process Door' analysis i.e. project lead should be able to apply some of the process map based tools like VA/NVA analysis to identify the wastes to be removed (again Level 2 and Level 3 will allow one to do process door analysis)
 
If the process is too complex and process map is too big, usually Level 2 map (activity level) is created for end to end process. Each Activity is then treated as a sub-process and a Level 3 (Task Level) is created separately.
 
Also, another practical approach in checking about the details being covered in the process map is whether you are working with the aspirational (or what it should be) or the actual process map (what it actually is). If the team responds like 'it should be done like this' or on similar lines, then the project lead should get a hint that team is working on an aspirational process map and in such cases the details are usually vague or unclear. However, if the team is working with the actual As-Is map, then the team will be confident of even the minutest details and statements will be like 'it is done in this way' etc.

What is Bessel's Correction? - It corrects the bias in the sample variance and standard deviation where the denominator is changed from N to N-1.
 
Why is it required? - It is required because it is difficult to determine the population variance and standard deviation. 
 
We all know, that due to the constraints of time and money, we prefer to work with samples and not populations. Once we have the sample, we apply Descriptive Statistics to get the sample statistics. These sample statistics are then used to make inferences about the Population Parameters (which happens to be our interest area).
 
Assume, that we need to determine the average and variance in weight of the Indian male. Here the average weight and variance in weight are the Population Parameters. And it is also obvious that we will not be able to get these numbers by considering the entire male population of India. Hence we revert to doing sampling. 
 
For example sake, let us assume that the average weight of the entire male population in India is 70 Kg. BUT we do not know it. Instead we need to determine it. So we picked a sample with a sample size of 10 and measured the weights
 

 
The sample average is 77 Kg. This is the sample statistic that is then assumed to be the population parameter. Therefore, one would assume that the population average weight is 77 Kg (instead of the actual 70 Kg).
 
Now, we need to estimate the population variance and standard deviation as well (remember weight is a continuous metric and hence we also need to determine the spread in the data).
 
Now in column 4 (in my example), I am working with the sample average of 77 kg and then computing the variance and standard deviations (variance = 201.8 and standard deviation = 14.2). While in column 6, I worked with the population standard deviation of 70 Kg (variance = 250.8 and standard deviation = 15.8). Ideally if the population mean was known, one should be working with 70 Kg (or column 6) but since it is unknown, one could only estimate it using the sample data and sample mean.
 
You will notice that the variance in column 4 (201.8) is less than variance as computed in column 6 (250.8). This highlights two important facts
 
1. The difference is the bias
2. This bias will always make the variance or standard deviation less than what it should be if population mean is considered
 
I have also calculated the variance and standard deviation with Bessel correction where (N-1) or 9 is used in the denominator (variance = 224.2 and standard deviation = 15.0). You will notice that the bias is corrected to some extent. This happens as the denominator is decreased, the overall value increases.
 
This is Bessel's correction which is applied when population variance and/or standard deviation is to be estimated from sample mean. Bessel correction is to applied only when population mean is unknown.
 
Another way of understanding the Bessel Correction is by the concept of 'Degrees of Freedom'. In my example, I had a sample size of 10. Now if I pick another sample and want to keep the sample mean same, then I have the freedom to change only 9 values. I will need to keep one value fixed. This fixed value is the pivot around which the other observations can change. The same concept is applied to a population. In order to keep the population mean same while picking multiple samples, one would need to keep at least 1 value fixed. Therefore if the population size is N, the degree of freedom becomes N-1. This same N-1 is used in the Bessel Correction.

DFA - Design for Assembly
 
Design for Assembly is one of the approaches in Design for Excellence (DFX). The X here can take many forms like Manufacturing, Safety, Cost, Service, Reliability etc. So how is DFA different from others and when should one go for it
 
DFA should be the preferred if the product that we are designing needs to be assembled and disassembled often. Because in such situations more than anything else, it is more important that the assembly should be
1. easy
2. efficient
3. effective
 
My top of the mind items that usually require to be assembled and disassembled are military guns and toys (especially track toys and Lego).
 
Elements that you need to consider in DFA
1. Number of parts - product with lesser number of parts is easier to assemble. Therefore the number of parts should be kept to a bare minimum. Parameters to check if a part can be removed or not are
a. Is it absolutely necessary to have the part made of a different material?
b. Does the part has a movement relative to the other parts of the product?
c. Is the part used as a fastener or for securing other parts?
2. Time taken to assemble or ease of assembly - there are quiet a few things that are considered here
a. Easy to handle parts - neither too small nor too big
b. Symmetry of the parts - symmetrical parts are easy to handle
c. Remove flexible, slippery, sticky parts along with parts that have sharp edges
d. Easy to insert - unidirectional, self inserting and easy to align
 
For a given design (after considering the above parameters), one could also compare the options using DFA-index i.e. Design for Assembly Index. It is given by the below formula
 
DFA = 100 Nm tm / ta
 
Nm - theoretical minimum number of parts
tm - minimum assembly time per part
ta - estimated total assembly time
 
Higher the DFA, better is the design for assembly.
 
Taking a hypothetical example below to explain
 
Soldiers are frequently required to disassemble and re-assemble their guns.
Soldiers will not be using revolvers, but typically their guns are also without too many screws and fasteners. Most of parts are easily assembled using uni-direction motion and fit into one another.
 
 Considering two revolvers here
 
Gun 1 - revolver with a rotating chamber for each bullet
Gun 2 - revolver with a magazine holder for bullets
 
Theoretical minimum number of parts in both the guns are same. Therefore Nm = 4
1. Barrel
2. Firing Pin
3. Ammunition Chamber (rotating or magazine)
4. Holder
 
tm - minimum assembly time per part remains 4 seconds.
 
ta - total estimated assembly time varies for each gun. In gun 1, it is 90 seconds because before closing you need to match the chamber with the barrel. In gun 2, it is 60 seconds.
 
DFA for gun 1 = 100*4*4/90 = 17.78 
 
DFA for gun 2 =100*4*4/60 = 26.67
 
DFA index for gun 2 is better, therefore as a manufacturer you should go for the design of 2nd gun.
 
Gun 1 - Rotating Chamber Revolver

Magazine Type Revolver

P.S. - Images only for illustration
 
 
 
 

Defects Per Million Opportunities (DPMO) is a very powerful metric in understanding the performance of the process. However, following are the pitfalls while using DPMO
 
1. Calculation of DPMO makes sense only if we have Discrete (Attribute) data. It is difficult to imagine the number of opportunities for a Continuous (Variable) data. E.g. if we are monitoring temperature with an USL of 30. Then what is an opportunity? Defect is easy to tell (temp. going above 30) but determining the opportunity is difficult. Should be each second / minute etc. It is for this reason that for Continuous Data we first calculate the Sigma Level which is then converted to DPMO
 
2. Even for Discrete Data, DPMO is a metric that could portray a false picture about the process performance. Let's take an example.
Number of Units made = 1000
Opportunities for error (OFE) = 10
Total # of Defects = 124
Total # of Defectives = 36 (i.e. all these 124 defects were found in 36 units only).
Now, one could calculate the following metrics
Defects Per Unit (DPU) = 124/1000 = 0.124
Defective % = 36/1000*100= 3.6%
Defects Per Million Opportunities (DPMO) = 124 / (1000*10)*1000000 = 12400
 
Converting all these numbers to Sigma Level
DPU = 0.124; Z (long term) = 1.19
Defective % = 3.6%; Z (long term) = 1.80
DPMO = 12400; Z (long term) = 2.24
 
It is evident from the above example that for the same process and same numbers, the DPMO provides the best Sigma Level which might be misleading. This is the primary reason that vendor always wants to calculate quality in terms of DPMO while the client always insists on either DPU or Defective %.
 
3. For DPMO calculation, all defects have same importance. This sometimes becomes a challenge in service industries where some of the defects are considered more critical than others
 
4. DPMO does not give any indication on the number of units which have defects. It is quite likely that most of the defects could be found in only a handful of units while on the other hand it could also mean that same kind of defect could happen in multiple units. E.g. in my example 124 defects happened only in 36 units. However, these 124 could also happen in 124 units (1 defect in each of the 124 units).