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# Applicability of Hypothesis Testing in DMAIC

DMAIC

DMAIC - is a data driven incremental process improvement methodology in the Six Sigma philosophy. It is acronym which stands for

D - Define
M - Measure
A - Analyse
I - Improve
C - Control

Hypothesis Testing

Hypothesis Testing - it is the process of using statistical tests to determine if the observed differences between two or more samples is statistically significant or not. A null hypothesis (Ho) is a stated assumption that there is no difference or the difference is due to a random chance while the alternate hypothesis (Ha) is a statement that there is a true difference. With the help of hypothesis testing, we arrive at one of the following conclusions.

1. Fail to reject the Null hypothesis (accept the Null hypothesis)
2. Reject the Null hypothesis (accept the Alternate hypothesis)

From a practical point of view, hypothesis testing allows to collect sample sizes and make decisions based on facts and it takes away the decisions based on gut feeling or experience or common sense. You have statistical proof of whatever you "feel" or "think" is right.

Applause for all the respondents- Prashanth Datta.

Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

## Question

Q﻿﻿. 139  In which phase of DMAIC, can hypothesis testing NOT be used? Explain with reasons.

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

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Benchmark Six Sigma Expert View by Venugopal R

If the question had been “During which phases of DMIAC TOH (Test Of Hypothesis) is largely made use of?” then the answer would be very obvious. Having asked to identify the phase where TOH does not find an application, we need to put some thoughts on every phase. My discussion here is not to be taken as a counter for any of the other responses, but may be viewed as a thought inciter.

TOH is a statistical tool that will help to compare a characteristic of a population with that of another population or standard and take a decision whether we have sufficient reason to believe they are equal or not…. The decision is based on evaluation of few samples that represent the population.

The phases of DMAIC that predominantly use the TOH are Analyse and Improve, and hence I will keep these 2 phases aside and look at others.

DEFINE phase is where the business case has to be evolved and the management buy-in obtained.

For example, if we need to decide on taking a project on  improving the market share of a product for a segment of customer across geographies; we may use TOH in the form of Chi-square comparison with a competitor’s product while trying to get a management approval for the business case.

MEASURE PHASE is where the Measurements systems need to be finalized and the baseline measurements need to be done.

An important aspect of measure phase is to carry out a Measurement Systems Analysis. MSA practices use ANOVA, which is built upon TOH principle, for determining the existence of parameters like linearity, bias etc.

As indicated, I am skipping discussion on Analyse and Improve phases, which are most popular for use of TOH.

CONTROL phase is where the focus is on monitoring & ensuring sustenance of the gains. The Control plans, Mistake proofing are very prevalent methods here. Control charts that would have been initiated during the Measure phase, continue to be used for monitoring performance in this phase. Usage of control charts is possible when we obtain sample data points periodically.

There could be certain situations where we may have practical difficulties in using a control chart. For example, consider a project whose objective is to improve Training effectiveness. Here, we can monitor the sustained effectiveness, only as and when the training happens. Another example could be a project whose objective is to improve the cycle time to ‘go live’ for New Product Development Process. Here, we can monitor the sustained effectiveness only when the next new product is developed and launched.

Wouldn't TOH find suitable application for comparing the performance indicators of an improved process with previous / or with a standard to assure sustenance, in such situations?

Let me conclude this discussion with the thought…. “TOH is well known to be applied during Analyse and Improve phases – however, aren't there situations in other phases, where it could find useful application for practical decision making?”

I look forward to see the views by others on this question.

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In order to answer above question, let me break down the question into two parts...

1. What is Hypothesis testing?

2. What is the most desired "output" from each phase of a DMAIC project?

While we understand that there are few tools and techniques that can be applied across Phases, what we need to caution exercise is not to force fit tools as it can result in experimentation and possibly delay the project timelines.

Now let's look at what Hypothesis testing is all about. Hypothesis testing is a part Inferential Statistics which is used to predict the behavior of the population by analyzing the sample data (two or more sets) to primarily determine if there is any "true" difference between the sample OR there are no differences in parameters between compared samples. The inferences are made through Null and Alternate Hypothesis. In a Null Hypothesis, we state that there are no differences or impact or the status remains status quo. However in Alternate Hypothesis we say that there is an impact or difference.

Further, the type of Hypothesis testing is determined by the type of input(x) and output(y) data type ie if it is discrete or continuous data.

Let's now delve on the second part of the question which is desired output from each phase of a DMAIC project

a. Define Phase ----: Desired output is Approved Project Charter

b. Measure Phase ---: Desired output is Baseline - Current As Is performance of identified focus CTQ

c. Analyse Phase ---: Desired output is Validated root cause(s) or Critical Xs

d. Improve Phase ---: Desired output is Selected Solution leading to improved results

e. Control Phase ---: Desired output is Control Plan.

Given significant usage of data analytics happen in Analyze and Improve phase it will be more appropriate to use the Hypothesis testing during these two phases to  validate critical x(s) and to confirm if implemented solution(s) have really made the desired change respectively.

Given the desired output for Define, Measure and Control phase focuses on setting up Project Charter, drawing the Baseline performance of to be improved metric(Y) and have the Control Plan in place to ensure the desired results are performing within limits, it could possibly be a force fit if Hypothesis testing is implemented in these Phases.

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As mentioned by Venugopal, there may be a need to use Hypothesis testing in any of the phases. Some examples are given below

1. Define phase - To check if the current performance is indeed below the expected performance. improvement (difference from existing performance)

2. Measure phase - During MSA as mentioned by Venugopal. After capability assessment - to verify if the Goal really indicates a significant improvement over the current performance.

3. Analyze Phase - To verify root causes.

4. Improve Phase - To compare before and after improvement performances.

5. Control Phase - To check if improved performance has been sustained and no difference is found after controls are put in place.

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