Phases of Six Sigma Methodology [DMAIC Framework]

# Phases of Six Sigma Methodology [DMAIC Framework]

Published
04th Jul, 2024
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Six Sigma is basically the application of Statistical formulas and Methods to eliminate defects, variation in a product or a process. For example, if you want to find the average height of male population in India, you cannot bring the entire population of more than 2 billion into one room and measure their height for a scenario like this we take samples that is we pick up a sample (people) from each state and use statistical formulas to draw the inference about the average height of male population in a population which is more than 2 billion.

In this article, we discuss the six sigma methodology and provide an overview of the steps in each phase and the tools that can be used in each phase.

## What is Six Sigma Methodology?

The Six Sigma methodology was based on the bell curve created by Carl Frederick Grauss in the 19th century. In the 1920s, a founder member of the Institute of Mathematical Statistics, statistician Cark Shewhart, showed that the process had deviated from the mean by 3 sigmas and had to be corrected. Fast forward to the 1970s, Art Sundry, Senior Executive at Motorola, complained that there was a lack of consistent quality products in the company. Bill Smith responded to the complaint by implementing the six sigma methodology in 1986. Over time, other management improvement strategies influenced the system like Zero Defects and Total Quality Management.

Example:

One more example would say a company manufactures pistons used in motor cycles the customer demand is that the piston should not a diameter more than 9 cm and less than 5 cm anything manufactured outside this limits is said to be a variation and the six sigma consultant should confirm that the pistons are manufactured within the said limits else if there is variation in the range then the company is not operating at 6 sigma level it is operating at a very low level.

A company is operating at six sigma level implies that there are only 3.4 defects per million opportunities for example an airline company operating at six sigma level means that it loses only 3.4 baggage’s per million of the passenger it handles.

Below is Shown the Six Sigma Table and a graph explaining the meaning of various levels of Six Sigma.

 Sigma Level Defect Rate Yield Percentage 2 σ 308,770 dpmo (Defects Per Million Opportunties) 69.10000 % 3 σ 66,811 dpmo 93.330000 % 4 σ 6,210 dpmo 99.38000 % 5 σ 233 dpmo 99.97700 % 6 σ 3.44 dpmo 99.99966 %

Six Sigma is Denoted by the Greek alphabet σ which is shown in the table above and is called as Standard deviation. The father of Six Sigma is Bill Smith who coined the term Six Sigma and implemented it in Motorola in the 1980’s.

## Phases of Six Sigma Methodologies

Six Sigma is implemented in five phases which are Define, Measure, Analyze, Anova, Improve, Control. We will discuss each phase in brief and the various six sigma methods used.

## 1. Define

The objectives within the Define Phase which is first phase in DMAIC framework of Six Sigma methodology are:-

### Define the Project Charter

• Define scope, objectives, and schedule
• Define the Process (top-level) and its stake holders
• Select team members
• Assemble and train the team.

Project charters the charter documents the why, how, who and when of a project include the following elements

• Problem Statement
• Scope
• Deliverables
• Team members
• Project schedule (using GANTT or PERT as an attachment)
• Other resources required

Tools that can be used in the Define phase

• CTQ Definitions
• DMAIC Work Breakdown Structure
• Process Flowchart
• Project Charter
• SIPOC Diagram
• RACI Diagram
• Stakeholder Analysis
• Voice of the Customer gathering

### Work break down Structure

It is a process for defining the final and intermediate products of a project and their relationship. Defining Project task is typically complex and accomplished by a series of decomposition followed by a series of aggregations it is also called top down approach and can be used in the Define phase of Six Sigma framework.

Central tendency is defined as the tendency for the values of a random variable to cluster round its mean, mode, or median.

Where mean is the average for example if you have taken 10 sample of pistons randomly from the factory and measured their diameter the average would be sum of the diameter of the 10 pistons divided by 10 where 10 the number of observations the sum in statistics is denoted by ∑. In the above table X, Xi are the measures of the diameter of the piston and µ , XBar is the average.

Mode is the most frequently observed measurement in the diameter of the piston that is if 2 pistons out 10 samples collected have the diameter as 6.3 & 6.3 then this is the mode of the sample and median is the midpoint of the observations of the diameter of the piston when arranged in sorted order.

From the example of the piston we find that the formulas of mean, median , mode does not correctly depict variation in the diameter of the piston manufactured by the factory but standard deviation formula helps us to

find the variance in the diameter of the piston manufactured which is varying from the customer mentioned upper specification limit and lower specification limit.

The most important equation of Six Sigma is Y = f(x) where Y is the effect and x are the causes so if you remove the causes you remove the effect of the defect. For example headache is the effect and the causes are stress, eye strain, fever if you remove this causes automatically the headache is removed this is implemented in Six Sigma by using the Fishbone or Ishikawa diagram invented by Dr Kaoru Ishikawa.

## 2. Measure Phase

In the Measure phase we collect all the data as per the relationship to the voice ofcustomer and relevantly analyze using statistical formulas as given in the above table. Capability analyses is done in measure phase.

The process capability is calculated using the formula CP = USL-LSL/6 * Standard Deviation where CP = process capability index, USL = Upper Specification Limit and LSL = Lower Specification Limit.

The Process capability measures indicates the following

1. Process is fully capable
2. Process could fail at any time
3. Process is not capable.

When the process is spread well within the customer specification the process is considered to be fully capable that means the CP is more than 2.In this case, the process standard deviation is so small that 6 times of the standard deviation with reference to the means is within the customer specification.

### Steps in the Measure phase

• Developing data collection plan
• Collecting the data
• Beginning Developing y = f(x) relationship
• Defining unit, opportunity, and defect
• Detailing the process map of different, appropriate areas
• Determining sigma baseline and process capability
• Validating the measurement system

### Tools that can be used in the Measure phase

• Benchmarking
• Data Collection Plan/Example
• Measurement System Analysis
• Process Flowchart & Value Stream Map
• Process Sigma Calculation
• Voice of the Customer Gathering

Example: The Specified limits for the diameter of car tires are 15.6 for the upper limit and 15 for the lower limit with a process mean of 15.3 and a standard deviation of 0.09.Find Cp and Cr what can we say about Process Capabilities ?

Cp= USL-LSL/ 6 * Standard deviation = 15.6 – 15 / 6 * 0.09 = 0.6/0.54 = 1.111

Cp= 1.111

Cr = 1/ 1.111 = 0.9

Since Cp is greater than 1 and therefore Cr is less than 1; we can conclude that the process is potentially capable.

## 3. Analyze Phase

In this Phase we analyze all the data collected in the measure phase and find the cause of variation. Analyze phase use various tests like parametric tests where the mean and standard deviation of the sample is known and Nonparametric Tests where the data is categorical for example as Excellent, Good, bad etc.

Parametric Hypothesis Test – A hypothesis is a value judgment made about a circumstance, a statement made about a population .Based on experience an engineer can for instance assume that the amount of carbon monoxide emitted by a certain engine is twice the maximum allowed legally. However his assertions can only be ascertained by conducting a test to compare the carbon monoxide generated by the engine with the legal requirements.

If the data used to make the comparison are parametric data that is data that can be used to derive the mean and the standard deviation, the population from which the data are taken are normally distributed they have equal variances. A standard error based hypothesis testing using the t-test can be used to test the validity of the hypothesis made about the population. There are at least 3 steps to follow when conducting hypothesis.

• Null Hypothesis: The first step consists of stating the null hypothesis which is the hypothesis being tested. In the case of the engineer making a statement about the level of carbon monoxide generated by the engine , the null hypothesis is

H0: the level of carbon monoxide generated by the engine is twice as great as the legally required amount. The Null hypothesis is denoted by H0

• Alternate hypothesis: the alternate (or alternative) hypothesis is the opposite of null hypothesis. It is assumed valid when the null hypothesis is rejected after testing. In the case of the engineer testing the carbon monoxide the alternative hypothesis would be

H1: The level of carbon monoxide generated by the engine is not twice as great as the legally required amount.

• Testing the hypothesis: the objective of the test is to generate a sample test statistic that can be used to reject or fail to reject the null hypothesis .The test statistic is derived from Z formula if the samples are greater than 30.

Z = Xbar-µ/σ/ √n

If the samples are less than 30, then the t-test is used

T= X bar -µ/ s/√n where X bar and µ is the mean and s is the standard deviation.

• Sample t Test : such as an ideal off center (Mean v/s Target) this test is used to compare the mean of a process with a target value goal to determine whether they differ it is often used to determine whether a process is
• Sample Standard Deviation: This test is used to compare the standard deviation of the process with a target value such as a benchmark whether they differ often used to evaluate how consistent a process is
• 2 Sample T (Comparing 2 Means): Two sets of different items are measured each under a different condition there the measurements of one sample are independent of the measurements of other sample.
• Paired T: The same set of items is measured under 2 different conditions therefore the 2 measurements of the same item are dependent or related to each other.
• 2-Sample Standard: This test is used when comparing 2 standard deviations
• Standard Deviation test: This Test is used when comparing more than 2 standard deviations

Non Parametric hypothesis Tests are conducted when data is categorical that is when the mean and standard deviation are not known examples are Chi-Square tests, Mann-Whitney U Test, Kruskal Wallis tests & Moods Median Tests.

### Steps in the Analyze phase

• Defining performance objectives
• Determining important few x’s and y=f(x) relationship
• Identifying value as well as non-value added process steps
• Identifying sources of variation
• Determining root causes
• Prioritize the root causes

### Tools that can be used in the Analyze phase

• 5 Whys
• Cause and Effect
• Fishbone Diagram
• Histogram
• Hypothesis Testing
• Non-Normal Data Analysis
• Pareto Chart
• Process Map Analysis and Review
• Regression Analysis
• Run Chart
• Scatter Plot
• Statistical Analysis
• Time Series

## 4. Anova

If for instance 3 sample means A, B, C are being compared using the t-test is cumbersome for this we can use analysis of variance ANOVA can be used instead of multiple t-tests.

ANOVA is a Hypothesis test used when more than 2 means are being compared.

If K Samples are being tested the null hypothesis will be in the form given below

H0: µ1 = µ2 = ….µk

And the alternate hypothesis will be

H1: At least one sample mean is different from the others

If the data you are analyzing is not normal you have to make it normal using box cox transformation to remove any outliers (data not in sequence with the collected data).Box Cox Transformation can be done using the statistical software Minitab.

## 5. Improve Phase

In the Improve phase we focus on the optimization of the process after the causes are found in the analyze phase we use Design of experiments to remove the junk factors which don’t contribute to smooth working of the process that is in the equation Y = f(X) we select only the X’s which contribute to the optimal working of the process.

Let us consider the example of an experimenter who is trying to optimize the production of organic foods. After screening to determine the factors that are significant for his experiment he narrows the main factors that affect the production of fruits to “light” and “water”. He wants to optimize the time that it takes to produce the fruits. He defines optimum as the minimum time necessary to yield comestible fruits.

To conduct his experiment he runs several tests combining the two factors (water and light) at different levels. To minimize the cost of experiments he decides to use only 2 levels of the factors: high and low.

In this case we will have two factors and two levels therefore the number of runs will be 2^2=4. After conducting observations he obtains the results tabulated in the table below.

 Factors Response Water –High Light High 10 days Water high – Light low 20 days Water low – Light high 15 days Water low – Light low 25 days

Steps in the Improve phase

• Assessing potential solution’s failure modes
• Correcting or re-evaluating potential solutions
• Defining the potential system’s operational tolerances
• Developing potential solutions
• Performing design experiments
• Validating potential improvements through pilot studies

### Tools that can be used in the Improve phase

• 5 S
• Brainstorming
• Design of Experiments
• Failure Modes and Effects Analysis
• House of Quality
• Mistake Proofing
• Pugh Matrix
• QFD
• Simulation Software

## 6. Control Phase

In the Control phase we document all the activities done in all the previous phases and using control charts we monitor and control the phase just to check that our process doesn’t go out of control. Control Charts are tools used in Minitab Software to keep a check on the variation. All the documentation are kept and archived in a safe place for future reference.

### Steps in the Control phase

• Closing project and finalizing documentation
• Defining and validating control system and monitoring
• Determining process capability
• Developing handoff to process owner and transfer plan
• Developing procedures and standards
• Implementing statistical process control
• Verifying cost savings/avoidance, benefits, and profit growth

### Tools that can be used in the Control hase

• Control Charts
• Control Plan
• Cost Savings Calculations
• Process Sigma Calculation

Each of the five DMAIC phases come together in the implementation of six sigma methodology, which can turn the business around for any organization.

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## Implementation of DMAIC

In this section, we will take a look at two examples of DMAIC implementation that use varied continuous improvement models for specific applications:

### Floor yield improvement in a manufacturing shop

The first example is of a repetitive manufacturing process, where the yield is increased by making products:

• Define: Identify the product flow, the specific products, and the goal
• Measure: Define the metrics that will be used as the first-pass yield, rolled first-pass yield, or OTIFNE; it will also include monitoring for time to gather baseline data that is statistically meaningful.
• Analyze: Look for trends, assess the standard deviation and mean from data, address, and identify outliers; this also includes identifying variables impacting the yield using root cause analyses.
• Improve: Define and put in place countermeasures o address the identified root causes; monitor the process to confirm the achievement of desired yield improvement.
• Control: Implement measures to maintain improved performance.

### Impact on Hospital outcomes through evidence-based care

The second example shows how improvements can be driven in a hospital through observation and usage of principles of Lean in a DMAIC framework or six sigma methodology:

• Define: Ask questions like how often infections occur in a hospital, over what time frame will infection’s treatments will improve.
• Measure: Measuring the current state
• Analyze: Determine the root cause like the procedures introducing contamination and specific process steps.
• Improve: Implement a checklist like basic hygiene steps, sterile barriers, disinfectants, enhancing equipment, and avoiding susceptible areas.
• Control: Incorporate reinforcement and training to internalize the process and improve the culture; this can also include empowerment of nursing staff to ensure enforcement of the measures introduced.

## Conclusion

From the paper we come to understand that selection of a Six Sigma Project is Critical because we have to know the long term gains in executing these projects and the activities done in each phase the basic building block of the Six Sigma methodology is the define phase where the problem statement is captured and then in measure phase data is collected systematically against this problem statement which is further analyzed in Analyze phase by performing various hypothesis tests and process optimization in Improve phase by removing the junk factors that is in the equation y = f(x1, x2,x3…….) we remove the causes x1, x2 etc.

Experiments and factorial methods. Finally we can sustain and maintain our process to the optimum by using control charts in Control Phase.

1What is the formula used in Six Sigma?

Six sigma is based on the mathematical formula of the breakthrough equation i.e. representation of the relationship between the input and output variables i.e. x and Y respectively. The basic formula of six sigma is calculated as

Y= f(x) where, Y = output variable/outcome; x = input variable that affects the output

With this formula, six sigma aims to build a relationship between the inputs and outputs to reduce the number of defects and variations in the processes.

2What is the formula for Six Sigma defect?

Six sigma defects are based on DPMO or NPMO i.e. Defects per million opportunities or nonconformities per million opportunities which is the ratio of the number of defects in the sample to the number of defect opportunities multiplied by 1 million. Therefore, the formula for six sigma defects is:

DPMO = [total number of defects in the sample / (sample size units x number of defect opportunities per unit in the sample)] x 1,000,000

3What is the sigma method used to determine?

Six sigma is a quality methodology used to improve the business processes by identifying areas of challenges i.e. defects and errors, minimizing the occurrences of process variations, and increasing overall quality and efficiency in the process. It is a data driven approach used to determine predictability and improvise processes.

4What type of method is Six Sigma?

Six sigma is a data driven and disciplined approach to analyze each step of the process based on quality tools and techniques such as DMAIC (Define, Measure, Analyze, Improve, Control), DMADV (Define, Measure, Analyze, Design, Verify), Root Cause Analysis, Five Why Analysis, and Critical to Quality (CTQ) method.

5What type of method is Six Sigma?

Six sigma is a process improvement application methodology used when there are multiple unknowns, process challenges and variations that are widespread or undefined, and when complex problems are required to be solved. It also applies to cases where the processes are closely related to costs and revenues in the project.

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