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Analyze Phase (DMAIC)

Analyze phase is the third phase of DMAIC. The main activity in the Analyze phase is to identify the potential root cause of the problem and arrive at the actual root cause. In other words, let’s use the data obtained in the Measure Phase to identify the root causes that we want to fix. One of the key activities here is process characterization: identifying and quantifying the significant sources of variation in the process.

During the measure phase of DMAIC, the project team should clearly understand the problem statement. Six sigma teams use various statistical tools in the Analyze phase to identify the root cause(s).

Six Sigma Phases

Six Sigma is a systematic problem-solving approach that is centered around defect elimination and variation reduction. This leads to process improvement.

One of the principal tools in Six Sigma is using the DMAIC methodology. (Also see DMAIC Overview). Particularly, DMAIC is a logical framework that helps you think through and plan improvements to a process to achieve a Six Sigma level of excellence.

There are five phases that are used in the DMAIC method.

During the Analyze phase, use the data-driven approach to identify the problem’s root cause(s). Often, teams conclude the root cause without proper analysis; hence, the Analyze phase is critical in DMAIC. At the end of this phase, the six sigma team identifies the most significant impact on CTQs.

Analyze Phase of DMAIC Goals

Use measure data to identify the probable causes of the problem
Identify the actual root cause using brainstorming, 5 why, and other techniques
Find the critical root cause that has the highest impact on CTQ
Verify the root causes using appropriate statistical tools and techniques like hypothesis testing

Analyze Phase of DMAIC Overview

The Analyze phase is approximately 2 to 3 weeks process based on the project inputs. In particular, all the relevant stakeholders’ involvement is key in identifying the root causes.

The Analyze phase is all about reviewing the process map to improve efficiency, listing the probable root causes, and identifying important factors/inputs that greatly impact the output using statistical tools like hypothesis testing. Multiple tools and concepts are available in the Analyze phase of Six Sigma.

Process map Analysis (Identify Value and non Value activities)

Detailed Process Map: A process map is a tool that graphically shows the inputs, actions, and also outputs of a process in a clear, step-by-step map of the process.

The process map illustrates the relationship between inputs (X) and outputs (Y). Create a process map of all the activities required to convert raw materials into output (Y) and then identify the critical to quality (CTQs) factors in the process.

Value Stream Mapping: Value stream mapping visually represents the flow of materials and information throughout the organization. Value stream mapping constitutes all the value-added as well as non-added values required to make the product. It consists of the process flows starting from the raw materials to making the product finally available in the hands of the customers.

Waste Analysis

Classic Wastes are looked at as a blockage against productivity. It is not possible to enhance the top line in a highly competitive world by increasing the prices. Hence, it is necessary to build effective systems, and one of the ways is to understand the ‘wastages’ and eliminate them. Following are the seven classical wastes in an organization.

Overproduction: This wastage occurs when the production output is much more than the requirement of the next process or customer.
Inventory: Inefficient planning of inventory and ordering either less or more of inventory further leads to wastage.
Waiting: Wastage of the operator time in avoidable events like failure of equipment, late arrival of necessary tools, lack of trained staff, inefficient planning, and idle machine time leads to wastage.
Motion: Wastage due to unnecessary movement of parts and products between different processes and places.
Defects: Defects and broken parts add to customer dissatisfaction, and the company would be busy solving problems, reworking, and even paying off to the customers for the defects.
Over-processing: Unnecessary performance of any process due to design failure or usage of poor quality tools and processes.
Transport & Handling: This Muda can be observed in many activities, like shipping damage and packing material wastage.

List Potential Causes

The focus of analyze phase is to identify the possible root causes of the problem.

Root Cause Analysis: Root cause analysis is a collection of tools and processes we can use to determine the most important causes for an issue we are trying to resolve.

Organize the potential causes to show relationships

Brainstorm: Brainstorming is a method for generating a large number of creative ideas in a short period of time.
5 Whys: It is a simple tool to ask “Why” until we can’t ask “Why” again. 5 is a good rule of thumb (of course arbitrary). By often querying “Why”, we can quickly reach the underlying causes of a problem.
Fishbone Diagram: It is a pictorial diagram showing possible causes (process inputs) for a given effect (process outputs). In other words, it is a visual representation to find out the cause(s) of a specific problem.
Fault Tree Diagram: Fault tree analysis (FTA) is a graphical tool to explore the causes of system-level failures. It uses boolean logic to combine a series of lower-level events. It is basically a top-down approach to identify the component level failures (basic event) that cause the system level failure (top event).
Affinity Diagram: An affinity diagram is a good technique for identifying & displaying potential root causes for unfamiliar problems.
Tree Diagram: A Tree diagram helps you break down big concepts into progressively greater detail. The idea here is to systematically break down a concept into its constituent pieces.
Interrelationship Diagram: An interrelationship digraph (aka network diagram) helps you see relations and influences between several concepts. You can also use it to identify critical issues and key drivers of a problem.
FMEA: Failure Mode Effects Analysis (FMEA) is a tool that helps us anticipate what might go wrong with a product or process.

Prioritize final list

Put the diagram of the current process steps, defined outputs & the factors influencing those outputs, and a table listing the process analysis results. Include all data sources used, how data was collected, and the tools used in analyzing the data (hypothesis testing). Use this to prioritize the final Potential Cause list.

Data Analysis & Identify the Root Cause

After the six sigma team identifies the Potential Cause list, it is required to determine its true root cause. This is where we use various methods and mathematical tools to verify our assumptions. We can also use advanced techniques to compare data against each other and even to make predictions.

Mathematical Tools

Central Limit Theorem: The Central Limit Theorem states that the distribution of the sample means approaches normal regardless of the shape of the parent population.

Distribution Types: Data distribution is a function that specifies all possible values for a variable. It also quantifies the relative frequency (probability of how often they occur). It’s important to determine the kind of distribution of that population. It helps to choose the correct statistical methods when analyzing it.

Continuous distribution

A continuous distribution containing infinite (variable) data points that may be displayed on a continuous measurement scale.

Normal Probability: It is a symmetrical bell shape curve with higher frequency (probability density) around the central value. The frequency sharply decreases as values are away from the central value on either side.
Lognormal Distribution: A continuous random variable x follows a lognormal distribution if its natural logarithm, ln(x) follows a normal distribution.
F Distribution: The F distribution extensively use to test for equality of variances between two normal populations
Chi-Square: The chi-square distribution results when independent variables with standard normal distribution are squared and summed.

Exponential Distribution: The exponential distribution is the probability distribution of the widely used continuous distributions. Often used to model items with a constant failure rate.
Student’s t Distribution: t distribution or student’s t distribution is a bell shape probability distribution, symmetrical about its mean. Also, see Paired t-Test and Two-sample t-test

Discrete Distributions

A discrete distribution resulting from countable data that has a finite number of possible values. Furthermore, discrete distributions can be reported in tables, and the respective values of the random variable are countable. Ex: rolling dice, choosing a number of heads, etc.

Binomial Probability Distribution: The binomial distribution measures the probability of the number of successes or failure outcomes in an experiment on each try.
Poisson Distribution: The Poisson distribution is the discrete probability distribution that measures the likelihood of several events occurring in a given time period when the events occur one after another in time in a well-defined manner.
Hypergeometric Distribution: Hypergeometric distribution is a discrete distribution that measures the probability of a specified number of successes in (n) trials, without replacement, from a relatively large population (N). In other words, sampling without replacement.

Odd distribution

Analyzing Bivariate Data: bivariate distribution is a probability of a certain event occurring in case two independent random variables exist. It may be a continuous or discrete distribution.
Bi-modal: A bi-modal distribution that has two modes. In other words, two outcomes are most likely to compare the outcomes of their region.

Hypothesis Testing

Hypothesis Testing is a key procedure in inferential statistics to make statistical decisions using experimental data. It is basically an assumption that we make about the population parameter. There are two basic types of errors that can occur in hypothesis testing:

Type A or 1 Error: The null hypothesis is correct but rejected incorrectly.
Type B or 2 Error: The null hypothesis is incorrect, but is not rejected.

Design of Experiments (DOE)

Design of Experiments aims to establish optimal process performance by finding the right settings for key process input variables. It is a way to intelligently form frameworks to decide which course of action you might take. See DOE terminology here.

Factorial Designs: Full Factorial Design leads to experiments where at least one trial is included for all possible combinations of factors and levels.
Fractional Factorial Designs: Because full factorial design experiments are often time- and cost-prohibitive when a number of treatment factors are involved, many people choose to use partial or fractional factorial designs.
Taguchi Loss Function Robust approach in design is a key aspect as it produces reliable design both during manufacturing and also during product use.
Evolutionary Operations (EVOP): The basic purpose of the evolutionary operations methodology (EVOP) is to improve a process through systematic changes in the operating conditions of a given set of factors.
Latin Square: Latin square design is a fractional factorial experiment that requires less experimentation to determine the main treatment results.
Graeco-Latin Square Design: Graeco-Latin square design is similar to Latin square design, but in some designs where the experimenter needs to block in the three directions. It is also useful to eliminate more than two sources of variability in an experiment.
Hyper-Graeco-Latin Square Design: A Hyper-Graeco-Latin Square design is to study of treatments with more than three blocking factors.

Analyze Phase of DMAIC Deliverables

Detailed process map
Identify value and non value activities
List of potential causes
Data Analysis and results
“Vital few” x’s

Analyze Phase (DMAIC) Videos

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Data Analysis

Posted by Ted Hessing

Data analysis is a fundamental requirement in the Six Sigma methodology for identifying process inefficiencies and reducing defects. It helps identify root causes of process variation and defects, allowing organizations to address underlying issues rather than just symptoms.

Furthermore, data analysis enables data-driven decision-making, ensuring that decisions are based on evidence rather than assumptions. Data analysis also helps quantify the impact of process changes, allowing organizations to measure improvement objectively and track progress over time.

It enhances accountability and ensures that efforts are focused on improvement in the right direction. Hence, data analysis is essential in Six Sigma for identifying problems, guiding improvements, and ensuring desired outcomes to improve the process.

Why Data Analysis?

Why should we do data analysis? Brilliantly put in the movie Moneyball and applicable to Six Sigma, it’s so we can get past biases and to the truth. We must be careful. The goal isn’t to eliminate judgment. We want to use data to make better decisions.

Data analysis in DMAIC

Six Sigma team systematically examines the data collected in the Define and Measure phases to identify causes for variations in the process. During the Analyze phase, the team identifies the areas for process optimization and eliminating waste, to enhance efficiency and quality.

Moreover, data analysis plays a crucial role in evaluating the effectiveness of improvement initiatives during the Improve phase. In the control phase, ensuring that desired outcomes are sustained over time through the implementation of control mechanisms such as statistical process control (SPC).

By using data analysis, organizations can predict future performance, identify challenges, and proactively address them. It helps organizations to focus on continuous improvement and enhance customer satisfaction.

Types of Data

Data is a set of values that can be either qualitative or quantitative. It may be a number, a measurement, an observation, or even a description.

Qualitative data: Qualitative data, also known as non-numeric data, essentially describes the traits of a value or data point. It consists of a finite number of possible categories into which each data point may fall.

Types of Qualitative Data

Nominal data: A type of descriptive data with more than two categories; it can refer to the names or labels of the data points. For example, Hair color: black, brown; Gender: male or female.
Ordinal data: Ordinal data provides good information about the order of choices. In other words, it arranges information in a particular order without indicating a specific relationship between items. Example: pass or fail, customer service, good or bad, etc.

Quantitative data: It is also known as numerical data. The data points are counts or measurements. Unlike Qualitative data, it consists of an infinite number of possible categories into which each data point may fall. The Quantitative data is further divided into two data types:

Discrete data: The data is discrete if the measurements are whole numbers or counts. For example, the number of customer complaints, weekly defects data, etc.
Continuous data: The data is continuous if the measurement takes on any value, usually within some range. For example, Stack height, distance, cycle time, etc.

Discrete Data

Discrete data comprises distinct, separate values with clear boundaries between each possible value. It assumes specific, individual values and cannot be infinitely subdivided. Typically, discrete data is counted and often represented by whole numbers. Examples: Number of defects in a product, or number of red balls in a bowl.

Discrete Data analysis tools

Discrete data analysis involves techniques specifically tailored for data that consists of distinct, countable values. Here are some common tools used for analyzing discrete data:

Contingency Table

A contingency table, also known as cross-tabulation or a two-way frequency table, typically summarizes and analyzes the relationship between two categorical variables. Contingency tables are a type of table in a matrix format that displays the frequency distribution of the variables. In other words, contingency tables represent a 2-way classification table containing frequencies of how often things appear, and they can determine if two variables are independent or significantly associated.

Pareto Chart

The Pareto Chart (Pareto Diagram) is a graphical tool that maps and grades business process problems from the most recurrent to the least frequent. In other words, it helps identify the most frequently occurring problems or separates the vital few from the trivial many. The Pareto Chart combines both a bar chart and a line chart. The bar chart shows the frequency of occurrence or defects, while the line graph displays the cumulative data percentage in descending order.

Attribute charts are a kind of control chart to display information about defects and defectives. They help you visualize the enemy: variation!

Defect:

A defect is a non-conformity that does not meet the customer’s requirements. A product or service may have one or more defects but is defective only if defects prevent the product from functioning.

Defect analysis is carried out based on the Poisson distribution (evaluates the rate of defects in the process) using the following methods.

c chart: c chart also known as the control chart for defects (counting the number of defects), is generally used to monitor the number of defects in constant-sized units. There may be a single type of defect or several different types, but the c-chart tracks the total number of defects in each unit, assuming that the underlying data approximate the Poisson distribution.

u chart: u chart is also known as the control chart for defects per unit chart. It is generally used to monitor the count type of data where the sample size is greater than one. There may be a single type of defect or several different types, but the u chart tracks the average number of defects per unit, and it assumes the underlying data approximate the Poisson distribution.

Defective:

A product or service that has one or more defects and it is not suitable for use. In other words, a product or service is defective if the defect(s) existing in it affects its functionality.

Using the following methods, a defective analysis is carried out based on Binomial distribution (evaluates the proportion of defectives in the process).

p chart: p chart is also known as the control chart for proportions. It is used to analyze the proportions of non-conforming or defective items in a process. It uses a Binomial Distribution to measure the proportion of defective or non-conforming units in a sample.

np chart: np chart is also known as the control chart for defectives (d-chart). It generally monitors the number of non-conforming or defective items in the measurement process. It uses binomial distribution to measure the number of defective or non-conforming units in a sample. An np chart is very similar to a p chart. np chart plots the number of items, while the p chart plots the proportion of defective items.

Continuous Data

Continuous data encompasses values that can take on any value within a given range and allows measurement to any level of precision. It is characterized by its infinite divisibility, lacking clear boundaries between adjacent values. Measurements or observations represented in fractional or decimal form fall under continuous data.

Examples: Height, weight, temperature, time, etc.

Continuous Data Analysis tools

Statistical techniques and tools often specifically address data capable of assuming any value within a given range in continuous data analysis. Following are the Continuous data analysis tools.

Descriptive statistics

Values that describe the traits of the sample or population. In other words, it provides a simple summary of the sample and the measures.

Central Tendency

Refers to the statistical measure used to determine the center of a distribution of a data set. Based on the situation, the measure of central tendency could be either Mean, Median, or Mode.

Mean: The mean is the total of all data values divided by the number of data points.
Median: The median is the middle value when the data is arranged in order from least to greatest or vice versa. If the data set has even values, the median is the average of the middle two values.
Mode: The mode is the value that often occurs in the data set.

Measure of dispersion

Dispersion is the degree of variation in the data. Dispersion measures the extent to which different items tend to disperse from the central tendency.

Different types of measures of dispersion

Range: Range is the difference between the maximum and the minimum value.

Variance: Variance measures the dispersion of a set of data points around their mean value.

Standard Deviation: Standard deviation is the most popular measure of dispersion. The main purpose is to measure the amount of variation in a process. One of the most common measures of variability in a dataset or population is the Standard Deviation.

Box-and-Whisker Plot

Box-and-Whisker plot, also known as a Box and Whisker plot, is a pictorial representation of continuous data. Box plots show the Max, Min, median, interquartile range Q1, Q3, and outlier data.

Run Chart

Run charts, also known as Time Series Plots, plot data over time using line graphs. They help to identify the pattern of the data in the time series. Because they don’t use control limits, we cannot judge whether the process is stable or not. However, run chat shows how the process is behaving. The advantage of the run chart is that it identifies the special cause(s) in a process.

Scatter Diagram

Scatter diagrams, also known as Correlation Charts or XY Graphs, plot the relationship between two continuous variables. These can include the independent variable on the x-axis and the dependent variable on the y-axis.

Histogram

A Histogram is the graphical representation of a frequency distribution. It is in the form of a rectangle with class intervals as the base and the corresponding frequencies as the height. Particularly, there are no gaps between any two successive rectangles.

Normal Probability Plot

The Normal Probability Plot is a graphical method to assess whether the data set follows a normal distribution or not. This includes identifying outliers, skewness, etc. Furthermore, the Normal Probability Plot is one example of a Quantile-Quantile (Q-Q) plot.

Regression Analysis

A Regression Analysis is a method for assessing relationships between variables by examining system behavior. Researchers employ various analysis techniques to determine the relationship between dependent and independent variables, with Regression Analysis standing out as one of the most effective. For example, they can utilize transformations to mitigate higher-order terms within the model.

ANOVA

Analysis of Variance (ANOVA) is a parametric statistical technique used to compare data sets. This technique was invented by R.A. Fisher; hence, it is also referred to as Fisher’s ANOVA. It is similar to techniques such as t-test and z-test to compare means and also the relative variance between them.

Data Analysis: Selection of Control chart for Discrete Data and Continuous Data

The control chart is a graph used to study how a process changes over time. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. The control limits are ±3σ from the centerline.

Selection of an appropriate control chart is very important in control chart mapping, otherwise ended up with inaccurate control limits for the data.

X̅ and R charts charts use measurable quantities such as length, weight, and height. Attribute control charts use attribute data. In other words, the data that counts the number of defective items or the number of defects per unit.

Advantages of Data Analysis

Data analysis identifies inefficiencies and areas for improvement, enabling targeted problem-solving.
Insights from data drive efficiency improvements, cost reductions, and resource optimization efforts.
Data analysis supports evidence-based decision-making
Analysis helps to get insights from data, trends, correlations, and predictive patterns.
Data Analysis identifies and mitigates risks by examining historical data and helps to predict potential issues.
Understanding customer data informs tailored strategies to meet customer needs and preferences effectively.
Data Analysis tracks progress, evaluates performance against metrics, and assesses intervention effectiveness.

Using Data to Make Better Decisions

Great TED presentation on using data to make better decisions.

Basic Six Sigma Statistics

Posted by Ted Hessing

Basic Six Sigma statistics is the foundation for Six Sigma projects. It allows us to describe the data that makeup processes X and Y in terms of numbers. Today, statistics is an important part of the day-to-day activities of any organization. Numbers and data play a vital role in Six Sigma projects; hence Six Sigma professionals and other stakeholders must have basic Six Sigma statistics knowledge.

Data Types

Data is a set of values that can be either qualitative or quantitative. It may be a number, a measurement, an observation, or even a description.

Qualitative data: Qualitative data, also known as non-numeric data, is basically data that describes the traits of a value or data point. It is made of a finite number of possible categories into which each data point may fall.

Types of Qualitative data

Nominal data: A type of descriptive data with more than two categories; it can refer to the names or labels of the data points. For example, Hair color – black, brown; Gender – male or female.
Ordinal data: Ordinal data provides good information about the order of choices. In other words, it arranges information in a particular order without indicating a specific relationship between items. Example: pass or fail, customer service, good or bad, etc.

Discrete data: The data is discrete if the measurements are whole numbers or counts. For example, the number of customer complaints, weekly defects data, etc.
Continuous data: The data is continuous if the measurement takes on any value, usually within some range. For example, Stack height, distance, cycle time, etc.

Population Parameters

Population parameters refer to the characteristics of a population. In other words, it describes some aspect of the population. These are used to make inferences about a larger group based on a smaller sample.

Sample Statistics

Sample statistics are measures calculated from a sample of individuals that are used to estimate or make inferences about the population parameters.

Furthermore, sample statistics is to estimate the population parameters, as it is often impossible or impractical to measure the characteristics of an entire population. The accuracy of the estimates obtained from sample statistics depends on the sample size and how the sample was selected from the population. Larger sample sizes generally lead to more accurate estimates of the population parameters.

A few common population parameters and sample statics are:

Mean: The mean is the average value of a variable in a population or sample. It is calculated by adding all data values divided by the number of data points.

Standard Deviation: Standard deviation is the most popular measure of dispersion. It is used to measure the amount of variation in a process. It indicates how much the individual values in a population or sample deviate from the population mean.

Proportion: The proportion is the number of individuals in a population or sample who holds a certain characteristic divided by the total number of individuals in the population or sample. For example, the proportion of male in a population or sample would be the number of males divided by the total population or sample.

Variance: Variance measures the dispersion of a set of data points around their mean value. It is calculated by taking the average of the squared differences of each value from the population or sample mean.

Distinguish between population parameters and sample statistics

Population parameters are descriptive measures that summarize a characteristic of a whole population. Whereas, Sample statistics, are descriptive measures that summarize a characteristic of a sample from a population.
Population parameters are fixed and constant, while sample statistics can vary depending on the sample selected from the population.
Population parameters are typically of greater interest to researchers than sample statistics, as they provide a more accurate description of the population.
Since it is often impractical to measure characteristics of an entire population, sample statistics are important in helping to make inferences about the population.

Basic Types of Statistics used in Six Sigma

Statistics are made of principles and methodologies for collecting, analyzing, interpreting, and presenting data in a meaningful way. Statistics helps to understand the data behavior, identify improvement opportunities, and predict future process performance.

Types of statistical analysis: