Measuring Variation in The Process
By:
1. Fdwa ………
Mohamed Hdidan Submitted
2.
To : Dr, Faraj Eldabee
Course Name: Six Sigma
2024
What is Process Variance?
Process variance refers to the natural fluctuations in the output of a process.
These variations can be caused by controllable factors (e.g., equipment
settings) or uncontrollable factors (e.g., raw material variations).
Understanding variance is crucial for achieving consistent quality and
reducing defects.
Interpreting Variance Data
Common Cause Variation: Inherent fluctuations within a stable process due to multiple,
unidentified factors.
Special Cause Variation: Assignable variations caused by specific events or changes in the process.
By analyzing control charts and other data, we can differentiate between these two types of variance.
Why Measure Process Variance?
 Identify opportunities for improvement: By analyzing variance, we can
pinpoint areas where the process deviates excessively, leading to potential
defects or inefficiencies.
 Reduce waste: Understanding variation allows us to tighten tolerances and
minimize the production of out-of-specification products.
 Enhance customer satisfaction: Consistent quality, achieved through
controlled variance, translates to satisfied customers who receive reliable
products or services.
How to Measure Variance in Six Sigma?
In Six Sigma, there are two main ways to measure variation depending on whether
you're dealing with the entire population (σ^2) (all possible data points) or a sample
(s^2) (a smaller subset of the population):
σ^2 = Σ (X - µ)^2 / N
s^2 = Σ (X - x̅)^2 / (N-1)
Six Sigma also heavily utilizes the concept of standard deviation. It expresses the variation
in the same units as the original data, making it easier to interpret.
Control charts, a key Six Sigma tool, rely on variance calculations to establish upper and
lower control limits (UCL and LCL) for a process. Data points falling outside these limits
signal potential issues in the process consistency.
By understanding and applying these concepts, you can effectively measure variation
within your industrial processes and implement Six Sigma methodologies for
improvement.
Six Sigma offers a robust toolbox for measuring and analyzing process variation. Here are some
key tools and how they help:
1.
Control Charts:
•Function: These visual tools track a process over time,
plotting data points along with statistically determined control
limits.
•Identifying
Variation:
Control
charts
become
"battlegrounds" for identifying special causes of variation.
Points falling outside the control limits indicate a significant
deviation, potentially due to a specific event or change in the
process.
Types of Control Charts
2. Statistical Measures:
•Function: These numerical tools quantify the spread of data within a
process.
•Understanding Variation: Common measures include standard
deviation (describes how spread out the values are from the mean ),
range (difference between highest and lowest values), and coefficient of
of variation (CV - standard deviation divided by the mean, expressed as
as a percentage). It's useful for comparing variability between datasets
with different means.
• Statistical Software: Minitab, JMP, or Excel: Used for statistical
analysis and variation measurement.
3. Gage Repeatability and Reproducibility (GR&R):
•Function: is a tool for analyzing the variation present in each inspection,
measurement, and test equipment type. It is the system used to assess the
quality of the measurement system.
•Ensuring Reliable Measurement: GR&R studies involve multiple
measurements of the same item by different operators and with different
measurement tools. By analyzing the variation in these measurements, we
can determine if the measurement system itself is a significant source of
variation.
4.Histograms:
• Function: These bar charts depict the frequency of specific values
within a dataset.
• How they combat variation: Histograms provide a clear picture of
how data is distributed. They can reveal skewed distributions or
outliers, indicating areas where variation might be concentrated.
5. Pareto Charts (80/20 Rule):
• Function: These bar charts prioritize problems by illustrating that
often, 80% of the problems stem from 20% of the causes.
• How they combat variation: Pareto charts help identify the causes
responsible for the majority of variation. By focusing on these key
contributors, efforts to minimize variation can be targeted and
impactful.
6. ANOVA (Analysis of Variance):
ANOVA is a statistical technique used to analyze differences between
means across multiple groups or factors. It helps determine if there are
significant variations between groups and identifies which specific
factors contribute to these variations.
Here is example from scientific papers in industrial engineering that utilize Six Sigma and
control charts to measure variation:
Research titled "A Six Sigma approach to reducing dimensional
variation in a CNC machining process" (Link to paper) This
published research directly applies Six Sigma to control
dimensional variations in parts produced by a CNC machine.
The major problem has been identified related to function of the
product which is the parts can’t assemble properly due to
dimension of the product is out of specification.
Measure
In this stage, a check sheet has been developed in order to
record all the data from the measured part. The data has been
separated into two categories, dimension A and dimension B.
All measured data for dimension of A & B are highlighted in
Table
Further analysis is to calculate the standard deviation and also process capability (Cp) value based on process
capability chart. The Cp is a measurable property of a process to the specification, expressed as a process
capability index.
It shows almost all the dimensions from 25 unit parts are out of specification. The standard deviation for
this data is not too large (0.05), meaning it does not deviate much from the average. While for the Cp we
get the value is 0.05. Based on literature review, the best Cp must be above than 1.2. If the value is less
than 0.5 it means that the variability of the process is more than the specification limits.
7-Capability Study Analysis (CSA): Assesses the process's ability to meet specifications and
requirements. Process capabilities compare the output of a process to its specification limits. In
other words, how often does a process yield the desired results with a range of acceptable
outcomes?
8-Process Capability Indices (Cpk and Ppk): Measure the process's ability to produce outputs
within specifications.
9-Failure Mode and Effects Analysis (FMEA): Identifies potential failure modes and their
consequences
Historically, the sooner a failure is discovered, the less it will cost.
If a failure is discovered late in product development or launch,
the impact is exponentially more devastating.
FMEA is one of many tools used to discover failure at its earliest
possible point in product or process design.
Discovering a failure early in Product Development (PD) using FMEA
provides the benefits of:
1- Multiple choices for Mitigating the Risk.
2- Higher capability of Verification and Validation of changes
3- Collaboration between design of the product and process
4- Improved Design for Manufacturing and Assembly (DFM/A).
5- Lower cost solutions
6- Legacy, Tribal Knowledge, and Standard Work utilization
10-Error Tree Analysis (ETA): Identifies potential errors in the system or process and their impacts.
Event Tree Analysis (ETA) is a graphical tool used in Quantitative Risk Assessment (QRA) and
decision analysis to evaluate the possible outcomes of a series of events. The overviews of how
Event Tree Analysis (ETA) are as follows.
11-Regression Analysis: Determines relationships between variables and predicts outcomes.
Regression is a statistical method used in finance, investing, and other disciplines that attempts
to determine the strength and character of the relationship between a dependent variable
and one or more independent variables.
Linear regression is the most common form of this technique. Also called simple regression or
ordinary least squares (OLS), linear regression establishes the linear relationship between two
variables.
12- R Charts: Monitor the range between consecutive data points, revealing patterns or trends in
variation
R charts are used to monitor the variation of a process based on samples taken from the process
at given times (hours, shifts, days, weeks, months, etc.). The measurements of the samples at a
given time constitute a subgroup. Typically, an initial series of subgroups is used to estimate the
standard deviation of a process.
The standard deviation is then used to produce control limits for the range of each subgroup.
During this initial phase, the process should be in control.
13 -Root Cause Analysis: Uncovers the underlying causes of variation or issues.
Root cause analysis (RCA) is the quality management process by which an organization
searches for the root of a problem, issue or incident after it occurs.
Root cause analysis helps organizations decipher the root cause of the problem, identify the
appropriate corrective actions and develop a plan to prevent future occurrences. It aims to
implement solutions to the underlying problem for more efficient operations overall.
14- Total Quality Management (TQM): A management approach focusing on quality improvement
and variation reduction.
Variance reduction is sometimes considered as a goal of quality improvement.
15- Design for Manufacturing (DFM): A design approach to reduce variation and enhance quality.
Design for Manufacturing or Design for Manufacturability (DFM) is the optimisation of a part,
product, or component’s design, to create it cheaper and more easily. DFM involves efficiently
designing or engineering an object,
generally during the product design
stage, when it is easier and less
expensive to do so, to reduce
manufacturing costs.
This allows a manufacturer to
identify and prevent mistakes .
16- Design of Experiments (DOE): A systematic method for testing variables and optimizing
processes.
Design of experiments (DOE) is a statistical method for planning and conducting
experiments. DOE is used to identify the factors that affect a process and to determine the
optimal levels of those factors, as shown in Figure 1. DOE can be used to improve the
quality of products and processes, reduce costs, and increase efficiency
Conclusion
Measuring process variance is a cornerstone of Six Sigma. It empowers you to take
control, identify improvement opportunities, and achieve operational excellence.
Remember, a well-understood process is a predictable and ultimately, a successful
process.
The End