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Chapter 5: Standard Deviation - Coggle Diagram
Chapter 5: Standard Deviation
Variation
Variance is the root of many defects
Removing variation alone isn’t enough
Six Sigma Improvement Approach
Determine if process is functional
Remove variation that causes deviations
Focus on outputs deviating from the intended result
Standard Deviation (σ)
Statistical measure of process variation
Measures distance between data points and the mean
Interpretation:
Large standard deviation → wide spread of data points
Small standard deviation → data points closely clustered
Symbol: σ (lower-case Greek Sigma
Graphical Representation of Deviation
Vertical axis → measure of time
Horizontal axis → measure of temperature
Center line = mean temperature
Observation:
Greater variation → data points spread further from mean
Smaller variation → points closely clustered around mean
Formula:
\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}
Formula Key:
σ = standard deviation
μ = mean of the population
Σ = sum of all results from calculations in parentheses
N = number of data elements in the population
xᵢ = each individual data element
Key Concepts
Standard deviation quantifies variation in a dataset
Large σ → wide spread of data points
Small σ → data points closely clustered
Helps identify process consistency and predict defec
Standard Deviation
Purpose
Indicates variation in performance or process outputs
Helps pinpoint areas for investigation
Key Insight:
Serves as foundation for further statistical analysis and process control
SD alone doesn’t solve problems; it points to where investigation is needed
When to Use Population Formula
Use only when you have all data elements of a population
Example: Measuring all pizzas made in a day
If only a sample → use sample standard deviation formula
Pareto Principle (80/20 Rule)
Definition:
20% of causes → 80% of effects
Also called the law of the vital few
Few inputs often drive majority of outputs
Origin:
Named by Joseph Juran after economist Vilfredo Pareto
Original observation: 20% of Italy’s people owned 80% of the land
Applications:
Business: 80% of sales from 20% of customers
Volunteer organizations: 20% of volunteers do 80% of work
Six Sigma: Helps identify key inputs/root causes that impact outcomes most
Focuses resources on improvements that create maximum effect
Visualization:
Pareto chart:
Ranked bar chart, highest bar on left, lowest on right
Highlights vital few causes
Can be created in Excel or statistical software
Key Insight:
Helps prioritize which inputs to improve for maximum process impact
Supports data-driven decision making in Lean Six Sigma projects
Medical Claim Denials
Scenario
Medical office experiencing cash flow problems due to claim denials
Denials require rework, resubmission, or appeals
Some denials are not appealable → lost revenue
Data Collection
Team gathers data on claim denials
Reasons for denial and counts:
Pareto Chart Insight
Top 3 reasons (Duplicate claim, Timely Filing, No beneficiary found)
→ Account for ~80% of denials
Visual ranking: highest bar left → lowest bar right
Focuses on “vital few” causes
Voice of the Customer
Definition: Captures customer needs, expectations, and feedback
Purpose: Ensures quality improvements actually satisfy customers
Timing: Collect VOC data before, during, and after improvement projects
Goal:
Consistently meet customer expectations
Align product/process improvements with real customer value
Building a VOC Campaign
Goal: Ask the right questions in the right way to get usable data
Types of VOC Campaigns:
General Feedback
Collected via forms, complaints, websites, social media
Provides overall temperature check satisfaction/dissatisfaction trends
Example: Fast food restaurant surveys
General VOC Feedback
Purpose: Acts as a “smoke alarm” for issues
Alerts organization to potential problems early
Early action can prevent bigger or costlier issue
Critical to Quality Factors
Measures elements important to customer satisfaction
Basis for VOC campaign design
Applications
Monitor trends over time → detect drops in quality
Reward employees based on scores → boosts morale & performance
Specific VOC Feedback
urpose: Targeted feedback on particular products, services, or problems
Methods
Beta testing → apps, digital products
Focus groups → products, ideas, campaigns
Surveys tailored to specific issues
Key Points
Ask specific questions to gather actionable insights
Clarifies and expands upon general feedback
Example: Cleanliness issue → identify whether problem is lighting, shelves, or maintenance practices
Selecting the Right VOC Tool
Goal: Choose tools that fit project needs, budget, and timeline
Example Tool: Feedback Forms
Cost: Low
Benefits
Collects large amounts of data from many sources
Numeric data → easier analysis
Disadvantages:
Only motivated individuals provide feedback → may skew results
First Time Yield
Definition: Percentage of units produced correctly the first time without rework.
Rolled Throughput Yield
Definition: Probability that a unit will be completed without defects or rework across the entire process. RTY accounts for rework and scrap.
Key Takeaways
FTY ignores rework; it only measures the first attempt success.
RTY gives a true picture of process efficiency by including scrap and rework.
RTY will always be lower than FTY if any rework exists.
Useful for identifying processes with hidden inefficiencies or waste (muda).