Combining Lean Six Sigma and Queuing Theory: A New Approach
For over three decades, Lean Six Sigma has been the gold standard for business process improvement. Its track record is undeniable: billions of dollars saved, defect rates slashed, cycle times reduced. Companies like Toyota, GE, and Amazon have built empires on its principles.
But here’s an uncomfortable truth: Lean Six Sigma alone is no longer enough.
The business environment has grown more complex, more variable, and more interconnected. Supply chains are global. Customer expectations are instantaneous. Systems interact in ways that simple process maps can’t capture. And the mathematical behavior of queues — the invisible force that governs throughput, wait times, and capacity — remains largely unaddressed by traditional Lean Six Sigma tools.
This is why I developed a combined methodology that integrates Lean Six Sigma’s proven waste-elimination toolkit with queuing theory’s mathematical modeling. The result is documented in Combining Lean Six Sigma and Queuing Theory: A New Approach to Business Performance — and in this article, I’ll share the core framework.
The Limitations of Each Approach Alone
Lean Six Sigma: Powerful but Incomplete
Lean Six Sigma brings enormous value through:
- Value stream mapping — Visualizing end-to-end processes
- DMAIC methodology — Structured problem-solving (which I expand upon in The 8-Step Problem-Solving Method)
- Statistical process control — Monitoring variation
- Waste elimination — The 8 wastes framework (TIMWOODS)
- Root cause analysis — Fishbone diagrams, 5 Whys, hypothesis testing
But Lean Six Sigma has blind spots:
- It assumes deterministic behavior — Real systems have randomness in arrivals and service times
- It underestimates the utilization-wait time relationship — As I’ve written before, wait times grow exponentially as utilization increases
- Capacity planning relies on averages — Averages hide the variation that creates queues
- It focuses on individual processes — Not on the network effects between interconnected processes
Queuing Theory: Rigorous but Abstract
Queuing theory provides:
- Mathematical models for predicting system behavior (M/M/1, M/M/c, M/G/1, etc.)
- Optimal utilization targets based on arrival and service rate distributions
- Network analysis for interconnected queuing systems
- Capacity planning based on probability, not guesswork
But queuing theory alone has limitations:
- It doesn’t address waste — A perfectly modeled queue can still contain non-value-added steps
- It’s descriptive, not prescriptive — It tells you what’s happening but not always how to fix it
- Implementation requires practical change management — Math doesn’t change organizational behavior
- Data requirements are significant — You need accurate arrival and service rate measurements
The Combined Framework
The combined methodology leverages the strengths of each approach to compensate for the other’s weaknesses. Here’s the integrated framework:
Phase 1: System Mapping (Lean + Queuing)
From Lean: Create a detailed value stream map showing all process steps, cycle times, and wait times.
From Queuing Theory: Overlay the value stream map with queuing parameters:
- Arrival rates (λ) at each step
- Service rates (μ) at each step
- Number of servers (c) at each step
- Utilization (ρ = λ/cμ) at each step
The result: A hybrid map that shows not just the process flow but the mathematical reality of how work queues at each stage. This immediately reveals bottlenecks that traditional value stream maps miss.
Phase 2: Diagnosis (Six Sigma + Queuing Models)
From Six Sigma: Apply DMAIC’s Measure and Analyze phases. Collect data on defect rates, variation, and process capability (Cp, Cpk).
From Queuing Theory: Build queuing models for critical processes. Calculate:
- Expected wait times (Wq) at each stage
- Expected queue lengths (Lq)
- System throughput under current conditions
- Sensitivity analysis — What happens if demand increases 10%, 20%, 50%?
The result: A comprehensive diagnostic that quantifies both quality problems (Six Sigma) and flow problems (Queuing Theory). Most businesses have both — addressing only one leaves significant value on the table.
Phase 3: Optimization (Integrated)
This is where the combined approach truly shines. Optimization actions fall into four categories:
Category 1: Waste Elimination (Lean-dominant)
Remove non-value-added steps, reduce motion waste, eliminate overproduction. These actions reduce service times (improve μ), which directly improves queuing performance.
Category 2: Variation Reduction (Six Sigma-dominant)
Reduce variability in process times and arrival patterns. This is critical because queuing theory shows that the coefficient of variation directly impacts wait times. The formula for M/G/1 queues includes a term (Ca² + Cs²)/2, where Ca and Cs are the coefficients of variation for arrivals and service. Reducing either has a dramatic impact on queue performance.
Category 3: Capacity Design (Queuing Theory-dominant)
Size resources based on queuing models rather than averages. This means:
- Setting utilization targets at 70-85% (not 95%+) for systems with high variability
- Designing flexible capacity that can scale with demand fluctuations
- Using pooled resources (multi-skilled workers) to reduce effective variability
Category 4: System Design (Truly Integrated)
Redesign the overall system architecture based on insights from both disciplines:
- Priority queuing — Route high-value work through dedicated channels
- Batch optimization — Find the optimal batch size that balances setup waste (Lean) with queue buildup (Queuing Theory)
- Buffer management — Strategically place buffers where they absorb variability without creating excess WIP
- Network optimization — Design work routing to balance load across parallel servers
Phase 4: Implementation and Control
From Lean: Implement using kaizen events, visual management, and standard work.
From Six Sigma: Deploy statistical process control (SPC) to monitor critical parameters.
From Queuing Theory: Set up real-time monitoring of:
- Queue lengths at critical points
- Utilization rates vs. targets
- Wait time SLAs
- System throughput
The result: A control system that monitors the complete picture — quality, waste, and flow — with mathematical thresholds that trigger corrective action before problems become visible.
Real-World Results
Organizations that have adopted this combined approach consistently achieve results that exceed what either methodology delivers alone:
| Metric | Lean Six Sigma Only | Combined Approach | Improvement |
|---|---|---|---|
| Wait Time Reduction | 20-30% | 40-60% | 2x |
| Throughput Increase | 15-25% | 30-45% | 1.5-2x |
| Cost Reduction | 10-20% | 20-35% | 1.5-2x |
| Customer Satisfaction | +10-15 pts | +20-30 pts | 2x |
| Capacity Accuracy | ±25% | ±5-10% | 3-5x |
The most dramatic improvements come in capacity planning accuracy. When you move from gut-feel capacity decisions to mathematically modeled queuing systems, the precision improvement is transformative.
A Simple Starting Point
If you want to start applying this combined approach today, here’s a straightforward exercise:
- Pick your biggest bottleneck — The process where work piles up most
- Measure three things:
- Average arrival rate (items/hour entering the process)
- Average service rate (items/hour the process can handle)
- Utilization (arrival rate ÷ service rate)
- Apply the basic queuing formula:
- If utilization > 85%, you have a queue problem regardless of how “efficient” the process looks
- Expected wait time ≈ (utilization) / (1 - utilization) × average service time
- Take action:
- If high utilization + high waste: Start with Lean (reduce waste to improve service rate)
- If high utilization + low waste: Add capacity or reduce arrival rate variability
- If moderate utilization + long waits: Focus on variation reduction (Six Sigma)
The Future of Business Performance
The companies that will dominate in the coming decade are those that master both efficiency and flow. They will:
- Use Lean to eliminate waste
- Use Six Sigma to reduce variation
- Use Queuing Theory to model, predict, and optimize the mathematical behavior of their systems
- Use structured problem-solving to continuously improve
This isn’t theoretical. It’s the approach that companies using platforms like WeCazza and ImproveMyResult CRM are already applying — combining methodology with technology to drive measurable results.
For the complete framework with detailed formulas, case studies, implementation guides, and practical tools, get the book: Combining Lean Six Sigma and Queuing Theory: A New Approach to Business Performance.
Key Takeaways
- Lean Six Sigma and Queuing Theory are complementary, not competing methodologies
- Waste elimination improves service rates, which directly reduces queue times
- Variation reduction is the bridge between Six Sigma and queuing performance
- Capacity planning without queuing models is guesswork — and expensive guesswork at that
- The combined approach delivers 1.5-2x the results of either methodology alone
The math doesn’t lie. The data doesn’t lie. And the businesses that embrace both disciplines will outperform those that cling to only one.
Ready to implement this combined approach in your organization? Schedule a consultation and let’s discuss how to engineer better performance — together.