Improve Phase

Design of experiments (DOE), lean methods, cycle-time reduction, kaizen, and implementation planning.

5 minutes 5 Questions

The Improve Phase is the fourth phase of the DMAIC (Define, Measure, Analyze, Improve, Control) methodology in Lean Six Sigma. This critical phase focuses on developing and implementing solutions to address the root causes identified during the Analyze Phase. Key objectives of the Improve Phase in…

Concepts covered

DOE Terminology (Factors, Levels, Response, Treatment)DOE Design Principles Power, Sample Size, and Balance in DOE Interaction and Confounding in DOE Two-Level Fractional Factorial Experiments Full Factorial Experiments Pull Systems and Kanban Standard Work Cycle-Time Reduction Techniques Continuous Flow Kaizen and Kaizen Blitz Overall Equipment Effectiveness (OEE)Solution Evaluation and Selection Randomization and Blocking Planning and Evaluating Experiments Completely Randomized and Latin Square Designs Waste Elimination Tools 5S Methodology Poka-Yoke (Mistake Proofing)Single-Minute Exchange of Die (SMED)Heijunka (Production Leveling)Theory of Constraints (TOC)Pilot Tests and Simulations One-Factor Experiments

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Question 1

In DOE, what is the primary purpose of randomization as a design principle?

To ensure that each factor level combination is replicated equally across all experimental blocks To minimize the effect of lurking variables and reduce systematic bias in experimental results To distribute factor interactions evenly and improve the precision of main effect estimates To balance the allocation of treatment combinations so that confounding patterns are fully resolved

Correct Answer: To minimize the effect of lurking variables and reduce systematic bias in experimental results

Randomization in DOE ensures that the order in which experimental runs are conducted is random, thereby minimizing the influence of lurking (nuisance) variables and preventing systematic bias from contaminating the results, which validates the assumption of independently distributed error terms.

The second option describes replication and blocking principles, not randomization. The third option refers to confounding resolution, which is addressed through design resolution and aliasing structure, not randomization. The fourth option describes benefits associated with replication and orthogonality rather than randomization.

Key concept tested: understanding randomization as a fundamental DOE principle that protects against unknown and uncontrolled sources of variation.

Question 2

A team notices that their assembly line has three steps: Step 1 produces 200 units/hour, Step 2 produces 100 units/hour, and Step 3 produces 180 units/hour. A new team member asks which step the team should focus improvement efforts on first. What is the most basic reason for choosing Step 2?

Step 2 has the largest gap compared to Step 1, so reducing that variance optimizes throughput Step 2 has the highest utilization rate, so balancing its capacity with Step 3 improves flow Step 2 sits in the middle of the process, so improving it creates the best overall line balance Step 2 has the lowest output rate, making it the bottleneck that limits the entire system

Correct Answer: Step 2 has the lowest output rate, making it the bottleneck that limits the entire system

Step 2 produces only 100 units/hour, which is the lowest rate among all three steps, making it the bottleneck that constrains the entire system's throughput to 100 units/hour regardless of how fast the other steps operate.

One option incorrectly frames the issue as a utilization or balancing problem between Steps 2 and 3 rather than identifying the fundamental constraint. Another option wrongly suggests that physical position in the process determines improvement priority. Another option focuses on variance between steps rather than the core issue of system constraint.

Key concept tested: Theory of Constraints, specifically identifying the bottleneck as the process step with the lowest capacity that limits total system output.

Question 3

A team is designing a 2^4 full factorial DOE with 3 center points to study a chemical process. Initial power analysis shows 72% power to detect a 2-sigma shift in the response. The team wants at least 90% power but faces budget constraints limiting total runs to 25. Which approach best balances the competing demands of statistical power and resource limitations?

Replicate the entire 2^4 full factorial once and reduce alpha from 0.05 to 0.10 to compensate for the resulting 35 runs exceeding the budget by accepting higher Type I error risk Increase the number of center points from 3 to 8 within the full factorial design, boosting power through additional degrees of freedom for pure error estimation Add 2 replicates of a half-fraction (2^4-1) to the base full factorial, reaching 24 runs plus the original center points adjusted to fit the budget Switch to a 2^4-1 fractional factorial with 3 replicates and 1 center point, leveraging the resolution IV design to maintain estimability of all main effects and two-factor interactions

Correct Answer: Add 2 replicates of a half-fraction (2^4-1) to the base full factorial, reaching 24 runs plus the original center points adjusted to fit the budget

Adding two replicates of a half-fraction (8 runs each = 16 runs) to the base full factorial (16 runs) would yield 32 runs, but by adjusting center points and strategically selecting which fraction to replicate, the team can stay within 25 total runs while substantially increasing power through additional replication of key factor combinations without sacrificing the ability to estimate all main effects and interactions.

Increasing center points from 3 to 8 only improves pure error estimation and curvature detection, not power for detecting factorial effects. A 2^4-1 with 3 replicates gives 24 factorial runs plus 1 center point equaling 25, but a resolution IV design confounds two-factor interactions with each other, compromising estimability. A full replicate of the 2^4 requires 35 runs, exceeding the budget, and relaxing alpha is a poor compensating strategy.

The key concept tested is optimizing experimental design power within resource constraints through strategic partial replication.

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