Six Sigma | DMAIC Cp Cpk, Control Charts DPMO, Variation Analysis | 100+ MCQ with Answers
Q1. What is the primary goal of Six Sigma as a management philosophy?
A. To increase customer complaints
B. To reduce process variation and improve quality
C. To increase production costs
D. To maintain average performance
✅ Answer: B. To reduce process variation and improve quality
Q2. What type of variation is expected in every process due to natural causes?
A. Assignable cause
B. Common cause
C. External variation
D. Productive variance
✅ Answer: B. Common cause
Q3. Which type of variation can be traced to a specific event or reason?
A. Chance cause
B. Natural cause
C. Assignable cause
D. Random variation
✅ Answer: C. Assignable cause
Q4. What is the objective of process control in Six Sigma?
A. To identify and eliminate special causes of variation
B. To reduce customer tolerance limits
C. To increase production time
D. To remove common causes of variation entirely
✅ Answer: A. To identify and eliminate special causes of variation
Q5. Which statement is true regarding tolerance limits in Six Sigma?
A. They are based on machine capability only
B. They are set by the customer or design requirements
C. They are the same as control limits
D. They are used to calculate mean deviation only
✅ Answer: B. They are set by the customer or design requirements
Q6. If there are no tolerance limits, what does that imply for Six Sigma?
A. The process is already optimal
B. Six Sigma cannot be applied meaningfully
C. The process is defect-free
D. There is no natural variation
✅ Answer: B. Six Sigma cannot be applied meaningfully
Q7. What do control limits (UCL/LCL) represent in a control chart?
A. Customer requirements
B. Expected range of natural variation
C. Cost boundaries
D. Operator performance levels
✅ Answer: B. Expected range of natural variation
Q8. Control limits are generally set at how many standard deviations from the mean?
A. ±1σ
B. ±2σ
C. ±3σ
D. ±4σ
✅ Answer: C. ±3σ
Q9. What percentage of natural process variation is covered within ±3σ limits?
A. 68.27%
B. 95.45%
C. 99.73%
D. 99.99%
✅ Answer: C. 99.73%
Q10. What is the standard metric used in Six Sigma to measure process defects?
A. DPU
B. DPMO
C. RTY
D. PPM
✅ Answer: B. DPMO
Q11. What does DPMO stand for?
A. Defects Per Million Output
B. Defects Per Million Opportunity
C. Defective Products Measured Output
D. Defects Per Manufacturing Operation
✅ Answer: B. Defects Per Million Opportunity
Q12. Which of the following is not a characteristic of variable data?
A. Measured on a continuous scale
B. Expressed in exact numerical terms
C. Pass/fail outcome
D. Can use control charts
✅ Answer: C. Pass/fail outcome
Q13. Attribute data is typically represented by:
A. Numerical measures
B. Discrete categories
C. Ratios and intervals
D. Regression lines
✅ Answer: B. Discrete categories
Q14. Which statistical concept allows averages of samples to form a normal distribution?
A. Central Limit Theorem
B. Regression Analysis
C. Law of Large Numbers
D. Pareto Principle
✅ Answer: A. Central Limit Theorem
Q15. Which control chart is used to monitor process averages?
A. R-chart
B. P-chart
C. X-bar chart
D. C-chart
✅ Answer: C. X-bar chart
Q16. The R-chart is primarily used to monitor:
A. Process mean
B. Customer satisfaction
C. Process variation
D. Production speed
✅ Answer: C. Process variation
Q17. Which universal constants are used to calculate control limits in X-bar and R charts?
A. A2, D3, D4
B. Z1, Z2, Z3
C. α, β, γ
D. C1, C2, C3
✅ Answer: A. A2, D3, D4
Q18. A process is said to be “in control” when:
A. Only X-bar chart is within limits
B. Only R-chart is within limits
C. Both X-bar and R-chart are within limits
D. Control limits exceed tolerance limits
✅ Answer: C. Both X-bar and R-chart are within limits
Q19. Using a narrow sigma range like ±1σ can result in:
A. More false alarms
B. Fewer process checks
C. Higher stability
D. Reduced detection
✅ Answer: A. More false alarms
Q20. What is the formula for calculating Process Capability ($C_p$)?
A. $(USL - LSL) / σ$
B. $(USL - LSL) / 3σ$
C. $(USL - LSL) / 6σ$
D. $(USL + LSL) / 6σ$
✅ Answer: C. $(USL - LSL) / 6σ$
Q21. What does the Process Capability Index ($C_p$) compare?
A. Process mean to control limits
B. Process variation width to tolerance width
C. Mean deviation to target value
D. Process time to production cost
✅ Answer: B. Process variation width to tolerance width
Q22. A $C_p$ of 1.0 corresponds to what sigma level?
A. 2σ
B. 3σ
C. 4σ
D. 5σ
✅ Answer: B. 3σ
Q23. A $C_p$ of 2.0 corresponds to which sigma level?
A. 4σ
B. 5σ
C. 6σ
D. 7σ
✅ Answer: C. 6σ
Q24. What is the defect count per million opportunities for a 3σ process?
A. 66,800
B. 27,000
C. 3.4
D. 2
✅ Answer: B. 27,000
Q25. What is the defect rate for a 6σ process (after accounting for 1.5σ shift)?
A. 2700 DPMO
B. 340 DPMO
C. 3.4 DPMO
D. 0 DPMO
✅ Answer: C. 3.4 DPMO
Q26. Why is the 1.5σ shift considered in Six Sigma calculations?
A. To simulate process drift over time
B. To reduce customer expectations
C. To simplify computation
D. To exaggerate performance
✅ Answer: A. To simulate process drift over time
Q27. What does the Germ Magic case primarily demonstrate?
A. Financial reporting optimization
B. Statistical quality control application
C. Customer satisfaction survey
D. Marketing campaign measurement
✅ Answer: B. Statistical quality control application
Q28. What was the target filling volume in the Germ Magic case?
A. 500 ml
B. 510 ml
C. 495 ml
D. 490 ml
✅ Answer: A. 500 ml
Q29. What were the upper and lower tolerance limits in Germ Magic’s process?
A. 510 ml and 490 ml
B. 520 ml and 480 ml
C. 505 ml and 495 ml
D. 515 ml and 485 ml
✅ Answer: A. 510 ml and 490 ml
Q30. Which chart did the intern recommend implementing for control?
A. Histogram
B. Pareto Chart
C. X-bar and R Chart
D. Scatter Diagram
✅ Answer: C. X-bar and R Chart
Q31. What was the sample size ($n$) used in Germ Magic control charts?
A. 3
B. 4
C. 5
D. 10
✅ Answer: C. 5
Q32. What did the calculated average of sample averages ($\bar{\bar{X}}$) equal?
A. 500.000 ml
B. 499.968 ml
C. 510.000 ml
D. 495.968 ml
✅ Answer: B. 499.968 ml
Q33. What conclusion was reached about Germ Magic’s process stability?
A. Process was unstable
B. Process was naturally behaving (in control)
C. Control charts were inaccurate
D. Specification limits were too tight
✅ Answer: B. Process was naturally behaving (in control)
Q34. What step could the company take next after confirming process stability?
A. Stop monitoring altogether
B. Start a Six Sigma project to reduce variation
C. Change tolerance limits
D. Increase filling speed
✅ Answer: B. Start a Six Sigma project to reduce variation
Q35. Which of the following represents a “defect” rather than a “defective”?
A. A product that completely fails
B. A product with a minor deviation but still usable
C. A fully damaged unit
D. A discarded component
✅ Answer: B. A product with a minor deviation but still usable
Q36. The formula $C_p = 1.33$ typically indicates:
A. Below-average process capability
B. Acceptable industrial capability
C. Process not centered
D. Excessive variation
✅ Answer: B. Acceptable industrial capability
Q37. The key difference between tolerance and control limits is:
A. Tolerance limits are customer-driven; control limits are process-driven
B. Both are customer-driven
C. Both are process-driven
D. Control limits always equal tolerance limits
✅ Answer: A. Tolerance limits are customer-driven; control limits are process-driven
Q38. What does it mean if data points fall outside control limits?
A. Process is in control
B. Process mean has improved
C. Assignable cause likely exists
D. Normal variation only
✅ Answer: C. Assignable cause likely exists
Q39. In Six Sigma, what does “defective” mean?
A. Product meets all requirements
B. Product is slightly off target but usable
C. Product fails to meet specifications
D. Product exceeds expectations
✅ Answer: C. Product fails to meet specifications
Q40. Why are ±3σ limits universally accepted in process control?
A. Covers almost all natural variation
B. Easier to calculate manually
C. Industry tradition
D. Reduces sample size requirement
✅ Answer: A. Covers almost all natural variation
Q41. What is the difference between $C_p$ and $C_{pk}$ in process capability analysis?
A. $C_p$ includes process centering; $C_{pk}$ ignores it
B. $C_p$ assumes the process is centered; $C_{pk}$ accounts for mean shift
C. Both measure only variation
D. $C_{pk}$ is always greater than $C_p$
✅ Answer: B. $C_p$ assumes the process is centered; $C_{pk}$ accounts for mean shift
Q42. A process has a $C_p$ of 1.5 and $C_{pk}$ of 0.8. What does this indicate?
A. The process is centered and capable
B. The process is not centered and may produce defects
C. The process has no variation
D. The process exceeds customer tolerance
✅ Answer: B. The process is not centered and may produce defects
Q43. In Six Sigma, the "Voice of the Customer" (VOC) primarily defines:
A. Control limits
B. Specification limits
C. Mean deviation
D. Sigma shift
✅ Answer: B. Specification limits
Q44. The “Voice of the Process” (VOP) is represented by:
A. Control limits
B. Specification limits
C. Customer feedback
D. Marketing surveys
✅ Answer: A. Control limits
Q45. When VOP exceeds VOC, what does it imply?
A. Process is better than customer requirement
B. Process variation exceeds customer tolerance
C. Customer is oversatisfied
D. Cp is infinite
✅ Answer: B. Process variation exceeds customer tolerance
Q46. Which phase of DMAIC focuses on quantifying the problem and current performance?
A. Define
B. Measure
C. Analyze
D. Improve
✅ Answer: B. Measure
Q47. The “Define” phase in DMAIC primarily aims to:
A. Collect sample data
B. Establish business case and customer CTQs
C. Perform regression analysis
D. Implement control plans
✅ Answer: B. Establish business case and customer CTQs
Q48. In the Analyze phase, teams typically use:
A. Hypothesis testing and regression
B. Control charts
C. Affinity diagrams
D. Brainstorming only
✅ Answer: A. Hypothesis testing and regression
Q49. The “Improve” phase emphasizes:
A. Documentation
B. Root cause validation and solution design
C. Reporting findings
D. Cost optimization only
✅ Answer: B. Root cause validation and solution design
Q50. The “Control” phase ensures:
A. Solutions are temporary
B. Process gains are sustained
C. Customer expectations are reduced
D. Data collection stops
✅ Answer: B. Process gains are sustained
Q51. What tool is often used in the Measure phase to identify where variation occurs?
A. Control Chart
B. Cause-and-Effect Diagram
C. SIPOC Diagram
D. Scatter Plot
✅ Answer: C. SIPOC Diagram
Q52. In Six Sigma, CTQ stands for:
A. Critical To Quality
B. Centralized Total Quality
C. Continuous Target Quality
D. Cost Tracking Quotient
✅ Answer: A. Critical To Quality
Q53. COPQ refers to:
A. Cost of Poor Quality
B. Control of Process Quality
C. Chart of Process Quality
D. Continuous Output Quality
✅ Answer: A. Cost of Poor Quality
Q54. The role responsible for overall Six Sigma program deployment is the:
A. Green Belt
B. Black Belt
C. Champion
D. Yellow Belt
✅ Answer: C. Champion
Q55. Which role typically leads cross-functional Six Sigma projects?
A. Green Belt
B. Black Belt
C. Yellow Belt
D. Sponsor
✅ Answer: B. Black Belt
Q56. Green Belts usually work on projects:
A. Full-time
B. Part-time alongside regular duties
C. Only at executive level
D. Only in R&D
✅ Answer: B. Part-time alongside regular duties
Q57. The Master Black Belt primarily focuses on:
A. Coaching Black Belts and strategy alignment
B. Running small-scale projects
C. Performing audits
D. Data entry and collection
✅ Answer: A. Coaching Black Belts and strategy alignment
Q58. What is the first step when analyzing a process in Six Sigma?
A. Verify the measurement system
B. Start root cause analysis immediately
C. Implement corrective actions
D. Skip Define phase
✅ Answer: A. Verify the measurement system
Q59. Measurement System Analysis (MSA) evaluates:
A. Machine speed
B. Accuracy and precision of measurement process
C. Customer satisfaction
D. Sampling frequency
✅ Answer: B. Accuracy and precision of measurement process
Q60. Gage R&R stands for:
A. Gage Repeatability and Reproducibility
B. General Accuracy and Reliability Ratio
C. Global Acceptance Rate
D. Group Analysis Result
✅ Answer: A. Gage Repeatability and Reproducibility
Q61. Which distribution is most used for Six Sigma analysis?
A. Poisson
B. Normal
C. Exponential
D. Binomial
✅ Answer: B. Normal
Q62. The area beyond ±3σ in a normal distribution represents:
A. Natural variation
B. Assignable causes
C. Random consistency
D. Target performance
✅ Answer: B. Assignable causes
Q63. What is the probability of a data point lying outside ±3σ limits?
A. 0.3%
B. 2%
C. 5%
D. 10%
✅ Answer: A. 0.3%
Q64. The main statistical principle behind control charts is:
A. Central Limit Theorem
B. Pareto Principle
C. Regression Linearity
D. Empirical Rule
✅ Answer: D. Empirical Rule
Q65. If a point on the X-bar chart exceeds UCL, what should be done first?
A. Stop process immediately and investigate
B. Ignore if single occurrence
C. Adjust tolerance limits
D. Continue operation
✅ Answer: A. Stop process immediately and investigate
Q66. What is a false alarm in process control?
A. A defect missed by control charts
B. Indication of out-of-control when none exists
C. Machine shutdown due to actual failure
D. A data recording error
✅ Answer: B. Indication of out-of-control when none exists
Q67. Excessively tight control limits lead to:
A. Higher defect detection
B. Frequent false alarms
C. Improved process centering
D. Reduced sampling
✅ Answer: B. Frequent false alarms
Q68. When both X-bar and R charts show all points within control limits, the process is:
A. Stable and predictable
B. Over-controlled
C. Defective
D. Miscalculated
✅ Answer: A. Stable and predictable
Q69. What is the main outcome of the Analyze phase in DMAIC?
A. Identified root causes
B. Improved product design
C. Recalibrated machines
D. Customer feedback report
✅ Answer: A. Identified root causes
Q70. Which tool visually separates vital few from trivial many causes?
A. Pareto Chart
B. Fishbone Diagram
C. Scatter Plot
D. Histogram
✅ Answer: A. Pareto Chart
Q71. The Fishbone Diagram is also known as:
A. Ishikawa Diagram
B. Histogram
C. Run Chart
D. P Chart
✅ Answer: A. Ishikawa Diagram
Q72. What principle does the Pareto Chart represent?
A. 20% causes lead to 80% of problems
B. 80% causes lead to 20% of defects
C. Random distribution
D. Binomial error principle
✅ Answer: A. 20% causes lead to 80% of problems
Q73. A Control Plan is developed in which DMAIC phase?
A. Define
B. Measure
C. Control
D. Improve
✅ Answer: C. Control
Q74. What does SPC stand for?
A. Statistical Process Control
B. Standard Product Calculation
C. Supplier Performance Charting
D. Systematic Process Check
✅ Answer: A. Statistical Process Control
Q75. Which type of data is required for X-bar and R charts?
A. Attribute
B. Variable
C. Nominal
D. Ordinal
✅ Answer: B. Variable
Q76. A P-chart monitors:
A. Proportion of defectives
B. Process mean
C. Continuous measurements
D. Average range
✅ Answer: A. Proportion of defectives
Q77. What chart is suitable for counting number of defects per unit?
A. C-chart
B. U-chart
C. P-chart
D. NP-chart
✅ Answer: A. C-chart
Q78. Which chart type should be used when sample sizes vary?
A. NP-chart
B. U-chart
C. X-bar chart
D. R-chart
✅ Answer: B. U-chart
Q79. The fundamental purpose of control charts is to:
A. Detect assignable causes
B. Measure profitability
C. Predict customer satisfaction
D. Estimate workforce needs
✅ Answer: A. Detect assignable causes
Q80. What type of process produces output exactly on target every time?
A. Stable
B. Perfectly centered
C. Capable
D. Ideal theoretical process
✅ Answer: D. Ideal theoretical process
Q81. Which of the following indicates a capable process?
A. $C_p < 1$
B. $C_p = 1$
C. $C_p > 1$
D. $C_p = 0$
✅ Answer: C. $C_p > 1$
Q82. What is a key assumption in the calculation of $C_p$?
A. Process is centered
B. Process is skewed
C. Process mean fluctuates
D. Sample size is less than 3
✅ Answer: A. Process is centered
Q83. A process at $C_p = 2$ has what sigma level?
A. 4σ
B. 5σ
C. 6σ
D. 7σ
✅ Answer: C. 6σ
Q84. A Six Sigma process targets how many defects per million opportunities?
A. 2700
B. 340
C. 3.4
D. 0.034
✅ Answer: C. 3.4
Q85. Who first popularized the term “Six Sigma”?
A. W. Edwards Deming
B. Bill Smith (Motorola)
C. Joseph Juran
D. Philip Crosby
✅ Answer: B. Bill Smith (Motorola)
Q86. The company that made Six Sigma famous in the 1990s was:
A. Toyota
B. General Electric (GE)
C. Ford
D. IBM
✅ Answer: B. General Electric (GE)
Q87. Which Six Sigma metric directly reflects customer impact?
A. DPMO
B. RTY
C. COPQ
D. Sigma Level
✅ Answer: C. COPQ
Q88. A “process shift” of 1.5σ means:
A. Mean has moved by 1.5σ
B. Process limits are narrower
C. Tolerances expanded
D. Data collection error
✅ Answer: A. Mean has moved by 1.5σ
Q89. Control limits are derived from:
A. Process data
B. Customer specification
C. Benchmark results
D. Supplier reports
✅ Answer: A. Process data
Q90. Specification limits are determined by:
A. Process variation
B. Customer requirements
C. Statistical limits
D. Company finance
✅ Answer: B. Customer requirements
Q91. What is the primary metric of process yield in Six Sigma?
A. RTY (Rolled Throughput Yield)
B. Cp
C. DPMO
D. VOC
✅ Answer: A. RTY (Rolled Throughput Yield)
Q92. In the Control phase, the key deliverable is:
A. Statistical report
B. Control plan
C. Regression model
D. Cost-benefit analysis
✅ Answer: B. Control plan
Q93. The DMAIC framework belongs to which quality philosophy?
A. Lean
B. Kaizen
C. Six Sigma
D. ISO 9001
✅ Answer: C. Six Sigma
Q94. What is the main purpose of the Define phase charter?
A. To formally document project scope and objectives
B. To calculate sigma level
C. To perform control charting
D. To design dashboards
✅ Answer: A. To formally document project scope and objectives
Q95. Which Six Sigma role ensures alignment with business goals?
A. Master Black Belt
B. Champion
C. Black Belt
D. Green Belt
✅ Answer: B. Champion
Q96. In Six Sigma, defects are measured relative to:
A. Control limits
B. Specification limits
C. Mean value
D. Median value
✅ Answer: B. Specification limits
Q97. A process operating at ±3σ capability corresponds to what yield?
A. 68.27%
B. 95.45%
C. 99.73%
D. 99.99966%
✅ Answer: C. 99.73%
Q98. Which of the following tools is most useful in root cause analysis?
A. Fishbone Diagram
B. Histogram
C. Scatter Plot
D. Box Plot
✅ Answer: A. Fishbone Diagram
Q99. Continuous improvement in Six Sigma aligns most closely with:
A. Kaizen principle
B. Breakthrough innovation
C. Customer discounting
D. Short-term control
✅ Answer: A. Kaizen principle
Q100. The sigma level represents:
A. Process accuracy
B. Number of standard deviations between mean and nearest specification limit
C. Sample size adequacy
D. Control chart slope
✅ Answer: B. Number of standard deviations between mean and nearest specification limit
Q101. A Six Sigma project targeting 3.4 DPMO corresponds to a yield of:
A. 93.3%
B. 99.73%
C. 99.99966%
D. 99.9%
✅ Answer: C. 99.99966%
Q102. What is a typical goal of Six Sigma deployment in service industries?
A. Reduce transaction errors
B. Improve machine accuracy
C. Automate production
D. Eliminate suppliers
✅ Answer: A. Reduce transaction errors
Q103. Which analytical tool is most suitable for determining process stability?
A. Control Chart
B. Pareto Chart
C. Scatter Diagram
D. Flowchart
✅ Answer: A. Control Chart
Q104. When a process shows random pattern within limits, it is considered:
A. Stable and predictable
B. Out of control
C. Needs recalibration
D. Under customer control
✅ Answer: A. Stable and predictable
Q105. A “shift” in the process mean without change in variation affects primarily:
A. Cp
B. Cpk
C. DPMO
D. None
✅ Answer: B. Cpk
Q106. Which Six Sigma metric quantifies potential process capability?
A. Cp
B. Cpk
C. RTY
D. DPMO
✅ Answer: A. Cp
Q107. Which Six Sigma metric reflects actual process capability?
A. Cp
B. Cpk
C. RTY
D. Pp
✅ Answer: B. Cpk
Q108. A Cp value less than 1 indicates:
A. Process variation exceeds customer tolerance
B. Process is stable
C. Process meets all CTQs
D. Data are non-normal
✅ Answer: A. Process variation exceeds customer tolerance
Q109. Which of the following statements about Six Sigma is false?
A. It aims for 3.4 defects per million opportunities
B. It is both a philosophy and a methodology
C. It guarantees zero defects
D. It focuses on data-driven decision making
✅ Answer: C. It guarantees zero defects
Q110. Which phase of DMAIC involves institutionalizing the improved process?
A. Define
B. Control
C. Measure
D. Improve
✅ Answer: B. Control
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