Six Sigma | DMAIC, SPC, Process Capability & Analyze Phase | 100+ MCQ with Answers
Q1. Which of the following best describes the main goal of Six Sigma?
A. Eliminating customer requirements
B. Reducing process variation and defects
C. Increasing production speed
D. Expanding product range
✅ Answer: B. Reducing process variation and defects
Q2. What differentiates Six Sigma from traditional quality control?
A. Six Sigma focuses only on inspection
B. Six Sigma aims to eliminate variation itself, not just control it
C. Six Sigma uses only qualitative analysis
D. Six Sigma disregards customer expectations
✅ Answer: B. Six Sigma aims to eliminate variation itself, not just control it
Q3. What are “chance causes” of variation?
A. Assignable causes due to human error
B. External variations like supplier issues
C. Natural or inherent process variation
D. None of the above
✅ Answer: C. Natural or inherent process variation
Q4. What are “assignable causes” in process variation?
A. Variation from expected process behavior
B. Unavoidable randomness
C. Stable long-term performance
D. Customer tolerance limits
✅ Answer: A. Variation from expected process behavior
Q5. What is the primary purpose of process control?
A. Eliminate all natural variation
B. Manage or remove assignable causes
C. Expand product specifications
D. Create marketing differentiation
✅ Answer: B. Manage or remove assignable causes
Q6. What defines whether a product is defective or not in Six Sigma terms?
A. Control limits
B. Specification limits
C. Standard deviation
D. Process average
✅ Answer: B. Specification limits
Q7. Control limits are based on:
A. Customer requirements
B. Process statistical behavior
C. Financial performance
D. Market competition
✅ Answer: B. Process statistical behavior
Q8. Which statement about tolerance and control limits is correct?
A. Tolerance limits are derived from process data
B. Control limits are customer-defined
C. Tolerance limits are customer-defined, control limits are statistically derived
D. Both are interchangeable
✅ Answer: C. Tolerance limits are customer-defined, control limits are statistically derived
Q9. The X-bar chart is primarily used to monitor:
A. Process variation
B. Sample mean of the process
C. Defect rates
D. Process flow
✅ Answer: B. Sample mean of the process
Q10. The R-chart monitors:
A. Process mean
B. Range or dispersion within samples
C. Process capability
D. Control limits
✅ Answer: B. Range or dispersion within samples
Q11. A process is said to be “in control” when:
A. All data points are outside control limits
B. Most points fall on the mean line
C. Data points fall within control limits without non-random patterns
D. Data points are randomly outside limits
✅ Answer: C. Data points fall within control limits without non-random patterns
Q12. What does Six Sigma level correspond to in DPMO terms?
A. 34 defects per 1 million
B. 3.4 defects per 1 million opportunities
C. 1.5 defects per 1 million
D. 0.34 defects per 1 million
✅ Answer: B. 3.4 defects per 1 million opportunities
Q13. The 1.5 sigma shift accounts for:
A. The process being perfectly centered
B. Long-term process drift
C. Machine calibration
D. Customer complaint margin
✅ Answer: B. Long-term process drift
Q14. Process capability ($C_p$) compares:
A. Actual defects with target defects
B. Natural process spread to specification limits
C. Mean shift to control limits
D. Customer complaints to tolerance width
✅ Answer: B. Natural process spread to specification limits
Q15. A $C_p$ of 1.0 indicates what Sigma level?
A. 2 Sigma
B. 3 Sigma
C. 4 Sigma
D. 6 Sigma
✅ Answer: B. 3 Sigma
Q16. A $C_p$ value of 2.0 corresponds to:
A. 6 Sigma
B. 3 Sigma
C. 4 Sigma
D. 2 Sigma
✅ Answer: A. 6 Sigma
Q17. If $C_p = 1.33$, the process is roughly at:
A. 3 Sigma
B. 4 Sigma
C. 5 Sigma
D. 2 Sigma
✅ Answer: B. 4 Sigma
Q18. $C_{pk}$ measures:
A. Process centering and alignment with specifications
B. Process variation only
C. Customer satisfaction level
D. Tolerance design width
✅ Answer: A. Process centering and alignment with specifications
Q19. If $C_p = 1$ but $C_{pk} < 1$, what does it indicate?
A. The process is centered
B. The process mean is shifting
C. Specification limits are too wide
D. The process is overperforming
✅ Answer: B. The process mean is shifting
Q20. A negative $C_{pk}$ implies:
A. High capability
B. The process is centered
C. Process output lies completely outside specifications
D. Variation is zero
✅ Answer: C. Process output lies completely outside specifications
Q21. Which formula calculates process standard deviation from the range chart?
A. $\sigma = R \times D_2$
B. $\sigma = \bar{R}/D_2$
C. $\sigma = \bar{R} + D_2$
D. $\sigma = \bar{R} - D_2$
✅ Answer: B. $\sigma = \bar{R}/D_2$
Q22. Z-value in a normal distribution represents:
A. The mean of the data
B. Standard deviation
C. Distance from the mean in standard deviations
D. Area under the curve
✅ Answer: C. Distance from the mean in standard deviations
Q23. The defect rate (PPM) can be found using:
A. Histogram
B. Normal area beyond specification limits
C. Pareto chart
D. Process mean value
✅ Answer: B. Normal area beyond specification limits
Q24. The Analyze phase focuses on:
A. Validating solutions
B. Identifying and validating root causes
C. Measuring defects
D. Controlling processes
✅ Answer: B. Identifying and validating root causes
Q25. Which tool is used for identifying potential causes (X factors)?
A. Histogram
B. Fishbone diagram
C. P-Chart
D. Scatter Plot
✅ Answer: B. Fishbone diagram
Q26. The Fishbone Diagram is also known as:
A. Pareto Chart
B. Cause-and-Effect Diagram
C. SIPOC Diagram
D. Failure Mode Diagram
✅ Answer: B. Cause-and-Effect Diagram
Q27. Which of the following is NOT a category in a Fishbone diagram?
A. Man
B. Machine
C. Market
D. Material
✅ Answer: C. Market
Q28. The “Five Why” technique is used for:
A. Root cause analysis
B. Process control
C. Customer satisfaction surveys
D. SPC charting
✅ Answer: A. Root cause analysis
Q29. The term “Gemba” or “Ginba” refers to:
A. Virtual process review
B. Going to the actual workplace to observe
C. Data sampling
D. Theoretical modeling
✅ Answer: B. Going to the actual workplace to observe
Q30. Pareto Analysis is based on which principle?
A. 60–40 Rule
B. 20–80 Rule
C. 10–90 Rule
D. 50–50 Rule
✅ Answer: B. 20–80 Rule
Q31. What is the main purpose of a Pareto Chart?
A. Identify all causes equally
B. Focus on trivial many
C. Identify the few causes that contribute to most defects
D. Compare process means
✅ Answer: C. Identify the few causes that contribute to most defects
Q32. Pareto Analysis can be enhanced by including:
A. Cost of Correction
B. Defect count only
C. Mean value
D. Standard deviation
✅ Answer: A. Cost of Correction
Q33. A Box Plot helps visualize:
A. Process control
B. Variation and outliers
C. Customer satisfaction
D. Cost distribution
✅ Answer: B. Variation and outliers
Q34. Histogram is used for:
A. Continuous data distribution
B. Categorical data comparison
C. Cause identification
D. Time series tracking
✅ Answer: A. Continuous data distribution
Q35. Bar chart is used for:
A. Continuous data
B. Categorical data
C. Process control
D. Range data
✅ Answer: B. Categorical data
Q36. Which type of graph shows relationship over time?
A. Line graph
B. Scatter plot
C. Pie chart
D. Histogram
✅ Answer: A. Line graph
Q37. Hypothesis testing helps to:
A. Visually identify variation
B. Statistically validate root causes
C. Calculate mean
D. Create control limits
✅ Answer: B. Statistically validate root causes
Q38. The null hypothesis ($H_0$) states:
A. There is a significant difference
B. There is no significant difference
C. Data is non-random
D. The process is out of control
✅ Answer: B. There is no significant difference
Q39. A P-value less than 0.05 implies:
A. Fail to reject $H_0$
B. Reject $H_0$ (significant impact)
C. Accept $H_0$
D. No effect observed
✅ Answer: B. Reject $H_0$ (significant impact)
Q40. If P-value is high (>0.05):
A. Evidence against $H_0$ is weak
B. Strong evidence against $H_0$
C. Hypothesis invalid
D. Data is abnormal
✅ Answer: A. Evidence against $H_0$ is weak
Q41. Which test compares one sample mean with a population mean?
A. Two-sample T-test
B. One-sample T-test
C. Chi-square
D. ANOVA
✅ Answer: B. One-sample T-test
Q42. Two-sample T-test is used to:
A. Compare more than two group means
B. Compare two independent group means
C. Compare categorical data
D. Validate P-values
✅ Answer: B. Compare two independent group means
Q43. ANOVA is used when comparing:
A. Two means
B. One mean
C. More than two means
D. Variance of one sample
✅ Answer: C. More than two means
Q44. Chi-Square test determines:
A. Relationship between categorical variables
B. Difference between means
C. Correlation strength
D. Confidence interval width
✅ Answer: A. Relationship between categorical variables
Q45. In the Malgudi Hospital case, the CTQ goal was to:
A. Reduce defect cost
B. Reduce registration time below 120 seconds
C. Improve hospital ratings
D. Increase patient volume
✅ Answer: B. Reduce registration time below 120 seconds
Q46. The process average ($\bar{\bar{X}}$) in the baseline was:
A. 120 seconds
B. 179 seconds
C. 60 seconds
D. 90 seconds
✅ Answer: B. 179 seconds
Q47. The $C_p$ value of 0.286 in the Malgudi case indicated:
A. High process capability
B. Very poor process capability
C. Stable process
D. No variation
✅ Answer: B. Very poor process capability
Q48. A negative $C_{pk}$ at Malgudi Hospital implied:
A. Centered process
B. Process mean outside specification
C. High sigma level
D. Excellent performance
✅ Answer: B. Process mean outside specification
Q49. The defect rate in the Malgudi Hospital case was approximately:
A. 3.4 DPMO
B. 800,000 DPMO
C. 34,000 DPMO
D. 1,200 DPMO
✅ Answer: B. 800,000 DPMO
Q50. The next phase after Measure in DMAIC is:
A. Improve
B. Define
C. Analyze
D. Control
✅ Answer: C. Analyze
Q51. In hypothesis testing, Type I error occurs when:
A. You reject a true null hypothesis
B. You accept a false null hypothesis
C. You fail to reject a false null hypothesis
D. You reject an alternative hypothesis
✅ Answer: A. You reject a true null hypothesis
Q52. Type II error occurs when:
A. You reject a false null hypothesis
B. You fail to reject a false null hypothesis
C. You reject a true null hypothesis
D. You misinterpret p-value
✅ Answer: B. You fail to reject a false null hypothesis
Q53. The significance level (α) represents:
A. Probability of making a Type I error
B. Probability of making a Type II error
C. Process mean
D. Sample variance
✅ Answer: A. Probability of making a Type I error
Q54. Confidence level is defined as:
A. 1 + α
B. 1 – α
C. α / 2
D. 1 / α
✅ Answer: B. 1 – α
Q55. A p-value of 0.03 means:
A. 97% probability the null hypothesis is true
B. 3% chance results are due to random variation
C. No statistical difference
D. Data cannot be trusted
✅ Answer: B. 3% chance results are due to random variation
Q56. In hypothesis testing, the decision to reject or fail to reject $H_0$ is based on:
A. Mean value
B. Control chart
C. p-value vs significance level
D. Standard deviation
✅ Answer: C. p-value vs significance level
Q57. The Chi-Square test is most suitable when data is:
A. Continuous
B. Discrete categorical
C. Normally distributed
D. Time-based
✅ Answer: B. Discrete categorical
Q58. In a Chi-Square test, a large χ² statistic means:
A. No association
B. Strong association between variables
C. Small variance
D. Large p-value
✅ Answer: B. Strong association between variables
Q59. ANOVA determines whether:
A. Variances of samples are equal
B. Mean differences exist among groups
C. Data are normally distributed
D. Null hypothesis is always true
✅ Answer: B. Mean differences exist among groups
Q60. A low ANOVA p-value (<0.05) suggests:
A. All group means are equal
B. At least one group mean differs significantly
C. No difference between groups
D. Sample error
✅ Answer: B. At least one group mean differs significantly
Q61. The control chart pattern “two consecutive points near control limits” often signals:
A. Random variation
B. Special cause
C. Normal variation
D. Stable process
✅ Answer: B. Special cause
Q62. A process is said to be “out of control” when:
A. 7 consecutive points lie on one side of mean
B. Data are symmetrically distributed
C. No points cross control limits
D. Mean remains constant
✅ Answer: A. 7 consecutive points lie on one side of mean
Q63. Which control chart is used for monitoring defect count per unit?
A. P-chart
B. U-chart
C. C-chart
D. X-bar chart
✅ Answer: C. C-chart
Q64. A P-chart monitors:
A. Continuous measurements
B. Proportion of defectives
C. Average range
D. Customer satisfaction
✅ Answer: B. Proportion of defectives
Q65. The U-chart is appropriate when:
A. Sample sizes are constant
B. Defects per unit vary
C. Data are continuous
D. Process mean is zero
✅ Answer: B. Defects per unit vary
Q66. Which control chart is used for variable data (e.g., time, weight, temperature)?
A. NP-chart
B. R-chart
C. X-bar chart
D. Both B and C
✅ Answer: D. Both B and C
Q67. In SPC, the primary purpose of a control chart is to:
A. Eliminate all variation
B. Detect signals of assignable causes
C. Maintain constant output
D. Measure profitability
✅ Answer: B. Detect signals of assignable causes
Q68. Which is NOT an assumption for using control charts?
A. Data are collected in rational subgroups
B. Process is consistent over time
C. Data come from a stable process
D. Data can be randomly collected without structure
✅ Answer: D. Data can be randomly collected without structure
Q69. A “run” in SPC refers to:
A. Consecutive points on one side of the mean
B. A single outlier
C. Constant standard deviation
D. Decreasing Cp
✅ Answer: A. Consecutive points on one side of the mean
Q70. A process with Cp = 1.0 and Cpk = 0.3 is:
A. Capable and centered
B. Not centered and poorly capable
C. Highly capable
D. Overperforming
✅ Answer: B. Not centered and poorly capable
Q71. Cp = 1.67 generally corresponds to which Sigma level?
A. 3 Sigma
B. 5 Sigma
C. 4.5 Sigma
D. 6 Sigma
✅ Answer: C. 4.5 Sigma
Q72. In service industries, the Analyze phase often focuses on:
A. Machine calibration
B. Human and procedural root causes
C. Material defect tracking
D. Supplier variation
✅ Answer: B. Human and procedural root causes
Q73. Which Six Sigma tool is best for visualizing customer wait times distribution?
A. Pareto chart
B. Histogram
C. Scatter plot
D. Fishbone diagram
✅ Answer: B. Histogram
Q74. When two continuous variables are plotted to examine their relationship, we use:
A. Scatter plot
B. Bar chart
C. Pareto chart
D. U-chart
✅ Answer: A. Scatter plot
Q75. A high positive correlation coefficient (r = 0.9) indicates:
A. Strong direct relationship
B. Weak relationship
C. No relationship
D. Negative relationship
✅ Answer: A. Strong direct relationship
Q76. In the Malgudi Hospital case, a histogram showing right-skewed data implies:
A. Registration times are consistent
B. Most registrations are faster than average
C. Most registrations are slower than average
D. Normal distribution
✅ Answer: C. Most registrations are slower than average
Q77. The main objective of root cause validation is to:
A. Quantify the root cause
B. Verify that the suspected X truly impacts Y
C. Compare customer feedback
D. Test multiple causes simultaneously
✅ Answer: B. Verify that the suspected X truly impacts Y
Q78. Which is the best approach before moving to the Improve phase?
A. Validate X–Y relationships statistically
B. Brainstorm more ideas
C. Collect more data without analysis
D. Skip validation for time saving
✅ Answer: A. Validate X–Y relationships statistically
Q79. When the process mean shifts by +1.5σ, what happens to defect rate?
A. It increases from 0.002 ppm to 3.4 ppm
B. It decreases to zero
C. It doubles
D. It becomes unpredictable
✅ Answer: A. It increases from 0.002 ppm to 3.4 ppm
Q80. Control limits are generally placed at:
A. ±1σ
B. ±2σ
C. ±3σ
D. ±6σ
✅ Answer: C. ±3σ
Q81. Which term best describes “Voice of the Customer”?
A. Specification limits
B. Control limits
C. Average range
D. Sigma value
✅ Answer: A. Specification limits
Q82. “Voice of the Process” corresponds to:
A. Control limits
B. Customer complaint data
C. Specification range
D. Target mean
✅ Answer: A. Control limits
Q83. The intersection between VOC and VOP defines:
A. Process capability
B. Financial efficiency
C. Customer satisfaction index
D. Supplier rating
✅ Answer: A. Process capability
Q84. If a process has Cpk < 1.0, it means:
A. Process meets specs comfortably
B. Process is barely meeting or failing specs
C. Process is overperforming
D. No defects present
✅ Answer: B. Process is barely meeting or failing specs
Q85. A Cp > 1 and Cpk < 1 indicates:
A. Process spread is good, but mean is off-center
B. Process is incapable
C. Process is centered and capable
D. Zero variation
✅ Answer: A. Process spread is good, but mean is off-center
Q86. The term DPMO stands for:
A. Defects per Million Operations
B. Defects per Million Opportunities
C. Defects per Monthly Output
D. Deviations per Mean Opportunity
✅ Answer: B. Defects per Million Opportunities
Q87. The Analyze phase primarily seeks to convert:
A. Symptom data into verified root causes
B. Causes into action plans
C. Control limits into tolerances
D. Outputs into specifications
✅ Answer: A. Symptom data into verified root causes
Q88. The “Y = f(X)” concept implies:
A. Output depends on multiple input factors
B. Process depends on customer behavior
C. Output is independent of inputs
D. Random outcomes only
✅ Answer: A. Output depends on multiple input factors
Q89. In Lean Six Sigma, which approach is often integrated into Analyze phase?
A. 5S workplace management
B. Kanban visualization
C. Value stream mapping
D. Benchmarking
✅ Answer: C. Value stream mapping
Q90. The measure of dispersion around the process mean is:
A. Range
B. Mean
C. Sigma (standard deviation)
D. Cp value
✅ Answer: C. Sigma (standard deviation)
Q91. In hypothesis testing, “rejecting the null” means:
A. There is no significant impact
B. There is a statistically significant impact
C. Data is random
D. Process is under control
✅ Answer: B. There is a statistically significant impact
Q92. The Malgudi Hospital’s registration process violated CTQ because:
A. Control limits were too tight
B. Average time exceeded the USL
C. Too many assignable causes
D. Poor data collection
✅ Answer: B. Average time exceeded the USL
Q93. The first step after defining the problem in Analyze phase is:
A. Develop regression model
B. Brainstorm potential causes
C. Validate customer satisfaction
D. Draw Pareto chart
✅ Answer: B. Brainstorm potential causes
Q94. Which of the following is an example of an assignable cause?
A. Random fluctuations
B. Machine breakdown
C. Natural material variation
D. Stable operator speed
✅ Answer: B. Machine breakdown
Q95. When histogram bars touch each other, it implies:
A. Categorical data
B. Continuous data
C. Poor data quality
D. Discrete defects
✅ Answer: B. Continuous data
Q96. The area under the normal curve between ±3σ covers:
A. 99.73% of data
B. 95.45% of data
C. 68.27% of data
D. 100% of data
✅ Answer: A. 99.73% of data
Q97. Which is the correct hierarchy in Six Sigma project flow?
A. Define → Measure → Analyze → Improve → Control
B. Measure → Analyze → Control → Define → Improve
C. Analyze → Define → Measure → Control → Improve
D. Control → Measure → Improve → Define → Analyze
✅ Answer: A. Define → Measure → Analyze → Improve → Control
Q98. The “3.4 DPMO” benchmark assumes:
A. 1.5σ mean shift
B. 0.5σ shift
C. No shift
D. Constant mean
✅ Answer: A. 1.5σ mean shift
Q99. Which of the following tools is NOT used in the Analyze phase?
A. Fishbone diagram
B. Pareto chart
C. Hypothesis test
D. Control plan
✅ Answer: D. Control plan
Q100. A normal distribution is symmetric around:
A. Mode
B. Median
C. Mean
D. All of the above
✅ Answer: D. All of the above
Q101. Process capability indices ($C_p$ and $C_{pk}$) are valid only when:
A. The process is in control
B. The process is unstable
C. The process has defects
D. Data are non-normal
✅ Answer: A. The process is in control
Q102. The symbol μ represents:
A. Sample mean
B. Population mean
C. Standard deviation
D. Process range
✅ Answer: B. Population mean
Q103. The Analyze phase helps in distinguishing:
A. Common causes from special causes
B. Defects from reworks
C. Inputs from outputs
D. Customers from suppliers
✅ Answer: A. Common causes from special causes
Q104. The overall average in an X-bar chart is denoted as:
A. $\bar{R}$
B. $\bar{\bar{X}}$
C. μ
D. σ
✅ Answer: B. $\bar{\bar{X}}$
Q105. The main statistical distribution assumed in Six Sigma is:
A. Binomial
B. Normal
C. Poisson
D. Exponential
✅ Answer: B. Normal
Q106. Process capability focuses on the relationship between:
A. Voice of the Process and Voice of the Customer
B. Control limits and sample size
C. Mean and standard deviation
D. Sigma and variance
✅ Answer: A. Voice of the Process and Voice of the Customer
Q107. A process with Cp < 1 means:
A. Process spread is wider than specification limits
B. Process spread fits within specification limits
C. Process is capable
D. Process mean is ideal
✅ Answer: A. Process spread is wider than specification limits
Q108. Which phase validates whether improvement efforts were successful?
A. Define
B. Analyze
C. Improve
D. Control
✅ Answer: D. Control
Q109. The relationship Y = f(X) implies that:
A. Controlling Xs will improve Y
B. Y influences X
C. Y is random
D. X and Y are unrelated
✅ Answer: A. Controlling Xs will improve Y
Q110. The ultimate goal of Six Sigma projects is to:
A. Optimize profitability through process excellence
B. Eliminate staff errors
C. Increase data collection frequency
D. Reduce management oversight
✅ Answer: A. Optimize profitability through process excellence
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