Lean Six Sigma Green Belt Practice Exam — All Questions

The main purpose of a control chart in the Control phase is to:

• a.Rank problems from most to least frequent
• b.Map the suppliers and customers of a process
• c.Prove a factor is statistically significant
• d.Distinguish common-cause variation from special-cause variation over time✓

Control charts plot data over time with control limits so teams can tell routine common-cause variation from special-cause signals that need action. Ranking, mapping, and significance testing are done with other tools.

A process has USL = 110, LSL = 90, mean = 100, and standard deviation = 2.5. What is the Cp (process capability)?

• a.0.67
• b.1.00
• c.2.00
• d.1.33✓

Cp = (USL - LSL) / (6 x sigma) = (110 - 90) / (6 x 2.5) = 20 / 15 = 1.33. A Cp of 1.33 corresponds to a four-sigma capable process when centered.

In Lean, which of the following is one of the classic categories of waste (muda)?

• a.Value-added processing
• b.Overproduction✓
• c.Standardized work
• d.Continuous flow

Overproduction, making more or sooner than needed, is one of the classic wastes and is often called the worst because it hides others. Standardized work, value-added processing, and continuous flow are goals, not wastes.

The 5S methodology (Sort, Set in order, Shine, Standardize, Sustain) is primarily aimed at:

• a.Calculating rolled throughput yield
• b.Organizing and maintaining an efficient, orderly workplace✓
• c.Performing a measurement system analysis
• d.Designing a full factorial experiment

5S creates and sustains a clean, organized, visual workplace that exposes abnormalities and supports flow. It is a workplace-organization method, not an experimental, yield, or measurement technique.

A control plan created at the end of a project is intended mainly to:

• a.Sustain the gains by specifying what to monitor, how, and the reaction plan if limits are exceeded✓
• b.Replace the need for any ongoing measurement
• c.Define the original problem statement
• d.Calculate the project's net present value

The control plan documents the key characteristics to monitor, the method and frequency, and the response if the process drifts, so improvements hold over time. It defines ongoing monitoring rather than eliminating it, and it is not a Define or finance tool.

You are monitoring a continuous measurement (part length in mm) collected in rational subgroups of 5 units each. Which control chart pair is the standard choice?

• a.p chart and np chart
• b.Individuals and moving-range (I-MR) chart
• c.X-bar and R chart✓
• d.c chart and u chart

For continuous (variable) data in subgroups of about 2-9, the X-bar and R chart is standard: X-bar tracks the subgroup average (process center) and R tracks the subgroup range (spread). p/np/c/u are attribute charts, and I-MR is for subgroups of size 1.

A process produces one measurable result at a time (a single reading per hour) so no rational subgroup can be formed. Which control chart is appropriate?

• a.p chart
• b.Individuals and moving-range (I-MR) chart✓
• c.X-bar and R chart
• d.X-bar and S chart

When the subgroup size is 1, the Individuals and Moving-Range (I-MR) chart is used: the individuals chart tracks each reading and the moving range (absolute difference between consecutive points) estimates short-term variation. X-bar charts require subgroups of 2 or more.

A team counts the number of defective (nonconforming) units in a constant sample of 100 units drawn each shift. Which attribute chart fits this data?

• a.u chart
• b.np chart✓
• c.X-bar and R chart
• d.c chart

The np chart plots the count of defective units when the sample size is constant. It tracks how many units fail, not how many defects each unit has. If the sample size varied you would use a p chart (proportion), and defect counts use c or u charts.

An auditor records the proportion of nonconforming invoices each day, but the number of invoices audited changes daily. Which control chart is correct?

• a.X-bar and R chart
• b.np chart
• c.p chart✓
• d.c chart

The p chart plots the proportion (fraction) defective and correctly handles a varying sample size, because its control limits are recomputed for each subgroup's n. The np chart requires a constant sample size, and c/u charts count defects rather than defective units.

A quality tech counts the total number of surface blemishes on one standard-size sheet of glass inspected each hour (constant area of opportunity). Which chart applies?

• a.p chart
• b.X-bar and S chart
• c.np chart
• d.c chart✓

The c chart plots the count of defects (nonconformities) per inspection unit when the area of opportunity is constant. Multiple blemishes can appear on one sheet, so this counts defects, not defective units. A varying area of opportunity would call for a u chart.

Inspectors count defects on rolls of fabric, but the rolls vary in length, so the area of opportunity changes from sample to sample. Which chart is correct?

• a.u chart✓
• b.p chart
• c.c chart
• d.np chart

The u chart plots defects per unit (count of defects normalized by the varying area of opportunity), so its limits adjust for each sample's size. The c chart requires a constant area; p and np track defective units, not defect counts.

Continuous data are collected in large subgroups of 12 measurements each. Which pair of charts is preferred over X-bar and R?

• a.c chart and u chart
• b.p chart and np chart
• c.I-MR chart
• d.X-bar and S chart✓

For subgroups of about 10 or more, the X-bar and S chart is preferred because the sample standard deviation (S) estimates spread more efficiently than the range for larger subgroups. The range works well only for small subgroups (roughly 2-9).

The key difference between a p chart and an np chart is that:

• a.A p chart plots the fraction defective (any sample size) while an np chart plots the count of defectives (constant sample size)✓
• b.A p chart is for continuous data and an np chart is for attribute data
• c.A p chart counts the individual defects present on each inspected unit, whereas an np chart counts whole defective units, so the two charts measure fundamentally different and unrelated quantities
• d.There is no difference; the terms are interchangeable

Both charts track defective units, but a p chart plots the proportion defective and accepts variable sample sizes, whereas an np chart plots the raw count of defectives and requires a constant sample size. Neither counts individual defects (that is c/u), and both are attribute charts.

Which statement best distinguishes a c chart from a u chart?

• a.A c chart requires a constant area of opportunity; a u chart handles a varying area of opportunity✓
• b.A c chart plots proportion defective; a u chart plots count of defective units
• c.A c chart may be used only when the subgroups are of size one, whereas the u chart is reserved exclusively for continuous variable measurement data
• d.A c chart is for continuous data; a u chart is for attribute data

Both c and u charts track defect (nonconformity) counts. The c chart assumes a constant inspection area, while the u chart normalizes to defects-per-unit so it works when the area of opportunity varies. Neither plots defective units (that is p/np).

Which underlying distribution is assumed for the counts on a c chart?

• a.Uniform distribution
• b.Poisson distribution✓
• c.Normal distribution
• d.Binomial distribution

The c chart (and u chart) model defect counts with the Poisson distribution, where the variance equals the mean, which is why the control limits use the square root of c-bar. Defective-unit charts (p, np) use the binomial distribution, and variable charts assume normality.

Which distribution underlies the p and np charts used for defective units?

• a.Poisson distribution
• b.Binomial distribution✓
• c.Exponential distribution
• d.Normal distribution

Defective-unit (pass/fail) data follow the binomial distribution, so p and np chart limits are built from p-bar and the binomial standard error. Defect-count charts (c, u) use the Poisson distribution, and variable charts assume approximate normality.

For an X-bar chart with subgroups of n=5, the average of subgroup means is 100 and the average range (R-bar) is 5. Using A2 = 0.577, what is the upper control limit (UCL) for the X-bar chart?

• a.97.115
• b.100.577
• c.102.885✓
• d.105.000

UCL(X-bar) = X-double-bar + A2 x R-bar = 100 + 0.577 x 5 = 100 + 2.885 = 102.885. The A2 constant (0.577 for n=5) converts the average range into three-sigma limits for the subgroup means. The matching LCL is 100 - 2.885 = 97.115.

Using the same X-bar/R data (n=5, X-double-bar = 100, R-bar = 5, A2 = 0.577), what is the lower control limit (LCL) for the X-bar chart?

• a.95.000
• b.99.423
• c.102.885
• d.97.115✓

LCL(X-bar) = X-double-bar - A2 x R-bar = 100 - 0.577 x 5 = 100 - 2.885 = 97.115. The control limits are symmetric about the center line at 100, giving 97.115 and 102.885.

For the R chart (n=5, R-bar = 5) with D4 = 2.114 and D3 = 0, what are the control limits for the range?

• a.UCL = 15.000, LCL = 5.000
• b.UCL = 10.570, LCL = 0✓
• c.UCL = 7.114, LCL = 0
• d.UCL = 5.577, LCL = 0

UCL(R) = D4 x R-bar = 2.114 x 5 = 10.570 and LCL(R) = D3 x R-bar = 0 x 5 = 0. For subgroups of 5 or fewer, D3 is 0, so the range chart has no lower limit. The D-constants convert the average range into three-sigma limits for the range.

An X-bar/R study uses subgroups of n=4. With X-double-bar = 50, R-bar = 8, and A2 = 0.729, the X-bar chart control limits are approximately:

• a.UCL = 58.000, LCL = 42.000
• b.UCL = 66.000, LCL = 34.000
• c.UCL = 50.729, LCL = 49.271
• d.UCL = 55.832, LCL = 44.168✓

UCL = 50 + 0.729 x 8 = 50 + 5.832 = 55.832 and LCL = 50 - 5.832 = 44.168. A2 = 0.729 corresponds to n=4. The limits are three-sigma bounds on the subgroup means, centered on 50.

For subgroups of n=4 with R-bar = 8 and D4 = 2.282, the upper control limit of the R chart is:

• a.8.282
• b.16.000
• c.18.256✓
• d.10.282

UCL(R) = D4 x R-bar = 2.282 x 8 = 18.256. With n=4, D3 = 0 so LCL(R) = 0. The R chart must be assessed for control before the X-bar limits are trusted, because the range estimates the process spread that feeds the X-bar limits.

When building an X-bar and R chart, which chart should be confirmed to be in control FIRST, and why?

• a.Either one; the order does not matter
• b.The R chart, because the X-bar control limits are calculated from R-bar and are meaningless if the spread is unstable✓
• c.The X-bar chart should always be confirmed first, because the location of the process average is far more important to the customer than the amount of spread present in the data
• d.Neither; both are read only after the process is closed out

Evaluate the R (range) chart first. The X-bar limits are computed using R-bar (via A2), so if the variation is unstable the X-bar limits themselves are invalid. Only once the spread is in control can the average be meaningfully assessed.

A p chart monitors invoice errors with p-bar = 0.04 and a constant sample of n = 200. Using three-sigma limits, the UCL is approximately:

• a.0.1200
• b.0.0816✓
• c.0.0400
• d.0.0600

UCL = p-bar + 3 x sqrt(p-bar(1 - p-bar)/n) = 0.04 + 3 x sqrt(0.04 x 0.96 / 200) = 0.04 + 3 x sqrt(0.000192) = 0.04 + 3 x 0.01386 = 0.04 + 0.0416 = 0.0816. The p chart standard error uses the binomial formula.

For the same p chart (p-bar = 0.04, n = 200), the lower control limit computes to 0.04 - 0.0416 = -0.0016. What is the correct LCL to plot?

• a.-0.0016
• b.0.0416
• c.0.0400
• d.0 (a proportion cannot be negative)✓

When the calculated LCL for a p chart (or any attribute chart) is negative, it is truncated to 0 because a proportion or count cannot be below zero. So the LCL is set at 0, meaning there is effectively no lower limit signal for this chart.

A c chart monitors defects on assembled boards with c-bar = 9 defects per board. Using three-sigma limits, the UCL and LCL are:

• a.UCL = 12, LCL = 6
• b.UCL = 27, LCL = 0
• c.UCL = 18, LCL = 0✓
• d.UCL = 21, LCL = -3

For a c chart, limits = c-bar plus/minus 3 x sqrt(c-bar) = 9 plus/minus 3 x sqrt(9) = 9 plus/minus 3 x 3 = 9 plus/minus 9. So UCL = 18 and the calculated LCL = 0. The Poisson square-root form drives the c chart limits.

A c chart has c-bar = 16 defects per inspection unit. What are its three-sigma control limits?

• a.UCL = 28, LCL = 4✓
• b.UCL = 24, LCL = 8
• c.UCL = 32, LCL = 0
• d.UCL = 20, LCL = 12

c chart limits = c-bar plus/minus 3 x sqrt(c-bar) = 16 plus/minus 3 x sqrt(16) = 16 plus/minus 3 x 4 = 16 plus/minus 12. So UCL = 28 and LCL = 4. Because c-bar is large enough, the LCL stays positive and can signal improvement.

A u chart tracks defects per unit with u-bar = 2.0 and a sample of n = 5 units per subgroup. Using three-sigma limits, the UCL is approximately:

• a.3.897✓
• b.5.000
• c.2.000
• d.2.632

UCL(u) = u-bar + 3 x sqrt(u-bar / n) = 2.0 + 3 x sqrt(2.0 / 5) = 2.0 + 3 x sqrt(0.4) = 2.0 + 3 x 0.6325 = 2.0 + 1.897 = 3.897. The u chart divides the Poisson variance by the subgroup size n, so limits tighten as n grows.

An np chart has a constant sample of n = 200 and average fraction defective p-bar = 0.03, so n x p-bar = 6. Using three-sigma limits, the UCL is approximately:

• a.18.00
• b.13.24✓
• c.9.00
• d.6.00

UCL(np) = n x p-bar + 3 x sqrt(n x p-bar x (1 - p-bar)) = 6 + 3 x sqrt(6 x 0.97) = 6 + 3 x sqrt(5.82) = 6 + 3 x 2.413 = 6 + 7.24 = 13.24. The np chart uses the binomial standard error on the raw defective count.

Why are control limits on a control chart typically set at plus or minus three standard deviations from the center line?

• a.Because three-sigma control limits are defined so that they line up exactly with the customer's upper and lower specification limits on every properly constructed chart
• b.Because three-sigma limits guarantee zero defects
• c.Because they balance the risk of false alarms against the risk of missing real special-cause signals✓
• d.Because regulators require exactly three sigma by law

Three-sigma limits (Shewhart's choice) capture about 99.73% of common-cause variation, keeping false alarms rare (about 0.27%) while still detecting genuine special causes reasonably well. They are derived from process data, not from specifications, and they do not guarantee zero defects.

What is the fundamental difference between control limits and specification limits?

• a.Control limits come from the process's own variation (voice of the process); specification limits come from customer/engineering requirements (voice of the customer)✓
• b.Specification limits are, by mathematical definition, always guaranteed to be wider than the control limits on any chart, because the control limits are computed as a fixed fraction of the specification tolerance itself
• c.They are the same thing computed two different ways
• d.Control limits come from the customer; specification limits come from the process data

Control limits are calculated from the process's actual variation (the voice of the process) and describe what the process does. Specification limits reflect customer or engineering requirements (the voice of the customer) and describe what is wanted. They are set independently and must never be plotted as one another.

A Green Belt draws the customer's specification limits directly onto an X-bar control chart to decide if points are 'out of control.' Why is this wrong?

• a.Specification limits are always tighter than the control limits, which means no plotted point could ever fall outside them and therefore the chart would never generate a single out-of-control signal
• b.Spec limits apply to individual units, not to subgroup averages, and control limits (from process variation) are what define statistical control✓
• c.Control charts cannot show any limits at all
• d.It is fine and is standard SPC practice

Specification limits apply to individual measurements, while an X-bar chart plots subgroup averages that vary less than individuals. Statistical control is judged against control limits derived from the process's own variation, never against spec limits. Mixing them leads to wrong signals.

A process can be 'in statistical control' yet still produce defects. What does this indicate?

• a.The process is stable (only common-cause variation) but not capable of meeting the specification✓
• b.The control chart is calculated incorrectly
• c.The specification limits must have been drawn inside the control limits by mistake, which is the only situation in which a truly stable process could ever produce a defective unit
• d.The process has a special cause that must be removed

In-control means only common-cause (routine) variation is present, so the process is stable and predictable. But stability says nothing about meeting specs; if the common-cause spread is wider than the tolerance, a stable process still makes defects. That is a capability problem, addressed by reducing variation or recentering.

Which pairing correctly maps the concept to its phrase?

• a.Control limits = voice of the customer; specification limits = voice of the process
• b.Both are the voice of the customer
• c.Both are the voice of the process
• d.Control limits = voice of the process; specification limits = voice of the customer✓

Control limits are the voice of the process (what the process actually delivers), while specification limits are the voice of the customer (what the customer requires). Capability analysis compares these two voices to see whether the process can satisfy requirements.

On a control chart, a single point falling beyond the upper control limit is a signal of:

• a.A guaranteed measurement error
• b.Common-cause variation that should be ignored
• c.A special (assignable) cause that warrants investigation✓
• d.The process being perfectly centered

A point outside the three-sigma control limits (Western Electric Rule 1) is the classic signal of a special or assignable cause, an unusual event not part of the routine process. The reaction plan should trigger an investigation to find and address the cause.

Western Electric Rule 2 flags a special cause when:

• a.Eight points in a row fall on one side of the center line
• b.One point falls beyond three sigma
• c.Six points in a row steadily increase or decrease
• d.Two out of three consecutive points fall beyond two sigma on the same side✓

Western Electric Rule 2 signals when 2 of 3 consecutive points are beyond the two-sigma line on the same side of the center. It detects a moderate shift that a single three-sigma point (Rule 1) might miss. Runs and trends are covered by other rules.

Western Electric Rule 3 signals a special cause when:

• a.One point falls beyond two sigma
• b.Two points alternate above and below the center line
• c.Four out of five consecutive points fall beyond one sigma on the same side of the center line✓
• d.Fifteen consecutive points in a row all hug tightly to the center line within the innermost one-sigma zone on both sides

Western Electric Rule 3 fires when 4 of 5 consecutive points lie beyond the one-sigma line on the same side. It catches a smaller sustained shift than Rules 1 or 2. The zones (one, two, three sigma) let these rules detect shifts of different sizes.

A run of 8 consecutive points all on the same side of the center line indicates:

• a.A special cause such as a process mean shift (Western Electric Rule 4)✓
• b.That the control limits are too wide
• c.A perfectly capable process
• d.Nothing; runs are always normal

Eight points in a row on one side of the center line (Western Electric Rule 4) is very unlikely by chance and signals a sustained shift in the process mean. A shift like this should trigger the reaction plan even though no single point may be outside the limits.

A Nelson-rule trend signal is triggered by:

• a.The appearance of any single individual point located anywhere inside the two outer three-sigma control limits
• b.Points randomly scattered around the center line
• c.Two points beyond three sigma
• d.Six (or seven) consecutive points steadily increasing or decreasing✓

A steadily rising or falling run of six or more points (Nelson Rule 3) signals a trend, often from tool wear, drift, or gradual change. Random scatter around the center is exactly what a stable, in-control process should show and is not a signal.

The control chart 'zones' (A, B, C) used by run rules divide the chart into bands of:

• a.The specification tolerance in thirds
• b.The distance between USL and LSL
• c.Equal counts of data points
• d.One-sigma-wide bands on each side of the center line✓

Zones C, B, and A are each one standard deviation wide, measured outward from the center line to the three-sigma control limits. Run rules (Western Electric/Nelson) count how points fall within these one-sigma zones to detect shifts and trends beyond just three-sigma exceedances.

A Nelson rule fires when 15 consecutive points fall within one sigma of the center line (in Zone C on both sides). What does this typically indicate?

• a.A perfectly ideal process with no issues
• b.A tool-wear trend
• c.Stratification or 'too good to be true' data, often from miscalculated limits or mixed data✓
• d.A sudden and unusually large upward shift in the underlying process mean that has pushed every one of the recent points far above the target

Fifteen points hugging the center line (Nelson Rule 7) is unnaturally low variation. It usually points to a problem such as incorrectly computed limits, stratified sampling, or data from mixed sources, not a genuinely excellent process. It is a signal to investigate, not to celebrate.