🎓 CSSBB Quest › Section V

Section V — Measure Phase ~17%

Measure is the largest section on the CSSBB exam. It tests quantitative skills more than any other phase — MSA calculations, capability indices, sampling theory, graphical analysis, and baseline sigma. It carries 25 of the 150 scored questions (about 17%).

Measure phase subtopics

Subtopic	Key exam content
Process characteristics	Process flow metrics (WIP, cycle time, throughput, takt time); process analysis tools such as detailed process maps, value stream maps, spaghetti diagrams and swim-lane maps; value-added vs. non-value-added steps
Basic statistics and probability	Descriptive statistics; central limit theorem; drawing valid statistical conclusions; probability concepts; normal, binomial, Poisson and other common distributions
Data collection	Data types (continuous vs. attribute), operational definitions, sampling plans, data collection plans and methods
Measurement system analysis (MSA)	Gauge R&R (ANOVA and average/range methods), bias, linearity, stability, discrimination; attribute agreement analysis
Process capability	C_p, C_pk, P_p, P_pk; capability studies; capability for attribute and non-normal data; short-term vs. long-term capability and the 1.5σ shift; DPMO and sigma level
Graphical methods	Histograms, box plots, run charts, scatter plots, normal probability plots, Pareto charts

Measurement system analysis (MSA) key numbers

The exam tests these thresholds. Know them cold:

Metric	Acceptable	Marginal	Unacceptable
%Gauge R&R (of study variation)	< 10%	10–30%	> 30%
Number of distinct categories (NDC)	≥ 5	—	< 5
%Gauge R&R of tolerance	< 10%	10–30%	> 30%

Exam trap: %Gauge R&R can look acceptable when compared to process variation but unacceptable when compared to the tolerance — or vice versa. The correct basis depends on the purpose: improvement projects use process variation (study variation); acceptance decisions use tolerance.

Capability indices

C_p  = (USL - LSL) / (6σ_st)          — potential capability (spread only)
C_pk = min[(USL-μ)/3σ_st, (μ-LSL)/3σ_st] — actual capability (centered + spread)
P_p  = (USL - LSL) / (6σ_lt)          — performance (long-term, all sources of variation)
P_pk = min[(USL-μ)/3σ_lt, (μ-LSL)/3σ_lt]

Rule: C_pk ≤ C_p always (process can't be more capable than its potential)
Rule: P_pk ≤ C_pk typically (long-term ≤ short-term — more variation over time)

A six sigma process (nearest spec limit 6σ from the mean) has C_p = C_pk = 2.0 when centered. The Six Sigma convention assumes the mean drifts by up to 1.5σ over the long term, which leaves the nearest limit 4.5σ away (C_pk = 4.5/3 = 1.5) and gives about 3.4 defects per million opportunities (DPMO) on that side.

Worked example: rolled throughput yield (RTY)

RTY is the probability that a unit passes every step of a process right the first time. It is the product of each step’s first-pass yield:

Step 1 FPY = 0.97, Step 2 FPY = 0.95, Step 3 FPY = 0.99
RTY = 0.97 × 0.95 × 0.99 = 0.912 (91.2%)

About 8.8% of units need rework or are scrapped at some step (the “hidden factory”),
even if final yield after rework looks high.

Continuous vs. attribute data: sample size implications

Continuous data (measured on a scale) generally needs much smaller samples than attribute data (pass/fail, count of defects). A gauge R&R study typically needs 10 parts × 3 operators × 2–3 replications = 60–90 measurements. An attribute agreement study typically needs more parts — often 50 or more, deliberately including borderline ones — assessed by 2–3 appraisers over 2–3 trials.

Graphical tools decision guide

Question	Best graph
Is the data normally distributed?	Normal probability plot; histogram overlaid with normal curve
Is the process stable over time?	Run chart or control chart (time-ordered)
Where is the process centered relative to spec?	Histogram with spec limits; box plot
Is there a relationship between X and Y?	Scatter plot (add regression line if linear relationship expected)
Which defect category is largest?	Pareto chart
How does variation compare across groups?	Box plot side-by-side comparison