Key Concepts

This page introduces the core concepts you need to understand ProcessBehavior effectively.

The Three-Step Workflow¶

ProcessBehavior follows a deliberate three-step workflow:

# 1. Wrap your data
pb = ProcessBehavior(df)

# 2. Formulate your study (DS detection happens here)
study = pb.formulate(response=..., factors=..., time=...)

# 3. Analyze and visualize
result = study.execute()
result.plot()

This separation ensures you understand your data structure before analyzing it.

Design States (DS)¶

The Design State describes the structure of your data. ProcessBehavior automatically detects which of six states applies:

Complete/Semi-Complete (no empty cells):

Incomplete (has empty cells):

See DS Definitions for the formal classification table per Dr. Thomas A. Bishop’s VAS methodology.

Why DS Matters¶

The DS determines:

• Which chart types are valid

• How within-group variance is estimated (R2 method: exact, ma2, or hybrid)

• Which VAS residuals can be computed

• What conclusions you can draw

study = pb.formulate(response='weight', factors=['lane'], time='batch')
print(f"DS: {study.analytical_design_state.sds}")  # e.g., 1
print(f"Reason: {study.ads_reason}")                # e.g., "full_replication"
print(f"Valid: {study.valid_charts}")                # e.g., ['Histogram', 'Xbar', 'S', 'X', 'mR']

Design State Traceability¶

ProcessBehavior tracks three Design States as data flows from intent through observation to analysis, providing transparent lineage at every step.

The Three States¶

The ADS drives all analysis decisions — valid charts, residual availability, R2 calculation method, and interaction analysis. The ODS and PDS provide diagnostic lineage so you can trace exactly how your data structure changed through processing.

Why Three States?¶

Raw data often contains garbage values, missing cells, and structural irregularities. The ODS captures this reality — including incomplete designs (DS 4-6) where some factor-time cells are entirely empty. After data cleansing removes invalid observations, the empty cells disappear and the remaining structure may be simpler:

• ODS 4 (Incomplete, no singletons) → ADS 1 (Full Replication)

• ODS 5 (Incomplete, no replication) → ADS 2 (No Replication)

• ODS 6 (Incomplete, with singletons) → ADS 3 (Partial Replication)

This separation means the system correctly identifies incomplete data collection (ODS) while still performing the most powerful analysis the clean data supports (ADS).

Viewing Design State Lineage¶

Use study.design() to see the full lineage:

report = study.design()
print(report)

# Design Report (2 factors)
#   Design lineage:
#     Planned Design State:    DS 1 (Full Replication)
#     Observed Design State:   DS 6 (Incomplete, With Singletons) — 3 empty cells
#     Analytical Design State: DS 1 (Full Replication)
#   ...

When ODS and ADS differ, the Study display shows both:

print(study)
# Study(response='weight', factors=[lane], time='pull', ods=6, ads=1)
#   Valid: Histogram, Xbar, S, X, mR | Recommended: Xbar

Key Properties¶

# Plan Design State (None if no plan was provided)
study.plan_design_state       # SDSResult or None

# Observed Design State (always available)
study.observed_design_state   # SDSResult — diagnostic/lineage

# Analytical Design State (drives analysis)
study.analytical_design_state # SDSResult — the authoritative state
study.ads_reason              # e.g., "full_replication" (machine-readable)
study.ads_description         # e.g., "Full replication (all cells n>=2)"

Bishop’s Variance Analysis System (VAS)¶

For replicated designs (DS 1-3), ProcessBehavior computes five residual decompositions:

Interpreting VAS Residuals¶

• R2 (Within-cell): Is measurement variation stable? Are there special causes within subgroups?

• R3 (Interaction): Does the factor effect change over time?

• R4 (Time): Are there trends, shifts, or time-related patterns?

• R5 (Factor): Do factors differ significantly from each other?

# Access residuals after formulation
print(study.dataset[['R1', 'R2', 'R3', 'R4', 'R5']].head())

# Chart residuals using the value parameter
result = study.execute(chart='X', by=['lane'], value='R4')
result.plot()

Chart Types¶

Standard Charts¶

Residual Charts¶

Use the value parameter to chart residuals instead of the response variable:

# Chart R5 residuals (factor effects) on an Xbar chart
result = study.execute(chart='Xbar', value='R5')

# Chart R4 residuals (time effects) on a stratified X chart
result = study.execute(chart='X', by=['lane'], value='R4')

The by Parameter¶

The by parameter controls how data is grouped or stratified:

# Xbar chart aggregated by all factors (default)
result = study.execute(chart='Xbar')

# Xbar chart aggregated by single factor
result = study.execute(chart='Xbar', by=['factor 1'])

# Xbar chart collapsed to grand mean
result = study.execute(chart='Xbar', by=[])

# X chart stratified by factor (separate chart per level)
result = study.execute(chart='X', by=['lane'])

Key concept: The by parameter creates views over the same underlying data. Residuals are computed once during formulation and never change regardless of how you view them.

Western Electric Rules¶

Signal detection uses the Western Electric (WECO) rules:

Rule Applicability¶

• Xbar/S charts: Only Rule 1 applies (beyond limits)

• X charts: All 8 rules apply

# Standard rules (1-4)
signals = result.detect_signals(rules='standard')

# Extended rules (1-8)
signals = result.detect_signals(rules='extended')

Terminology Mapping¶

ProcessBehavior uses Wheeler’s terminology consistently:

Philosophy¶

ProcessBehavior follows Wheeler’s philosophy:

1. Charts are for understanding, not control - The goal is insight into variation, not just limit checking.

2. Let the data speak - Automatic DS detection ensures appropriate analysis.

3. Separate formulation from analysis - Understanding your data structure comes first.

4. DataFrame-backed results - Access chart data, residuals, and effects as standard pandas DataFrames.

Next Steps¶

• Coffee Shop - Create your first chart, end to end

• Design States - Deep dive into DS

• VAS Residuals - Understanding VAS residuals