Chapter 6 of 8
Chapter 6: Statistical Process Control (SPC)
6.1 Introduction
Up to this point, metrology in MET 135 has focused on measuring individual parts and evaluating instruments. In modern manufacturing, quality is rarely judged one part at a time. Instead, engineers monitor process behavior over time to prevent defects before they occur. This approach is known as Statistical Process Control (SPC).
SPC uses statistical tools and control charts to distinguish between normal process variation and abnormal variation that signals a problem. This chapter introduces run charts, X-bar charts, R charts, and decision rules used to determine whether a process is in control or out of control.
6.2 Why SPC Is Used in Manufacturing
SPC is a predictive quality tool. Unlike confidence intervals, which are applied after parts are produced, SPC identifies problems before parts go out of specification.
SPC allows manufacturers to:
- Detect process instability early
- Reduce scrap and rework
- Improve consistency
- Make data-driven decisions
In industry, SPC is a core requirement for quality systems such as ISO 9001 and Six Sigma.
6.3 Common Cause vs. Special Cause Variation
Common Cause Variation
Common cause variation is the natural, random variability inherent in a stable process.
Characteristics:
- Always present
- Predictable within limits
- Caused by the system itself
Examples:
- Small material variations
- Machine tolerances
- Environmental conditions
A process with only common cause variation is considered stable and predictable.
Special Cause Variation
Special cause variation occurs when something unusual or assignable affects the process.
Characteristics:
- Unpredictable
- Outside historical behavior
- Indicates a change in the process
Examples:
- Tool wear or breakage
- Machine misalignment
- Operator error
- Power fluctuations
Special cause variation means the process is out of control and requires investigation.
6.4 Run Charts
A run chart plots measurement values over time without control limits. It is often the first step in SPC.
Run charts are used to:
- Visualize trends
- Observe shifts
- Identify obvious instability
Run charts do not determine control status by themselves.
6.5 Control Charts
Control charts add statistically calculated limits to distinguish normal variation from abnormal variation.
Key elements:
- Center line (process average)
- Upper Control Limit (UCL)
- Lower Control Limit (LCL)
Control limits are not specification limits. They describe process behavior, not customer requirements.
6.6 X-Bar and R Charts
SPC in MET 135 uses X-bar and R charts for variables data.
X-Bar Chart
- Monitors changes in the process mean
- Each point represents a subgroup average
R Chart
- Monitors process variability
- Each point represents the range within a subgroup
Both charts must be in control for the process to be considered stable.
6.7 Calculating Control Limits
For a subgroup size n, control limits are calculated as:
X-Bar Chart:
UCLx̄ = x̄̅ + A₂·R̄
LCLx̄ = x̄̅ − A₂·R̄
R Chart:
UCLR = D₄·R̄
LCLR = D₃·R̄
Constants A₂, D₃, and D₄ depend on subgroup size and are obtained from standard tables (see the SPC constants table in Appendix A).
Try It: Control Limit Calculator
Enter the grand mean (x̄̅), average range (R̄), and subgroup size. Constants A₂, D₃, D₄ are looked up automatically.
6.8 Interpreting Control Charts
A process is considered in control when:
- All points fall within control limits
- No non-random patterns appear
A process is out of control when one or more run rules are violated.
6.9 SPC Run Rules (Decision Rules)
Common SPC rules include:
- One point outside control limits
- Seven consecutive points on one side of the mean
- Seven consecutive points increasing or decreasing
- Cycles or repeating patterns
- Grouping or instability
These patterns indicate special cause variation and require action.
6.10 Relationship Between SPC and Specifications
A process can be:
- In control and capable
- In control but not capable
- Out of control but meeting specs temporarily
- Out of control and producing defects
SPC focuses on process behavior, not pass/fail inspection.
6.11 Chapter Summary — Study Points
- SPC monitors processes over time
- Common cause variation is normal
- Special cause variation signals problems
- X-bar charts track averages
- R charts track variability
- Control limits are not specifications
- Decisions are based on patterns, not single points
Chapter 6 Exercises
Each exercise includes a worked example followed by a student practice problem.
Exercise 1: Identifying Variation Type
Example (Solved)
A process shows small random fluctuations with no patterns.
Conclusion: Common cause variation
Student Practice
A process suddenly shows a large jump after tool replacement. Identify the variation type.
Show answer
Special cause variation — the jump is assignable to an identifiable event (the tool replacement).
Exercise 2: Control Limit Interpretation
Example (Solved)
All points fall within UCL and LCL with no patterns.
Conclusion: Process is in control
Student Practice
One point exceeds the UCL. Determine process status.
Show answer
Process is out of control — one point outside the control limits violates run rule 1.
Exercise 3: X-Bar and R Chart Purpose
Example (Solved)
The X-bar chart monitors changes in the process mean.
Student Practice
What does the R chart monitor?
Show answer
The R chart monitors process variability (the range within each subgroup).
Exercise 4: Specification vs. Control Limits
Example (Solved)
Control limits describe process behavior, not customer requirements.
Student Practice
Explain why a process can be in control but still produce out-of-spec parts.
Show answer
A stable process may be centered incorrectly relative to specifications (or its natural spread may be wider than the tolerance). Control limits come from process data, so a process can behave predictably while making parts the customer cannot accept.
Exercise 5: SPC Action Decision
Example (Solved)
Seven points appear above the center line.
Action: Investigate special cause
Student Practice
A chart shows cycling behavior over time. What action should be taken?
Show answer
Investigate and eliminate the source of the cycling variation — repeating patterns indicate a special cause (for example, temperature cycles or shift changes).
Chapter 6 Resources
- MET-135-Lab-06 — SPC and Control Charts (course handout)
- Examples of X-bar and R charts (course materials)
- Z-table and SPC constant tables (see Appendix A)