Module 3: Process Control & Statistical Process Control (SPC) | HNG Consulting

Module 3: Process Control & Statistical Process Control (SPC)

This module explores process control, manufacturing variation, control charts (X-bar, R-chart, p-chart, c-chart), interpretation of out-of-control signals, process capability indices (Cp, Cpk), and practical SPC implementation in a real manufacturing environment.

Section 1: Introduction to Process Control

1.1 What is Process Control?

Process Control is the systematic monitoring and adjustment of a production process to ensure it consistently produces products within required specifications. The goal is to maintain the process in a state where it reliably produces conforming products without generating excessive defects.

Think of process control like driving a car on the highway:

Target: Stay in your lane (specification)
Monitoring: Watch the road and your position (measure the process)
Adjustment: Turn the steering wheel left/right if you drift (take action)
Consistency: Reach your destination safely (consistent, conforming output)

1.2 Variation in Manufacturing

All manufacturing processes exhibit variation—no two parts are exactly identical. Understanding variation is central to process control.

Sources of Variation:

Common Cause Variation: Always present, results from small inevitable sources. Characteristics: Predictable, can be estimated, random pattern. Action: Don't overreact; it's normal.
Special Cause Variation: Results from specific unusual events. Characteristics: Unpredictable, identifiable, non-random pattern. Action: Find and correct the cause.

Section 2: Control Charts (Foundation of SPC)

2.1 What is a Control Chart?

A Control Chart (also called Shewhart Chart) is a time-series graph showing how a process measurement varies over time. It includes:

Data points: Individual measurements of the process
Center line: The average of all measurements
Control limits: Statistical boundaries indicating if the process is in control

Critical Point: Control limits are NOT the same as specification limits.

Specification limits: Customer requirements (what the product should be)
Control limits: Statistical boundaries (normal process variation)

2.2 Types of Control Charts:

Type	Measures	Use	Example
X-bar	Average of subgroups	Process centering	Each hour, measure 5 parts, calculate averages
R-chart	Range/variation	Process consistency	Calculate range (max-min) of 5 parts
p-chart	Proportion defective	Defect rate %	Batch of 100 parts, 2 defective = 2%
c-chart	Number of defects	Count of defects	After painting, count defects/part

Most common in manufacturing: X-bar and R-chart used together.

2.3 Calculating Control Limits

For an X-bar chart:

Center Line (CL) = X̄̄ (average of all subgroups)

Upper Control Limit (UCL) = X̄̄ + A2 × R̄
Lower Control Limit (LCL) = X̄̄ - A2 × R̄

Where:
- X̄̄ = Grand average
- R̄ = Average of ranges
- A2 = Statistical constant (for n=5, A2=0.577)

Practical Example:

If your process produces parts averaging 100mm with an average range of 4mm on subgroups of 5:

CL = 100mm
UCL = 100 + (0.577 × 4) = 102.31mm
LCL = 100 - (0.577 × 4) = 97.69mm

Interpretation: If a subgroup average falls outside 97.69-102.31mm, investigate!

Section 3: Out-of-Control Process Signals

A Process is Out of Control If:

Rule 1: One point beyond control limits
Rule 2: 8 or more consecutive points above/below center line
Rule 3: Trend (6-8 consecutive points moving up/down)
Rule 4: High variation (points consistently near limits)

Action Plan: When Points Go Out of Control:

Stop production of that item (or minimum, 100% inspection)
Investigate: What changed?
- Process parameters (temperature, pressure, speed)
- Materials (new lot? new supplier?)
- Equipment (machine maintained? tooling worn?)
- Operators (different person? different team?)
- Environment (temperature? humidity?)
Find root cause (use 5-Why or other analysis)
Implement corrective action
Verify the correction worked
Document (what, why, what we did)

Section 4: Process Capability Analysis

4.1 Cp and Cpk Indices

Beyond control limits, we also analyze process capability—how well the process meets specification limits.

Cp = (USL - LSL) / (6 × σ)

Where:
USL = Upper Specification Limit
LSL = Lower Specification Limit
σ (sigma) = Process standard deviation

Interpretation of Indices:

Cpk > 1.33: Process capable (produces <0.1% defects)
1.0 < Cpk < 1.33: Marginal capability (produces 0.1-0.5% defects)
Cpk < 1.0: Process not capable (produces >0.5% defects)

Example:

Specification: 50 ±0.5mm (range = 1.0mm) After SPC implementation: - Average = 50.02mm - Standard deviation = 0.08mm - Cp = 1.0 / (6 × 0.08) = 2.08 (excellent!) - Cpk = 2.02 (excellent!)

Conclusion: Process is highly capable; defect rate will be <0.01%

Conclusion: SPC as Early Warning System

SPC is not a solution—it's a detection system. It helps you identify problems BEFORE you produce defective parts, enabling quick correction.

Cp and Cpk Calculator

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Process Control & Statistical Process Control (SPC)