SPC — Statistical Process Control

Control Charts, Control Limits and Violation Rules

Markdown

Statistical Process Control (SPC)

Overview

Statistical Process Control (SPC) is a method for continuous monitoring and control of manufacturing processes using statistical techniques. The goal is to detect deviations from a stable process state early and take corrective action before defective parts are produced.

SPC is based on the fundamental idea that every process undergoes natural variation. As long as only random causes (Common Causes) are responsible for the variation, the process is considered statistically controlled. When special causes (Special Causes) occur, the variation behavior changes and the control chart shows anomalies.

SPC Overview

Basic Principle of SPC

Cause Type Description Examples Action
Random Causes (Common Causes) Inherent, unavoidable variation Material fluctuations, vibrations, temperature differences System improvement (long-term)
Special Causes (Special Causes) Unusual, identifiable disturbances Tool breakage, operator error, defective measuring instrument Immediate correction

Benefits of SPC

  • Prevention instead of reaction: Problems are detected before scrap is produced
  • Data-based decisions: Interventions are based on statistical signals, not intuition
  • Continuous improvement: Trends and patterns are made visible
  • Documentation: Comprehensive recording of process behavior
  • Regulatory compliance: Fulfillment of requirements from IATF 16949, VDA, ISO 9001, etc.

Info: SPC is not a one-time analysis, but a continuous process. The control charts are updated in real-time or at regular intervals during production.


Input and Configuration

Setting Up Subgroups

The formation of subgroups is a central aspect of SPC. Each subgroup consists of a small number of parts produced under conditions that are as similar as possible.

Configuration Parameters

Parameter Description Typical Value
Subgroup Size (n) Number of measurements per subgroup 3, 5, or 10
Sampling Interval Time interval between subgroups Hourly, every 2 hours, per shift
Number of Subgroups (k) Total number of subgroups >= 20 (minimum 25 recommended)
USL / LSL Specification limits According to drawing / customer specification

Subgroup Setup

Tip: Choose the subgroup size so that the variation within a subgroup reflects only random variation. Typically, 5 consecutive parts are used. For automated processes with low variation, 3 parts may also be sufficient.

Data Entry

Enter the measured values by subgroup in my8data. You have the following options:

  1. Direct Entry: Enter the measured values row by row (per subgroup)
  2. Import: Upload a CSV or Excel file with pre-structured data
  3. Clipboard: Paste copied data from other programs

Calculating Control Limits

my8data automatically calculates the control limits from the entered data. The calculation is based on the first 20-25 subgroups (startup phase). These limits can subsequently be fixed for ongoing monitoring.

Limit Type Calculation x̄-Chart Calculation R-Chart
UCL x̿ + A₂ * R̄ D₄ * R̄
CL x̿
LCL x̿ - A₂ * R̄ D₃ * R̄

The constants A₂, D₃, and D₄ are tabulated values that depend on the subgroup size.

Warning: Calculate control limits only from data from a stable process. First remove all points that are due to special causes, then recalculate the limits. Otherwise, the limits will be set too wide and special causes will not be detected.


Control Charts

Types of Control Charts

my8data provides various control chart types, which are selected depending on data type and subgroup size:

Control Charts for Continuous Characteristics (Variable Data)

Control Chart Pair Subgroup Size Description
x̄ / R-Chart n = 2 to 10 Mean and range chart; standard chart for small subgroups
x̄ / s-Chart n > 10 Mean and standard deviation chart; for larger subgroups
x / mR-Chart (Individual Values Chart) n = 1 Individual value and moving range chart; when only one measurement per time point is available

x-bar R Control Chart

Structure of a Control Chart

Each control chart consists of two parts:

  1. Location Chart (upper chart): Monitors the location of the process (mean)

    • Shows x̄ (subgroup mean) or individual values
    • Detects shifts and trends in process level
  2. Variability Chart (lower chart): Monitors the variation of the process

    • Shows R (range) or s (standard deviation)
    • Detects changes in process variability

Zones of the Control Chart

The area between UCL and LCL is divided into three zones, which are relevant for the application of violation rules:

Zone Range Description
Zone A Between ±2σ and ±3σ Outer zone; points here are rare (approximately 4.3% probability)
Zone B Between ±1σ and ±2σ Middle zone (approximately 27.2% probability)
Zone C Between CL and ±1σ Inner zone; most points should lie here (approximately 68.3% probability)

Info: In a stable, normally distributed process, approximately 99.73% of all points lie within the 3-sigma limits (UCL/LCL). A point outside these limits is therefore likely due to a special cause.

Interpretation of the Control Chart

Signal Description Typical Cause
Point outside UCL/LCL Single extreme value Tool breakage, measurement error, material defect
Upward/Downward Trend Steadily rising or falling values Tool wear, temperature increase
Jump (Shift) Sudden change in level Tool change, new material batch
Cycles Periodically recurring patterns Shift change, environmental fluctuations
Stratification Points unnaturally close to centerline Mixing of data from different sources

Violation Rules (Alarm Rules)

Western Electric Rules

The Western Electric Rules (also WECO rules) are a set of decision rules based on the zone division of the control chart. They detect not only individual extreme values but also systematic patterns that indicate a process change.

my8data applies the following rules by default:

Rule Description Significance
Rule 1 1 point outside the 3σ limits (Zone A) Single outlier; probably a special cause
Rule 2 2 of 3 consecutive points in Zone A or beyond (same side) Warning signal for beginning shift
Rule 3 4 of 5 consecutive points in Zone B or beyond (same side) Clear signal for process shift
Rule 4 8 consecutive points on the same side of the centerline Run; process level has shifted

Violation Rules Example

Nelson Rules

The Nelson Rules extend the Western Electric Rules with additional patterns. my8data supports the following Nelson rules:

Rule Description Detects
Nelson 1 1 point outside the 3σ limits Outlier
Nelson 2 9 consecutive points on one side of CL Shift
Nelson 3 6 consecutive points steadily rising or falling Trend
Nelson 4 14 consecutive points alternating up/down Systematic variation
Nelson 5 2 of 3 points in Zone A (same side) Increased variation
Nelson 6 4 of 5 points beyond Zone C (same side) Increased variation
Nelson 7 15 consecutive points in Zone C (both sides) Reduced variation / Stratification
Nelson 8 8 consecutive points outside Zone C (both sides) Mixing / Bimodality

Tip: Not all rules need to be active simultaneously. The more rules are active, the more sensitive the control chart reacts, but the higher the rate of false alarms. For getting started, rules 1-4 (Western Electric Rules) are recommended.

Configuration of Violation Rules

In my8data, you can individually specify which rules should be active:

  • Enable/disable individual rules via checkbox
  • Adjustment of rule parameters (e.g., number of consecutive points)
  • Color coding of violations in the control chart (red = violation)

Response to Violations

When a violation rule is triggered, proceed as follows:

  1. Verify: Check whether the violation is due to a measurement error
  2. Identify: Search for the special cause (5-Why, Ishikawa diagram)
  3. Correct: Eliminate the cause and document the action
  4. Monitor: Observe whether the process remains stable after correction

Warning: Do not respond to every alarm with a process adjustment without having identified the cause. Unjustified interventions in a stable process (called overadjustment) lead to an increase in variation and worsen product quality.

Example of a Rule Violation

The following table shows an example of how violation rules work in practice:

Subgroup x̄-Value Zone Violation
15 10.02 C -
16 10.03 C -
17 10.05 B -
18 10.04 B -
19 10.06 B -
20 10.08 A -
21 10.07 A Rule 3: 4 of 5 points in Zone B or beyond
22 10.11 > UCL Rule 1: Point outside 3σ

Info: In this example, Rule 3 would have already triggered a warning signal at subgroup 21, before the point at subgroup 22 exceeded the control limits. Early detection is the major advantage of combined rule application.

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