HF-MES-manual/en/quality_control/spc_variable_charts.md

SPC Variable Charts

1. Function Overview

SPC Variable Charts belong to the core SPC (Statistical Process Control) functions in the quality management module of the MES system. They are used to perform statistical analysis and process control on continuous quality characteristic data (such as voltage, current, temperature, pressure, and other measurable values) during production processes. Based on sampling rules defined in SPC render condition configuration, the system automatically extracts samples from production line process inspection data, process data, and result data, generates various variable control charts and process capability analysis charts, helping quality managers monitor production process stability and capability in real-time.

Core Functions:

• XBar-R Control Chart: Monitor process mean and dispersion through subgroup means and ranges
• XBar-S Control Chart: Monitor process mean and dispersion through subgroup means and standard deviations (suitable for larger subgroup sample sizes)
• I-MR Control Chart: Individual-Moving Range control chart, suitable for scenarios with only 1 sample per subgroup
• CPK Process Capability Analysis: Calculate process capability indices including Cp, Cpk, Pp, Ppk to evaluate process capability in meeting specification requirements
• EWMA Control Chart: Exponentially Weighted Moving Average control chart, more sensitive to small process shifts
• CUSUM Control Chart: Cumulative Sum control chart, highly sensitive to detecting small process shifts
• Levey-Jennings Control Chart: Statistical control chart based on multi-subgroup samples, suitable for quality control scenarios
• MA Moving Average Control Chart: Statistical process control based on moving averages
• MAMR Moving Average-Moving Range Control Chart: Process control combining moving average and moving range
• MAMS Moving Average-Standard Deviation Control Chart: Process control combining moving average and standard deviation

Function Screenshot:

2. Term Explanation

Term	Definition	Description
Variable Data	Variable Data	Continuously measurable quality characteristic data, such as voltage, current, temperature, pressure, dimensions, etc.
Control Chart	Control Chart	Statistical chart with control limits, used to distinguish between normal and abnormal process variations
Subgroup	Subgroup	A group of sample measurements collected under similar conditions, used to calculate within-group statistics
Total Subgroups	Total Subgroups	Total number of subgroups to be collected in a single SPC analysis
Samples Per Subgroup	Samples Per Subgroup	Number of sample measurements contained within each subgroup
Subgroup Interval	Subgroup Sampling Interval	Sampling time interval between adjacent subgroups (in hours)
Upper Control Limit (UCL)	Upper Control Limit	Upper limit in control chart for determining process control status, calculated from process data statistics
Lower Control Limit (LCL)	Lower Control Limit	Lower limit in control chart for determining process control status, calculated from process data statistics
Upper Specification Limit (USL)	Upper Specification Limit	Maximum allowable value for product quality characteristic, defined by product specification or customer requirements
Lower Specification Limit (LSL)	Lower Specification Limit	Minimum allowable value for product quality characteristic, defined by product specification or customer requirements
Mean (XBar)	Mean / Average	Arithmetic mean of all sample measurements within a subgroup, reflecting process central tendency
Range (R)	Range	Difference between maximum and minimum values within a subgroup, reflecting within-group dispersion
Standard Deviation (S)	Standard Deviation	Standard deviation of sample measurements within a subgroup, reflecting within-group dispersion
Moving Range (MR)	Moving Range	Absolute difference between two consecutive individual measurements
CPK	Process Capability Index	Measures actual process capability under controlled conditions, considering mean shift
CP	Process Capability	Measures potential process capability (without considering mean shift)
PPK	Process Performance Index	Measures long-term actual process performance
PP	Process Performance	Measures long-term total process variation
EWMA	Exponentially Weighted Moving Average	Exponentially weighted moving average, assigning higher weights to recent data
CUSUM	Cumulative Sum	Cumulative sum, accumulation of deviations from target value
Levey-Jennings	Levey-Jennings Chart	Statistical control chart used with multi-level quality control rules, commonly used in laboratory quality control and medical statistics
SPC Render Configuration	SPC Render Configuration	Configuration defining data sources, sampling parameters, and calculation rules required for generating SPC reports

3. SPC Variable Charts Interaction Flow

3.1 SPC Variable Charts Description

The SPC Variable Charts page provides 10 types of variable control charts and process capability analysis tools. Users select conditions such as process, SPC item, and time range, and the system automatically extracts corresponding data from the MES database and generates visual charts.

Operation Path: Go to [Quality Management] → [SPC Statistical Process Control] → [SPC Variable Charts] → Select the corresponding report type

General Query Condition Description:

Query Condition	Description	Required
Process Subclass	Select the process unit to monitor. After filtering, the SPC item dropdown will automatically load SPC items configured under this process	Yes
SPC Item	Select the specific SPC monitoring item (corresponding to the item name in SPC render condition configuration)	Yes
Time Range	Select the start and end time for data collection (accurate to hour:minute:second)	Yes
Batch Number	Filter data by production batch number (optional)	No
Roll Number	Filter data by roll number (optional). After entering the roll number, the system automatically obtains the corresponding production time range	No

[Note] Batch number and roll number cannot be entered simultaneously; they are mutually exclusive.

Function Screenshot:

---

3.2 XBar-R Mean-Range Control Chart

3.2.1 XBar-R Chart Description

XBar-R (Mean-Range) control chart is one of the most commonly used variable control charts, consisting of two sub-charts: the upper chart is the Mean Chart (XBar Chart), used to monitor process mean variation; the lower chart is the Range Chart (R Chart), used to monitor process dispersion. Suitable for scenarios with 2~10 samples per subgroup.

Application Scenarios:

• Production processes requiring simultaneous monitoring of mean and variation for quality characteristics
• Continuous production processes with moderate subgroup sample sizes (2~10 samples/group)
• Key process parameter monitoring such as cell injection volume, welding temperature, coating thickness

Chart Characteristics:

• Display subgroup means (XBar) and ranges (R)
• Automatically calculate and draw Upper Control Limit (UCL) and Lower Control Limit (LCL)
• Display process capability indices Cpk and Ppk
• Support chart scrolling and display option switching
• When specification limits (USL/LSL) are configured, specification lines are marked on the chart

Operation Steps:

1. Go to [Quality Management] → [SPC Statistical Process Control] → [SPC Variable Charts] → [XBar-R]
2. Select [Process Subclass] in the query area. The system automatically loads SPC items configured under this process
3. Select [SPC Item] (e.g., "OCV2 Voltage", etc.)
4. Select [Time Range], and optionally enter [Batch Number] or [Roll Number] for further filtering
5. Click [Query] button. The system retrieves data and generates the XBar-R control chart
6. Adjust display content using toggle buttons in the upper right corner of the chart
7. Click [Export Sample Data] to export chart source data as CSV file

Control Chart Anomaly Detection Rules:

The system automatically marks the following abnormal conditions on the XBar-R chart:

• Data points exceeding control limits (UCL/LCL)
• Consecutive points on the same side of the center line
• Data points showing trending changes (continuous increase or decrease)
• Data points showing periodic fluctuations

Function Screenshot:

---

3.3 XBar-S Mean-Standard Deviation Control Chart

3.3.1 XBar-S Chart Description

XBar-S (Mean-Standard Deviation) control chart is similar to XBar-R, but uses standard deviation (S) instead of range (R) to measure within-group dispersion. Standard deviation utilizes sample information more fully than range, so it is suitable for scenarios with larger subgroup sample sizes (n > 10).

Application Scenarios:

• Production processes with larger subgroup sample sizes (typically n ≥ 10)
• Scenarios requiring more precise measurement of process variation
• Automated high-speed continuous production lines

Chart Characteristics:

• Display subgroup means (XBar) and standard deviations (S)
• Automatically calculate and draw control limits
• Display process capability indices Cpk and Ppk
• Support chart scrolling and display option switching
• When specification limits are configured, specification lines are marked on the chart

Operation Steps:

1. Go to [Quality Management] → [SPC Statistical Process Control] → [SPC Variable Charts] → [XBar-S]
2. Select [Process Subclass] and [SPC Item] in the query area
3. Select [Time Range], and optionally enter [Batch Number] or [Roll Number] for filtering
4. Click [Query] button. The system retrieves data and generates the XBar-S control chart
5. Click [Export Sample Data] to export chart source data as CSV file

Function Screenshot:

---

3.4 I-MR Individual-Moving Range Control Chart

3.4.1 I-MR Chart Description

I-MR (Individual-Moving Range) control chart is suitable for scenarios where only 1 measurement value can be obtained per subgroup. The upper chart (I Chart) displays individual measurement values, and the lower chart (MR Chart) displays moving ranges between consecutive measurements. I-MR charts are suitable when production processes are highly automated and produce only one measurement per cycle, or when measurement costs are high and testing cycles are long.

Application Scenarios:

• Continuous production processes with only 1 sample per subgroup
• Automated inspection equipment testing item by item
• Destructive testing or high-cost testing scenarios
• Industries with slowly changing process parameters such as chemical and metallurgical processes

Chart Characteristics:

• Display individual measurement values (I Chart) and moving ranges (MR Chart)
• Automatically calculate and draw control limits
• When specification limits (USL/LSL) are configured, specification lines are marked on the chart
• Display process capability and calculated statistics
• Support chart scrolling and display option switching

Control Chart Anomaly Marking Description:

• System automatically highlights data points exceeding control limits
• Mark with special symbols when data points continuously show abnormal patterns

Function Screenshot:

---

3.5 Levey-Jennings Control Chart

3.5.1 Levey-Jennings Chart Description

Levey-Jennings control chart is a statistical control chart based on multi-subgroup samples, monitoring process stability through subgroup means and standard deviations. Widely used in medical testing, laboratory quality control, and manufacturing for process monitoring with multi-level quality control rules.

Application Scenarios:

• Scenarios requiring strict process monitoring with multi-level quality control rules
• Daily quality control of laboratory analytical instruments
• Continuous monitoring of critical electrical performance indicators in battery manufacturing

Chart Characteristics:

• Display subgroup means and standard deviations
• Automatically calculate and draw control limits
• Display process capability indices Cpk, Cpm, and Ppk
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Function Screenshot:

---

3.6 EWMA Exponentially Weighted Moving Average Control Chart

3.6.1 EWMA Chart Description

EWMA (Exponentially Weighted Moving Average) control chart assigns greater weights to recent observations, providing higher detection sensitivity for small shifts in process mean compared to traditional XBar charts. EWMA charts control the decay rate of historical data through weighting coefficient λ.

Application Scenarios:

• Scenarios requiring high sensitivity to small process shifts
• Need rapid detection of effects after process adjustments
• As a supplement to traditional control charts for early warning
• Industries with extremely high process precision requirements such as semiconductors and precision electronics

Chart Characteristics:

• Display EWMA statistics and process mean
• Automatically calculate and draw control limits
• Calculate EWMA values and mean statistics
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Operation Steps:

1. Go to [Quality Management] → [SPC Statistical Process Control] → [SPC Variable Charts] → [EWMA]
2. Select [Process Subclass] and [SPC Item] in the query area
3. Select [Time Range], and optionally enter [Batch Number] for filtering
4. Click [Query] button. The system retrieves data and generates the EWMA control chart

Function Screenshot:

---

3.7 CUSUM Cumulative Sum Control Chart

3.7.1 CUSUM Chart Description

CUSUM (Cumulative Sum) control chart detects small process shifts by accumulating deviations between actual values and target values. Similar to EWMA, CUSUM is highly sensitive to small changes in process mean and can detect abnormal trends earlier than traditional control charts.

Application Scenarios:

• Scenarios requiring extremely high detection sensitivity for small process shifts
• Continuous production processes where frequent false alarms are undesirable but real anomalies need rapid detection
• Process optimization and improvement effect evaluation
• Strict process control scenarios such as chemical reaction processes and precision machining

Chart Characteristics:

• Display positive cumulative sum (C+) and negative cumulative sum (C-)
• Automatically calculate and draw control limits
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Function Screenshot:

---

3.8 MA Moving Average Control Chart

3.8.1 MA Chart Description

MA (Moving Average) control chart smooths short-term fluctuations by calculating the average of consecutive data points, highlighting long-term trends. Moving average charts effectively filter random noise in production processes, providing clearer reflection of process mean changes.

Application Scenarios:

• Process data with significant random fluctuations
• Need to observe long-term process trend changes
• Noisy sensor data monitoring

Chart Characteristics:

• Display moving average sequence
• Automatically calculate and draw control limits
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Function Screenshot:

---

3.9 MAMR Moving Average-Moving Range Control Chart

3.9.1 MAMR Chart Description

MAMR (Moving Average-Moving Range) control chart combines moving average and moving range dimensions, simultaneously monitoring process central tendency and dispersion. The moving average component smooths random fluctuations and highlights trends, while the moving range component monitors process variation.

Application Scenarios:

• Need to simultaneously monitor process trends and variation
• Process control in single-value data scenarios
• Production processes requiring balanced sensitivity and stability

Chart Characteristics:

• Display moving averages and moving ranges
• Automatically calculate and draw control limits
• Calculate EWMA values and mean statistics
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Function Screenshot:

---

3.10 MAMS Moving Average-Standard Deviation Control Chart

3.10.1 MAMS Chart Description

MAMS (Moving Average-Moving Standard Deviation) control chart is similar to MAMR but uses moving standard deviation instead of moving range to measure process variation. Standard deviation provides more complete variation information and offers more comprehensive detection of abnormal fluctuations.

Application Scenarios:

• Need more comprehensive measurement of process variation
• Comprehensive process control for single-value data
• Scenarios requiring high sensitivity to process variation detection

Chart Characteristics:

• Display moving averages and moving standard deviations
• Automatically calculate and draw control limits
• When specification limits are configured, specification lines are marked on the chart
• Support chart scrolling and display option switching

Function Screenshot:

---

3.11 CPK Process Capability Index Analysis

3.11.1 CPK Chart Description

The CPK process capability analysis page provides comprehensive process capability index calculation and histogram visualization. Based on selected SPC items and sampling parameters, the system automatically collects data and calculates a series of process capability indicators, intuitively displaying data distribution characteristics and their relationship to specification limits through histograms overlaid with normal distribution curves.

Application Scenarios:

• Evaluate whether production processes meet product specification requirements
• New process validation and process improvement effect evaluation
• Supplier quality capability evaluation
• Provide process capability evidence during customer audits

Chart Characteristics:

• Histogram displays data distribution pattern
• Overlay two normal curves: overall distribution (red) and within-group distribution (blue)
• Mark Upper Specification Limit (USL), Lower Specification Limit (LSL), and Mean line
• Display comprehensive process capability statistics

Operation Steps:

1. Go to [Quality Management] → [SPC Statistical Process Control] → [SPC Variable Charts] → [CPK]
2. Select [Process Subclass] and [SPC Item] in the query area
3. Select [Time Range], and optionally enter [Batch Number] or [Roll Number] for filtering
4. Click [Query] button. The system retrieves data and generates the process capability analysis chart
5. Click [Export Sample Data] to export analysis data as CSV file

[Note] If specification limits (USL/LSL) are not configured, CPK-related indicators cannot be calculated. Please set specification limit values in SPC render condition configuration first.

3.11.2 Process Capability Indicator Description

Indicator	English Full Name	Description	Judgment Standard
Mean	Mean	Arithmetic mean of all sample measurements	—
Min	Minimum	Minimum measurement value in the sample	—
Max	Maximum	Maximum measurement value in the sample	—
Std Dev LT	Long-Term Standard Deviation	Overall standard deviation calculated based on all samples, reflecting long-term process variation	—
Std Dev ST	Short-Term Standard Deviation	Within-group standard deviation calculated using moving range averaging method, reflecting short-term process variation	—
Cp	Process Capability	Measures potential process capability	≥ 1.33 indicates sufficient capability
Cpk	Process Capability Index	Measures actual process capability considering process center shift	≥ 1.33 indicates controlled process with sufficient capability
Cpl	Lower Capability Index	Lower process capability index, measuring distance between mean and lower specification limit	—
Cpu	Upper Capability Index	Upper process capability index, measuring distance between mean and upper specification limit	—
Cpm	Taguchi Capability Index	Taguchi process capability index, measuring process deviation from target value	≥ 1.33 indicates process close to target value
Pp	Process Performance	Measures potential capability under long-term total variation	≥ 1.33 indicates sufficient long-term performance
Ppk	Process Performance Index	Measures long-term actual performance	≥ 1.33 indicates good long-term process performance
Ppl	Lower Performance Index	Lower process performance index	—
Ppu	Upper Performance Index	Upper process performance index	—

Process Capability Judgment Reference:

Capability Index Range	Judgment	Recommended Action
Cpk ≥ 1.67	Excellent capability	Consider simplifying control or reducing inspection frequency
1.33 ≤ Cpk < 1.67	Sufficient capability	Maintain current control level
1.00 ≤ Cpk < 1.33	Acceptable capability	Strengthen process monitoring, consider process improvement
0.67 ≤ Cpk < 1.00	Insufficient capability	Must implement process improvement
Cpk < 0.67	Severely insufficient capability	Urgent improvement required, production suspension adjustment if necessary

[Important] The system uses the moving range averaging method (MR-bar / d2) to calculate short-term standard deviation, where the d2 constant is 1.128 (corresponding to subgroup size n=2). This is an internationally accepted method for estimating SPC short-term standard deviation.

[Important] Difference between Cp and Cpk: Cp measures potential process capability (assuming process center coincides with specification center), while Cpk measures actual process capability (considering process center shift). Cpk ≤ Cp always holds. When Cpk is significantly smaller than Cp, it indicates process center shift, requiring process adjustment to bring mean closer to target value.

Function Screenshot:

---

4. SPC Variable Charts Data Collection Logic

4.1 Data Sources

Data for each variable chart comes from the data category specified in SPC render condition configuration:

Data Category	Description	Example
Process Inspection Data	Inspection data collected during first article and circuit inspections on the production line	Voltage and dimension values measured by inspectors
Process Data	Production process parameters automatically uploaded by equipment	Temperature, pressure, speed collected in real-time by equipment
Result Data	Inspection result data after process completion	OCV test voltage, internal resistance, capacity values

4.2 Data Sampling Flow

flowchart TB
    A[User Sets Query Conditions] --> B[System Reads SPC Render Condition Configuration]
    B --> C[Locate Data Source Based on Data Category]
    C --> D{Is Data Cleaning Configured?}
    D -->|Yes| E[Execute Data Cleaning]
    D -->|No| F[Use Raw Data Directly]
    E --> G[Sample According to Subgroup Rules]
    F --> G
    G --> H{Subgroup Data Collection Mode}
    H -->|Multi-Subgroup Mode| I[Split Data by Subgroup Interval]
    H -->|Single-Sample Mode| J[Collect Data by Time Interval]
    I --> K[Calculate Subgroup Statistics]
    J --> K
    K --> L[Calculate Control Limits]
    L --> M[Generate Control Chart/Analysis Report]

4.3 Data Collection Mode Description

The system supports three data collection modes, with different chart types using different modes:

Mode	Applicable Charts	Data Characteristics	Description
Multi-Subgroup Mode	XBar-R, XBar-S, I-MR, Levey-Jennings	Split data by subgroup count and subgroup interval, returning multiple subgroup samples	Each group contains multiple measurements and sampling times
Single-Subgroup Mode	CPK	Return all samples as one subgroup for capability analysis	All data participates in statistical calculation
Single-Sample Mode	MA, MAMR, MAMS, EWMA, CUSUM	Collect single measurement values at time intervals	One value collected per time point

[Important] Data cleaning rules (by value or by percentage) are set in SPC render condition configuration. Data cleaning only affects SPC report calculation results and does not modify original data in the MES system.

[Note] Subgroup sampling uses continuous sampling mode (Continuous), meaning subgroups are collected continuously from the data source at set intervals rather than random sampling.

---

5. Control Chart Selection Guide

Different production processes and data characteristics are suitable for different control chart types. The following is a selection reference:

Data Characteristics	Recommended Control Chart	Alternative Control Chart
Subgroup sample size 2~10, groupable sampling	XBar-R	—
Subgroup sample size > 10, groupable sampling	XBar-S	XBar-R
Only 1 sample per subgroup	I-MR	MA, MAMR, MAMS
Need to detect small process shifts	EWMA, CUSUM	I-MR
Need to evaluate process capability to meet specifications	CPK	—
Multi-level quality control rule monitoring	Levey-Jennings	XBar-R, XBar-S
Focus on long-term trends	MA, MAMR, MAMS	EWMA

[Note] For the same quality characteristic, multiple control charts can be used simultaneously for cross-validation. For example, XBar-R for daily monitoring, EWMA for early warning, and CPK for periodic capability evaluation.