SPC Basics

Core Concepts

1. Process Variation:

• Common Causes: Natural variations inherent in the process, usually stable and predictable.
• Special Causes: Variations caused by specific events or circumstances, typically abnormal and requiring investigation.

2. Specification Limits:

• Upper Specification Limit (USL): Maximum allowable value.
• Lower Specification Limit (LSL): Minimum allowable value.

3. Control Limits:

• Upper Control Limit (UCL): Predetermined upper limit in control charts, typically mean plus 3 standard deviations.
• Lower Control Limit (LCL): Predetermined lower limit in control charts, typically mean minus 3 standard deviations.

In Statistical Process Control (SPC), Cp, Cpk, Pp, and Ppk are four key process capability indices used to evaluate manufacturing process performance.

Cp & Pp: Measure process capability without considering centering. Higher values indicate better capability.

Cpk & Ppk: Measure process performance considering both centering and variation. Higher values indicate better performance.

Generally, Cpk is larger than Ppk because:

• Cpk reflects short-term capability using controlled subgroup data
• Ppk reflects long-term performance using overall process data that includes more variation sources

Shift vs Variation

Shift: Difference between process mean and target value.
Variation: Dispersion of process outputs around the mean (measured by σ).

Cp (Process Capability Index) - Short Term

Measures whether process variation fits within specification limits:

Criteria:

• Cp > 1.33: Good capability
• Cp = 1.33: Minimum acceptable
• Cp < 1.33: Requires improvement

Cpk (Process Capability Index) - Short Term

Considers both variation and centering:

Criteria:

• Cpk > 1.33: Good performance
• Cpk = 1.33: Minimum acceptable
• Cpk < 1.33: Requires improvement

Pp (Process Performance Index) - Long Term

Similar to Cp but uses overall process data:

Criteria:

• Pp > 1.33: Good performance
• Pp = 1.33: Minimum acceptable
• Pp < 1.33: Requires improvement

Ppk (Process Performance Index) - Long Term

Considers both variation and centering for overall process:

Criteria:

• Ppk > 1.33: Good performance
• Ppk = 1.33: Minimum acceptable
• Ppk < 1.33: Requires improvement

Control Charts

Common Types:

1. X-Bar & R Chart:

• X-Bar: Monitors sample means
• R Chart: Monitors sample ranges

2. X-Bar & S Chart:

• X-Bar: Monitors sample means
• S Chart: Monitors sample standard deviations

3. I-MR Chart:

• Individual Chart: Tracks single measurements
• Moving Range Chart: Tracks differences between consecutive points

4. P Chart: Monitors proportion defective
5. NP Chart: Tracks number of defectives in constant sample sizes
6. C Chart: Counts number of defects per unit
7. U Chart: Tracks defects per unit with variable sample sizes

Six Sigma
Quality improvement methodology aiming for 3.4 defects per million opportunities (DPMO). Key metrics:

• Sigma Level: Process capability measurement
• DPMO: Defects Per Million Opportunities