📘 Chapter 15 – Statistical Quality Control (FYI Only)

ℹ️ Note

This chapter is FYI only. We are not covering it in detail this term, but you can skim this page (and the slides) to see the kinds of tools used in industrial quality engineering.

🔗 Slides for Chapter 15 (Quality Control)

📂 Download Chapter 15 – Statistical Quality Control (PowerPoint)

🎯 Learning Objectives (Big Picture)

• Understand the role of statistical tools in quality improvement and process monitoring.
• Distinguish between common (chance) and assignable (special) causes of variation.
• Read and interpret basic control charts for process monitoring.
• Construct and interpret control charts for:
  • Variables data: X̄ (X-bar), R, S, and individuals charts
  • Attributes data: p charts (fraction nonconforming) and u charts (defects per unit)
• Compute and interpret simple process capability indices (e.g., PCR).
• Understand the idea of Average Run Length (ARL) as a measure of chart performance.
• Recognize time-weighted charts such as CUSUM and EWMA for detecting small shifts.
• See how SPC fits into a broader quality-improvement system in engineering and manufacturing.

🔧 15.1 – Quality Improvement & Statistics

• Quality = “fitness for use” (meets customer requirements, reliable, low defect rate).
• Two aspects:
  • Quality of design – choosing appropriate performance levels, tolerances, and features.
  • Quality of conformance – consistently hitting the target with low variability.
• Statistical tools help:
  • Measure and reduce variability
  • Detect problems early
  • Support continuous improvement (less scrap, rework, and waste)

📊 15.2 – Introduction to Control Charts

• Every process has natural variability (common causes) – small, random “background noise.”
• Assignable causes create larger, systematic shifts (bad material, wrong machine setting, operator error).
• A control chart plots a sample statistic over time with:
  • Center line (CL): in-control average
  • Upper Control Limit (UCL)
  • Lower Control Limit (LCL)
• If points stay inside limits with a random pattern ➜ process is “in statistical control.”
• Points outside limits or strange patterns (runs, trends, cycles) ➜ investigate for assignable causes.
• Western Electric rules use “zones” on the chart to flag suspicious patterns (not just single out-of-limit points).

📈 15.3 – X̄ and R / S Control Charts (Variables Data)

• Use when you measure a numerical quality characteristic (diameter, length, strength, etc.).
• X̄-chart: monitors the process average over time.
• R-chart: monitors the range (max − min) within each small sample.
• S-chart: monitors the sample standard deviation instead of range.
• Typical setup:
  • Take small samples (for example n = 4–5) at regular time intervals.
  • Plot the sample averages on the X̄-chart, and the ranges (or standard deviations) on the variability chart.
  • Look for points outside the limits or clear non-random patterns.

👤 15.4 – Control Charts for Individual Measurements

• Used when you only get one measurement at a time (n = 1), e.g., slow or expensive processes.
• Chart the individual values and a moving range (MR) of consecutive observations.
• Good for monitoring gradual shifts, but less sensitive to very small changes than some advanced charts.

🏭 15.5 – Process Capability

• Asks: “How good is this stable process compared to the specification limits?”
• Use histograms and “tolerance charts” to see how the process distribution fits inside [LSL, USL].
• Define process capability ratio (PCR) as:
  PCR = (USL − LSL) / (6σ)
• If PCR > 1: natural variation is narrower than the spec window (good). If PCR < 1: process too wide (lots of fallout).
• Off-center processes use a modified index (often written as PCR_k) that accounts for shifts away from target.

✅ 15.6 – Attribute Control Charts (p & u Charts)

• Used when each item is classified as conforming / nonconforming, or we count defects.
• p-chart: monitors the proportion defective in each sample.
• u-chart: monitors the average number of defects per unit (e.g., scratches per panel).
• Useful when measurements are pass/fail (go/no-go gauges, visual inspection).

⏱️ 15.7 – Control Chart Performance (ARL)

• Average Run Length (ARL) = the average number of points plotted before a signal occurs.
• Larger ARL in-control ➜ fewer false alarms.
• Smaller ARL out-of-control ➜ faster detection of real problems.
• Designing charts involves balancing these two goals.

📉 15.8 – Time-Weighted Charts: EWMA & CUSUM

• EWMA (Exponentially Weighted Moving Average) and CUSUM (Cumulative Sum) charts:
  • Give more weight to recent data.
  • React faster to small persistent shifts in the process mean than standard X̄ charts.
• Common in high-precision and automated processes (chemicals, semiconductors, etc.).

🧰 15.9 – Other SPC Problem-Solving Tools

• Classic 7 tools of SPC:
  • Histogram
  • Pareto chart
  • Cause-and-effect (fishbone) diagram
  • Defect-concentration diagram
  • Control chart
  • Scatter diagram
  • Check sheet
• These help teams find root causes and prioritize improvements.

🧮 15.10–15.11 – Decision Theory & Implementing SPC

• Decision theory gives a structured way to choose between actions under uncertainty (different loss functions, criteria).
• Implementing SPC is not just drawing charts:
  • Requires management support and training.
  • Needs clear action rules when charts signal a problem.
  • Goal is continuous, long-term reduction in variability, not just one-time fixes.