Quality in the industrial context means the degree to which a product or service fulfils the customer's requirements. It is not an abstract ideal — it is a measurable attribute that can be quantified, monitored, and improved through statistical methods.
The Japanese quality guru Genichi Taguchi defined quality as "the loss a product causes to society after being shipped" — meaning any deviation from the target specification is a quality loss, even if the product still passes inspection.
Statistical Quality Control (SQC) is primarily concerned with conformance and consistency — ensuring that every item produced stays within specification and that variation is minimised.
SQC provides a scientific, data-driven framework for monitoring and improving quality. It replaces the old "inspect at the end and reject the bad ones" philosophy with a prevention-oriented approach — detecting problems as they arise and fixing them before large volumes of defective output accumulate.
Any industrial process has four broad input categories that collectively determine output quality. These are known as the 4 M's:
| M Factor | What it Covers | Example of Influence on Quality |
|---|---|---|
| Man | Skill, training, motivation, fatigue of operators | An untrained operator may set machine incorrectly, causing out-of-spec output. |
| Machine | Equipment condition, calibration, wear & tear | A worn bearing causes excess vibration → dimensional variation in parts. |
| Material | Raw material properties, supplier consistency, storage | Steel with inconsistent carbon content leads to variable hardness after heat treatment. |
| Method | Process parameters, SOPs, temperature, speed, sequence | Curing temperature too high → paint blisters; too low → paint does not adhere. |
The 4 M's framework helps trace the root cause of a quality problem. When a control chart signals an out-of-control condition, the engineer checks each M in turn: Was it a new operator (Man)? Did a tool wear out (Machine)? Was a different batch of raw material used (Material)? Was a process recipe changed (Method)?
A CNC lathe produces shafts with a nominal diameter of 25.000 mm. Over three months the shaft diameters slowly drift upward from 25.000 to 25.015 mm. Investigation reveals the cutting tool is wearing (Machine). After tool replacement, diameters return to 25.000 mm. This is an assignable cause — the tool wear — that was detected and corrected.
A pharmaceutical company produces tablets of 500 mg. Suddenly the tablet weights jump from 498–502 mg to 510–518 mg. The control chart signals out-of-control. Investigation reveals a new supplier's active ingredient powder has a different bulk density (Material), causing the automatic filling machine to dispense more mass. Switching back to the original supplier's specification resolves the problem.
No two items are identical. Even in the most carefully controlled process, there will be variation. SQC distinguishes two fundamentally different types:
| Aspect | Chance Causes | Assignable Causes |
|---|---|---|
| Also known as | Common causes, random variation | Special causes, non-random variation |
| Number in any process | Many, each with tiny effect | Few, each with significant effect |
| Distribution effect | Stable, predictable pattern | Shift, trend, cycle, or outlier |
| Process state | In statistical control | Out of statistical control |
| Economic to eliminate? | No (requires process redesign) | Yes (identify and remove the cause) |
| On a control chart | Points within control limits | Points outside limits or showing patterns |
Bottles are filled with 1000 mL of juice by an automatic filling machine. Measurements on 50 bottles range from 998.2 to 1001.6 mL, with mean 1000.1 mL and SD 0.9 mL. The variation is small, random, and symmetric — no single cause can be identified. This is chance variation. The process is in control.
The same filling machine suddenly starts producing bottles with fill volumes of 1012–1018 mL. The \(\bar{X}\) chart shows a point above the UCL. Investigation reveals the filling nozzle is partially clogged, causing back-pressure and overfilling (Machine/Method). This is an assignable cause. After cleaning the nozzle the process returns to the 998–1002 mL range.
SQC has two complementary arms that address quality at different stages of production:
| Feature | Process Control | Product Control |
|---|---|---|
| Timing | During production | After production (lot acceptance) |
| Primary tool | Control charts | Sampling plans |
| Objective | Keep process in control | Accept or reject lots |
| Preventive? | Yes — detects shift early | No — detects after the fact |
| Typical metric | Process capability index | AQL, LTPD, AOQ |
A steel-rolling mill monitors the thickness of steel sheets every 30 minutes using an \(\bar{X}\)-R chart. When a point falls above the UCL, the line is stopped and the roll gap is adjusted. This is process control — the focus is on keeping the rolling process stable and preventing further defective sheets.
A supplier ships 10 000 bolts to a customer. The customer inspects a random sample of 200 bolts; if 5 or fewer are defective, the lot is accepted; otherwise it is rejected and returned. This is product control — the focus is on deciding whether the submitted lot is acceptable, not on monitoring the supplier's production line.
Walter A. Shewhart of Bell Telephone Laboratories introduced the control chart in 1924. His insight: if a process is influenced only by chance causes, the quality characteristic follows a stable probability distribution (often approximately normal). Any observation that falls far from the centre — beyond what this distribution predicts — signals an assignable cause.
Shewhart placed control limits at 3 standard deviations from the process mean:
Under normality, the probability of a point falling outside the 3\(\sigma\) limits by chance alone is approximately 0.27% (0.135% in each tail). So if a point does fall outside, we have strong evidence that the process mean has shifted — an assignable cause is likely present.
A Shewhart control chart has three horizontal lines plotted against the sample number (or time):
The subscript "stat" refers to the sample statistic being plotted (sample mean, range, proportion, count, etc.).
A process is in control when:
A process is out of control if any of the following occur:
A process fills packets with mean weight \(\mu\) = 500 g and \(\sigma\) = 5 g. The 3\(\sigma\) limits for individual measurements are UCL = 500 + 15 = 515 g and LCL = 500 − 15 = 485 g. A sample packet weighs 518 g — above the UCL. Conclusion: an assignable cause is likely present; investigate the filling mechanism.
On an \(\bar{X}\) chart for shaft diameter, no individual point falls outside the 3\(\sigma\) limits. However, the last 8 consecutive sample means are all above the centre line. This is a run of 8, which signals a likely upward shift in the process mean. Investigation shows that a new batch of raw material (Material) was introduced 8 samples ago, slightly increasing the average diameter.