Inherent, natural variation in the process due to countless small, uncontrollable factors (e.g., slight fluctuations in ambient temperature, minor inconsistencies in raw materials).

• A process experiencing only common cause variation is said to be In Statistical Control.
• Its output is predictable over time (usually following a normal distribution).

Variation caused by specific, identifiable factors that are not part of the normal process (e.g., a broken machine part, a new untrained operator, a defective batch of raw material).

• A process experiencing assignable cause variation is Out of Control.
• Its output is unpredictable, and immediate action must be taken to identify and eliminate the root cause.

• Center Line (CL): The historical average or target value of the process.
• Control Limits (UCL, LCL): Typically set at $\pm 3$ standard deviations from the center line. Because 99.7% of data in a normal distribution falls within $\pm 3\sigma$, any point falling outside these limits is extremely unlikely to be common cause variation. It is a signal that an assignable cause is present.

Monitors the average value of the process over time. Samples of size $n$ are taken periodically, and their means ($\bar{x}$) are plotted. It detects shifts in the process center.

Monitors the variability (spread) of the process over time.

• $R$ Chart (Range): Plots the range of each sample. Used for small sample sizes ($n < 10$) because it is simple to calculate.
• $S$ Chart (Standard Deviation): Plots the standard deviation of each sample. More statistically robust and preferred for larger sample sizes ($n \ge 10$).

Used when inspecting items that are simply classified as "conforming" or "non-conforming" (defective).

• $p$ Chart: Plots the proportion of defective items in a sample. Essential when the sample size $n$ varies from batch to batch.
• $np$ Chart: Plots the number of defective items. Used only when the sample size $n$ is constant.

Used when an item can have multiple defects, but the item itself is not necessarily "defective" or rejected outright (e.g., the number of surface blemishes on a precast concrete panel).

• $c$ Chart: Plots the total number of defects in a constant "area of opportunity" (e.g., exactly one 10ft pipe section). Follows a Poisson distribution.
• $u$ Chart: Plots the average number of defects per unit. Used when the area of opportunity varies (e.g., inspecting pipes of different lengths).

• Natural Tolerance Limits (NTL): The limits within which the process actually operates ($\mu \pm 3\sigma$). This represents the "Voice of the Process."
• Specification Limits (USL, LSL): The engineering tolerances required by the design or the client. This represents the "Voice of the Customer."

Metrics that quantify how well the process fits within the specification limits.

• $C_p$ (Capability Potential): Measures the ratio of the specification width to the process width. It ignores whether the process is centered.

If $C_p < 1$, the process is physically incapable of meeting specifications (its natural spread is too wide). A standard industry goal is $C_p \ge 1.33$.

• $C_{pk}$ (Capability Index): Takes centering into account. It is the minimum of capability relative to the upper and lower specs.

If $C_{pk} < 1$, the process is producing defects, either because it is too wide or it is off-center.

A statistical procedure used to determine whether to accept or reject a production lot of material. It involves taking a random sample from the lot and deciding to accept the entire lot if the number of defects in the sample is below a specified threshold, rather than inspecting every single item.

A set of techniques and tools for process improvement that aims to reduce defects to fewer than 3.4 per million opportunities. It emphasizes data-driven decision making, rigorous statistical analysis, and continuous process improvement methodologies like DMAIC (Define, Measure, Analyze, Improve, Control).