7.1 Statistical Process Control (SPC): Cp & Cpk

ManufacturingSPC processes naturally vary. The engineering question is not "did this part pass?" but "is the processdifference capablebetween inspecting quality in (reactive) and building quality in (proactive). Inspection tells you that you just made a bad part; SPC tells you that you are about to make a bad part. It is the practice of consistentlylistening producingto passingthe parts?"heartbeat" of the machine. If you ignore the statistical trends, you are driving blind, waiting for the crash (scrap) to tell you to stop.

Cp vs. Cpk: The Physics of Capability

We use two metrics to determine if a process can meet the customer's requirements. Do not mix them up.

Cp (Process Potential): The Width

• Definition: RelatesCan the car fit in the garage if we drive perfectly? It compares the width of the specification limitstolerance (Tolerance)Spec Limits) to the widthnatural variation of the process variation (6 sigma)6σ). It answers: "Could we fit inside the limits if we were perfectly centered?"
• Formula:The Logic:
  • If Cp =< (USL1.0 -→ LSL)Then /the 6sigmacar is wider than the garage door. No amount of operator skill will fix this. Action: Invest in better tooling or loosen the tolerance.
  • If Cp ≥ 1.33 → Then the process is potentially capable.

Cpk (Process Reality)Capability): The Centering

• Definition: MeasuresIs the actualcar capabilityactually byparked accountingin the center of the garage? It accounts for howthe centeredshift of the mean.
• The Logic:
  • If Cpk < 1.0 → Then parts of the distribution are hitting the wall (out of spec). You are producing scrap.
  • If Cpk = Cp → Then the process is relativeperfectly centered.

Pro-Tip: A high Cp and a low Cpk means your machine is precise (tight grouping) but inaccurate (aimed at the wrong target). This is the easiest problem to fix: just adjust the offset.

Control Limits vs. Specification Limits

This is the most common error on the shop floor. Operators often think the Control Limit is the "Fail" line. It is not.

• Specification Limits (USL/LSL): Defined by the Customer/Print. These are the "Cliffs." If you cross them, the part is dead.
• Control Limits (UCL/LCL): Defined by the Process Data (typically ±3σ from the mean). These are the "Guardrails."

The Rule of Law:

• If a point exceeds the Control Limit (UCL/LCL) → Then the process has changed. Stop and investigate. The part is likely still good (if inside USL/LSL), but the process is out of control.
• If you adjust the machine because a part is "close" to the limits.Spec ItLimit considersbut still inside the Control Limit → Then you are introducing "worstTampering" case"(over-correction), tailwhich ofactually increases variation.

Reaction Rules (The "Nelson" Logic)

When do you stop the distribution.line? Do not rely on "gut feeling." Use defined statistical triggers.

Stop & Fix If:

1. Formula:The Outlier: CpkOne =point minfalls outside the Control Limits (±3σ).
2. The 1.33 Standard:Trend: A Cpk of 1.33 (4 Sigma) is the minimum industry standard for a "stable" process. A Cpk of 1.67 (5 Sigma) is required for safety-critical automotive/medical features.
4. Cpk < 1.0: The process is incapable. Defects are statistically guaranteed. Inspection must be 100%.

Western Electric Rules (Stop Triggers)

Operators must stop the process if any of the following statistical anomalies occur on a Control Chart:

1. One point beyond the 3 sigma Control Limit.
2. Two out of threeSeven consecutive points beyondare moving in the 2same sigma zonedirection (Warning)Up or Down). Tool wear is occurring.
3. The Shift: Seven consecutive points are on onethe same side of the centerlineMean. (ProcessThe Shift).process center has shifted.

Final Checklist

IndexControl Point	TargetCritical ValueRequirement	MeaningRisk Avoided
CpCpk Target	≥ 1.33> (Standard), ≥ 1.67 (Safety Critical).	ProcessStatistical widthScrap is acceptableGeneration
CpkSampling	>Subgroup 1.33size n=5 is standard for X-bar charts.	ProcessInsufficient is centered and capablesensitivity
Sigma LevelReaction	Stop on 1 point > 4.0UCL/LCL.	DefectRunning probabilitya isdrifted lowprocess
ActionDiscipline	CpkNever <adjust 1.0a process that is "In Control."	Stop ShipTampering / 100%Over-correction
Calculation	Recalculate InspectLimits every 50 subgroups.	Stale control limits