How to use it
- 1. Run the lineSamples of n=5 appear on both charts; the first 15 in-control samples set the control limits.
- 2. Inject troubleArm a mean shift or a variance surge - the process drifts from the next sample onward.
- 3. Watch the catchPoints beyond 3σ turn red; eight-in-a-row on one side trips the run rule (amber).
- 4. Control ≠ capabilityMove the spec limits: Cp/Cpk change, the control charts don't. Two different questions.
The line
Sampling
Sabotage the process
Process healthy: μ=500, σ=4.
Specification limits
Specs are the customer's voice; control limits are the process's voice. They are not the same thing.
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Cp (potential)
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Cpk (actual)
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Est. % out of spec
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Samples to detect
X̄ chart - sample means vs ±3σ control limits (UCL/LCL = X̄̄ ± A₂R̄, A₂=0.577 for n=5). Catches mean shifts.
R chart - sample ranges vs D₃R̄, D₄R̄ (0 and 2.114·R̄ for n=5). Catches variance changes the X̄ chart can miss.
Try these experiments
- Arm a +1σ shift and count the samples until a red point - small shifts hide for a long time (that is why CUSUM/EWMA exist).
- Widen the specs until Cpk looks great while the armed shift is still undetected - capability improved, control did not. Explain the difference.
- Arm variance ×1.8: the R chart fires while the X̄ chart often stays quiet - means can look fine while spread rots.
About this tool
The concept
SPC separates common-cause noise from special-cause change. React to signals, not to noise - adjusting a healthy process makes it worse.
How it works
Limits come from the process itself: X̄̄ ± A₂R̄ and D₃/D₄·R̄, estimated from the calibration samples with σ̂=R̄/d₂.
Capability
Cp=(USL−LSL)/6σ̂ asks if the process could fit the specs; Cpk asks if it actually does, given where the mean sits.