Statistical Process Control Line

Process Controls

Process mean shift 0.0

Process variation σ 1.00

Line speed 1.4 u/s

Control Chart Status

IN CONTROL

Throughput

0/min

DPMO

C_pk

2.00

Sigma level

6.0σ

Inspected

Defects

How it works

Each part on the line gets a measured critical dimension X = mean + σ·Z, where Z is a standard normal draw (Box–Muller). Parts outside the spec limits [LSL, USL] = [-6, +6] are scrapped as defects — the "waste" a Lean/Six Sigma project tries to eliminate.

Process capability:  Cpk = min(USL-mean, mean-LSL) / (3σ)
Sigma level:         ≈ 3·Cpk  (short-term, no shift)
DPMO (defects/1e6):  from the normal-CDF tail(s) beyond spec
X-bar chart:         plot mean of each 5-part subgroup;
  UCL/LCL = ±3·σ0/√n  (σ0 = 1, the process's designed baseline)

Process mean shift — models special-cause drift (tool wear, mis-calibration) pushing the average off target.
Process variation σ — common-cause variability; a true "Six Sigma" line keeps σ small enough that ±6σ still fits inside spec.
Line speed — cycle time / throughput of the conveyor.
Apply Kaizen fix — a rapid-improvement event: recentres the mean and cuts σ by 30%, the textbook DMAIC "Improve" step.
Green points on the chart are subgroup averages inside the control limits; red points signal an out-of-control process — a real operator would stop the line and investigate.

In-spec part Defect (scrapped) X-bar subgroup avg

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