Control — Sustaining the Gains
Control locks in the improvement so the process does not drift back to its old behavior once the project team disbands. Green Belts monitor the vital few metrics with the right control chart, verify and re-verify capability against the customer's specifications, and hand off a control plan that tells operators exactly what to watch and how to react. Lean fundamentals — waste elimination, 5S, standard work, and equipment effectiveness — provide the stable foundation that makes the gains hold.
Control charts and the purpose of SPC
A control chart plots a process metric over time with a center line and statistically derived upper and lower control limits (typically ±3σ of the plotted statistic). Its purpose is to distinguish common-cause variation (the routine, inherent noise of a stable process) from special-cause variation (an assignable signal that something changed). This distinction drives the correct reaction: you act on special causes but leave common-cause variation alone. Reacting to common-cause noise as if it were a signal is 'tampering,' which Deming's funnel experiment shows actually increases variation. Control limits come from the process data and answer 'what does this process do?'; specification limits come from the customer and answer 'what does the customer want?' — the two are unrelated and must never be drawn on the same axis as if interchangeable.
Detecting special causes: out-of-control rules
A process is signaled out of control not only when a point falls outside the ±3σ limits but also by non-random patterns within them. The Western Electric / Nelson rules flag, for example, a single point beyond 3σ; two of three consecutive points beyond 2σ on the same side; four of five beyond 1σ on the same side; a run of eight or more consecutive points on one side of the center line; and clear trends, cycles, or hugging of the center line. Each pattern is statistically unlikely under pure common-cause variation, so it implies an assignable cause worth investigating. A process that shows only common-cause variation is 'in statistical control' — predictable, though not necessarily capable of meeting specifications, which is a separate question.
Selecting the right control chart
Chart choice follows the data type, and the exam drills the decision tree. For continuous (variable) data collected in rational subgroups: use X-bar and R when the subgroup size is small (about n = 2 to 9), and X-bar and S when subgroups are larger (n ≥ 10, roughly n > 9) because the standard deviation estimates spread more reliably than the range at larger n. When data comes one measurement at a time with no rational subgroup, use an Individuals and Moving Range (I-MR) chart. For attribute data on defectives (nonconforming units, binomial): use a p chart when the sample size varies (it plots the proportion defective) and an np chart when the sample size is constant (it plots the count of defectives). For attribute data on defects (counts of nonconformities, Poisson): use a c chart when the area of opportunity is constant (count per fixed unit) and a u chart when the area of opportunity varies (defects per unit of varying size, e.g., blemishes on rolls of different lengths). Remember the distributions: p and np assume the binomial (defective units); c and u assume the Poisson (defect counts).
Computing control limits: worked X-bar/R example
Control limits for an X-bar chart use tabulated constants that depend on subgroup size n. With subgroups of n = 5, the average of the subgroup means (X-double-bar) = 100, the average range (R-bar) = 5, and the constant A₂ = 0.577, the limits are: UCL = X̿ + A₂ × R̄ = 100 + 0.577 × 5 = 102.885, and LCL = X̿ − A₂ × R̄ = 100 − 0.577 × 5 = 97.115, with the center line at 100. The companion R chart uses D₄ and D₃: UCL_R = D₄ × R̄ and LCL_R = D₃ × R̄ (for n = 5, D₄ = 2.114 and D₃ = 0, so the R chart has no meaningful lower limit). These constants (A₂, D₃, D₄, d₂) come from a standard table; the Green Belt is expected to apply them, not memorize the full table.
Process capability: Cp and Cpk
Capability compares the voice of the process (its spread) to the voice of the customer (the specification width), and it is only meaningful once the process is in statistical control. Cp = (USL − LSL) ÷ 6σ measures potential capability — whether the process spread could fit inside the tolerance — but ignores where the process is centered. Worked example: USL = 110, LSL = 90, σ = 2.5, so Cp = (110 − 90) ÷ (6 × 2.5) = 20 ÷ 15 = 1.33. Cpk accounts for centering by taking the worse of the two one-sided ratios: Cpk = min[(USL − mean) ÷ 3σ, (mean − LSL) ÷ 3σ]. If the process is perfectly centered Cpk equals Cp; as it drifts off center Cpk falls below Cp. A Cp or Cpk of 1.33 (a '4-sigma' process) is a common minimum target and 1.67 a stretch target; Cpk ≥ 1.0 means the spread just fits the tolerance if centered. Cp and Cpk describe short-term potential; the long-term counterparts Pp and Ppk use overall (long-term) standard deviation.
Control plans and standardization
A control plan is the durable handoff document that keeps the improved process under control after the team leaves. For each critical input and output it records what to measure, the specification, the measurement method and sample size, the monitoring frequency, the person responsible, and — most importantly — the reaction plan that states exactly what to do when the metric goes out of control. The reaction plan is what prevents a signal from being ignored. Control plans work hand in hand with standard work (the documented current best method every operator follows), training, and visual management so the gains survive turnover and time. Without standardization, improvements erode as people revert to old habits.
Lean waste, 5S, and OEE
Lean sustains capability by removing the waste that destabilizes a process. The eight wastes (muda), often recalled by DOWNTIME, are Defects, Overproduction, Waiting, Non-utilized talent, Transportation, Inventory, Motion, and Excess processing. The 5S method (Sort, Set in order, Shine, Standardize, Sustain) builds the orderly, visual workplace that makes deviations obvious and standard work sustainable. Overall Equipment Effectiveness (OEE) is the standard single metric for how productively equipment runs, and it is the product of three factors: OEE = Availability × Performance × Quality. Availability is uptime versus planned production time (lost to breakdowns and setups); Performance is actual speed versus ideal speed (lost to minor stops and slow cycles); Quality is good units versus total units produced (lost to defects and rework). Worked example: 90% availability × 95% performance × 98% quality = 0.90 × 0.95 × 0.98 ≈ 0.838, so OEE ≈ 83.8%. Because the three multiply, a weak factor drags the whole score down, which tells the team precisely where to focus.
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