Learn how to distinguish common-cause and special-cause variation, choose and interpret control charts, calculate process capability only after stability has been demonstrated, analyse variable data using working I-MR or X̄-R charts, and build a controlled SPC implementation project for manufacturing and special processes.
Variation built into the current system: ordinary differences in material, equipment, environment, methods and people. A stable process contains common causes only.
A specific, identifiable influence not normally present: broken tooling, wrong setting, bath contamination, sensor failure, mixed material or an abnormal interruption.
A statistically stable process is predictable within its established control limits. Stable does not automatically mean capable or compliant with specification.
The actual formula depends on chart type, subgroup size and estimation method. Limits should normally be calculated from a suitable baseline period and revised only for a justified process change.
Select a meaningful process input or output linked to risk, performance or a control plan.
Confirm the measurement system, data definition, sampling method and rational subgroup.
Plot time-ordered data, investigate special causes and establish a trustworthy baseline.
Reduce common-cause variation, assess capability and sustain with a reaction plan.
| Data and situation | Recommended chart | Use | Important cautions |
|---|---|---|---|
| Continuous measurement, one value at each time | I-MR | Individual values and moving ranges | Successive values should be meaningfully time ordered. Autocorrelation can distort limits. |
| Continuous data, rational subgroup usually 2–10 | X̄-R | Subgroup averages and within-subgroup ranges | Subgroup members should be produced under nearly the same conditions. |
| Continuous data, larger subgroups | X̄-S | Subgroup averages and standard deviations | Use suitable constants or software for subgroup size. |
| Fraction nonconforming, variable sample size | p chart | Proportion of units classified nonconforming | Each unit must have a consistent opportunity to be classified. |
| Number nonconforming, constant sample size | np chart | Count of nonconforming units | Sample size must remain constant. |
| Number of defects, constant opportunity | c chart | Defect count per constant unit or area | One unit may contain multiple defects. |
| Defects per unit, changing opportunity | u chart | Defect rate where sample size or area varies | Opportunity must be measurable and appropriately modelled. |
| Rare events or long time between failures | g or t chart | Opportunities or time between events | Useful when conventional attribute charts contain mostly zeros. |
| Small sustained shift needs rapid detection | EWMA or CUSUM | Weighted or cumulative evidence of change | Requires deliberate design and disciplined interpretation. |
Group observations so within-subgroup variation represents short-term common causes, while differences between subgroup averages reveal changes over time.
Base frequency on process speed, change mechanisms, detection risk, batch structure, control-plan needs and the likely time between a cause and harmful output.
Use sufficient representative data from one defined process system. Remove points only after a documented special cause is confirmed, not merely to make limits look better.
Confirm the signal, data identity and measurement validity. Do not erase or remeasure merely because the point is inconvenient.
Identify the last known stable point, affected material, batches, equipment, time window and downstream exposure.
Check changes in material, machine, method, people, measurement and environment. Preserve evidence.
Correct the assignable cause, verify a stable restart, disposition product and capture learning in controls.
| Index | What it indicates | What it can hide |
|---|---|---|
| Cp | Potential short-term capability if the process were centred. | Off-centre mean, instability, non-normality and measurement error. |
| Cpk | Short-term capability considering the nearest specification limit. | Long-term shifts, unstable behaviour and incorrect within-sigma estimation. |
| Pp | Overall spread compared with tolerance. | Location relative to specifications. |
| Ppk | Overall performance including centring. | Root causes and time structure of variation. |
Values such as 1.33, 1.67 or 2.00 are often used, but the required threshold should be defined by customer, sector, risk and control strategy.
Do not force every characteristic into a normal model. Consider transformation, percentile methods, distribution fitting or a different performance measure.
Use the relevant one-sided index and consider physical boundaries. Examples include maximum contamination, minimum strength or maximum defect rate.
| Special process | Potential SPC characteristics | Typical chart/application | Risk and interpretation notes |
|---|---|---|---|
| Heat treatment | Soak temperature, furnace uniformity indicators, quench delay, hardness, vacuum level, dew point | I-MR for cycle metrics; X̄-R for hardness samples; rare-event charts for failed cycles | Separate furnace zones, recipes and alloy families where behaviour differs. Do not average away local excursions. |
| Electroplating | Bath temperature, pH, metal concentration, contaminants, current density, coating thickness | I-MR for analyses; X̄-R for thickness subgroups; EWMA for gradual chemistry drift | Replenishment creates expected shifts; establish rules around additions and solution maintenance. |
| Anodising | Acid concentration, dissolved aluminium, temperature, voltage/current profile, coating thickness, seal quality | I-MR for chemistry; profile monitoring for electrical cycle; X̄-R for thickness | Alloy, temper, racking and geometry can create separate process families. |
| Chemical conversion coating | Concentration, pH, temperature, contact time, rinse conductivity, coating mass or test results | I-MR for bath checks; p chart for pass/fail verification; trend charts for rinse quality | Attribute tests may be too infrequent for timely control; monitor leading process variables. |
| Painting / coating | Viscosity, mix ratio, pot life, booth temperature/humidity, WFT, DFT, cure profile, defects | X̄-R for film thickness; I-MR for viscosity; p/u charts for defect rate | Stratify by painter, gun, colour, geometry, batch and coating system where necessary. |
| Welding | Current, voltage, wire feed, travel speed, heat input, gas flow, weld dimensions, defect counts | I-MR/profile monitoring for parameters; u chart for defects per weld length | Procedure qualification ranges are not control limits. Monitor the actual production process within qualified boundaries. |
| Brazing | Furnace profile, vacuum, atmosphere, joint clearance, filler application, leak rate | Cycle/profile control; I-MR for leak results; p chart for acceptance outcomes | Load configuration and thermal mass can be important stratification factors. |
| NDT | Bath concentration, UV intensity, white light, sensitivity checks, equipment performance, indication rates | I-MR for control checks; p/u charts for indications with careful product-mix stratification | Indication rate is influenced by actual product quality; never use it alone to judge inspector performance. |
| Composite cure | Vacuum integrity, ramp rate, pressure, dwell temperature/time, exotherm, resin condition, porosity | Profile monitoring and I-MR of extracted cycle features | Use sensor-level data where local thermal response matters; an average may conceal a cold or hot location. |
| Printed circuit assembly | Paste height/volume, placement offsets, reflow profile, solder defects, first-pass yield | X̄-R for paste metrics; u chart for defects; EWMA for placement drift | Stratify by package type, stencil aperture, line and product family. |