Engineering Statistics

Start here: ten words every newcomer needs

Overheard on the job

Real-sounding lines from the floor, translated into plain English.

• Chart went OOC on a run of seven, but everything's still in spec, so work the OCAP and don't scrap anything.

  TranslationThe control chart signaled a process change through seven points on one side of the centerline. Product still meets specification, so follow the out-of-control action plan rather than discarding material.

• Cpk's fine but Ppk is 0.9. Lot-to-lot is killing us, not the tool.

  TranslationShort-term capability looks good, but long-term performance is poor because of variation between lots, so the fix lies in incoming material or other lot-level causes.

• Stop chasing the mean on the coater. That's common cause, you're just tampering.

  TranslationStop adjusting the coater after every reading. The variation is normal background noise, and reacting to it makes the output worse.

• It's only res III, so that big D effect could just be the AB interaction aliasing in. Fold it over.

  TranslationThe reduced experiment cannot separate factor D from the interaction of A and B. Run the mirror-image set of runs to separate them.

• Weibull's got a dogleg and the early leg has beta under one, so it's infant mortality from a bad build lot, not wear-out.

  TranslationThe life data show two failure populations, and the early failures have a falling failure rate typical of manufacturing defects rather than aging.

• Gauge R&R is 40 percent and P/T is 0.5, so that shift is probably just the two tools not being matched.

  TranslationThe measurement system adds too much variation to trust, and the apparent process change is likely a difference between the measuring tools.

• Excursion on etcher 4: bullseye on the wafer maps, bin 9 up threefold and D0 doubled. Lots are on hold.

  TranslationA sudden yield problem traced to one etch tool shows a radial failure pattern, a jump in one failure category and twice the defect density, so affected material is held.

• Split lot gave p of 0.04, but after that many cuts of the data it smells like a fishing expedition. Rerun it with enough wafers for power.

  TranslationThe comparison looked significant, but so many tests were tried that it may be a false positive. Repeat the experiment with a sample size large enough to detect the effect reliably.

Control charts, run rules and the language of telling routine noise from a real process change.

• Chasing the meanalso knob-turning, chasing the process
  Shop phrase for adjusting a process after each reading to pull it back to target, which only adds variation. Shop talk
• Common causealso chance cause, random variation
  Background variation built into a stable process from many small sources, present all the time.
• Control chartalso Shewhart chart, SPC chart
  Time-ordered plot of a process statistic with a centerline and limits that flag when the process has changed.
• Control limitsalso natural process limits, 3-sigma limits
  Boundaries on a control chart computed from the process's own variation, marking how far routine noise normally reaches.
• CUSUMalso cumulative sum, CUSUM chart
  Cumulative sum chart: adds up deviations from target so that a small persistent shift builds into a clear signal.
• Driftalso creep, trend
  Slow, steady creep of a process or gauge reading in one direction as something wears, depletes or ages.
• EWMAalso exponentially weighted moving average, geometric moving average
  Exponentially weighted moving average: a chart or controller that blends each reading with the past to catch small, slow shifts.
• Fat-fingeralso fat-fingered entry, keying error
  Data entry error from a mistyped number, such as a slipped decimal or swapped digits, that shows up as a false signal. Shop talk
• Flyeralso freak, wild point
  Single wild data point far from the rest, often a measurement or entry error rather than a real process change. Shop talk
• Hugging the centerlinealso hugging, stratification
  Chart pattern where points cluster unnaturally close to the centerline, usually a sign the limits are wrong. Shop talk
• I-MR chartalso individuals chart, XmR chart
  Individuals and moving range chart: the control chart for one measurement per period, such as one batch or one lot.
• OCAPalso out-of-control action plan, reaction plan
  Out-of-control action plan: the scripted checklist that tells operators exactly what to do when an SPC chart fires.
• OOCalso out of control, OOC event
  Out of control: shorthand for a point or chart that has violated a control limit or run rule. Shop talk
• p chartalso fraction defective chart
  Control chart for the fraction of nonconforming units in each sample, built on the binomial distribution.
• Rational subgroupalso subgroup, rational subgrouping
  Group of measurements chosen so that only routine, short-term variation can occur within it.
• Run of sevenalso seven in a row, run
  Seven consecutive chart points on one side of the centerline, or steadily rising or falling, read as a process shift. Shop talk
• Sawtoothalso sawtooth pattern, PM sawtooth
  Chart pattern of gradual drift and a sudden reset, repeating with each maintenance cycle or consumable change. Shop talk
• Shiftalso mean shift, level shift
  Sudden, sustained step change in a process mean, often after a maintenance event, material change or recipe edit.
• SPCalso statistical process control
  Statistical process control: using control charts and run rules to tell routine process noise from real changes.
• Special causealso assignable cause
  Specific, identifiable source of variation that is not part of the process's normal behavior and shows up as a chart signal.
• Tamperingalso overadjustment, overcontrol
  Adjusting a stable process in reaction to common cause variation, which makes the output worse rather than better.
• UCLalso upper control limit
  Upper control limit: the top boundary on a control chart, paired with the lower control limit (LCL) below the centerline.
• Western Electric rulesalso WECO rules, run rules
  Standard set of run rules that flag nonrandom patterns on a control chart, not just single points past the limits.
• X-bar and R chartalso Xbar-R, X-bar R chart
  Paired control charts for subgroup averages and subgroup ranges, the workhorse for measured data sampled in small groups.

Spec limits, capability indices, defect rates, wafer maps and the numbers that decide whether product is good.

• 1.5 sigma shiftalso sigma shift, long-term shift
  Six Sigma convention that assumes a process mean wanders by 1.5 standard deviations over the long term.
• Binalso test bin
  Test category that each die or unit is sorted into at probe or final test, with bin 1 usually meaning good.
• Bullseyealso donut, center spot
  Wafer map pattern of concentric rings or a center spot, the signature of a radial process nonuniformity. Shop talk
• Cpalso process capability ratio, process potential index
  Process capability ratio: the specification width divided by six process standard deviations, ignoring centering.
• Cpkalso C-P-K, capability index
  Process capability index that accounts for centering: distance from the mean to the nearest spec limit in units of 3 sigma.
• Defect densityalso D0, D-naught
  Number of yield-killing defects per unit area of wafer or panel, the main input to yield models.
• DPMOalso defects per million opportunities
  Defects per million opportunities: defect count scaled by the number of chances for a defect in each unit.
• Excursionalso yield excursion, defect excursion
  Sudden departure of yield, defect counts or a key parameter from its normal band, big enough to trigger holds and an investigation. Shop talk
• Killer defectalso killer, yield killer
  Defect that lands where it causes a die to fail, as opposed to a harmless cosmetic or nuisance defect. Shop talk
• OOSalso out of spec, out of specification
  Out of specification: a measured result outside the spec limits, meaning the product itself is nonconforming.
• Opening the specalso opening up the spec, spec relaxation
  Widening a specification limit so more product passes, instead of fixing the process that makes it. Shop talk
• Ppkalso process performance index, performance index
  Process performance index: a Cpk-style figure computed with the overall standard deviation, capturing long-term variation.
• Process capabilityalso capability, process capability study
  How well a stable process's natural spread fits inside the specification limits, usually expressed as an index.
• Sigma levelalso process sigma, sigma
  Process quality expressed as the number of standard deviations that fit between the mean and the nearest spec limit.
• Sortalso wafer sort, probe
  Either the wafer-level electrical test that bins every die, or a 100 percent inspection that screens suspect parts. Shop talk
• Specification limitsalso spec limits, specs
  Acceptance boundaries for a product characteristic set by design or customer requirements, labeled USL and LSL.
• Wafer mapalso bin map, die map
  Picture of a wafer showing each die's test result or measurement by location, used to spot spatial failure patterns.
• Yield
  Fraction of units that come out good at a step or across a whole process, the headline number for any production line.

Factors, factorial and fractional designs, aliasing, blocking and the slang of planned process experiments.

• Aliasingalso alias, alias structure
  Situation in a fractional design where two or more effects leave identical patterns in the data and cannot be told apart.
• Blockalso blocking, blocking factor
  Group of experimental runs made under similar conditions, used to remove a known nuisance source such as day, batch or tool.
• Center pointalso centerpoint, center run
  Run with every numeric factor set halfway between its low and high levels, used to detect curvature and estimate error.
• Confoundingalso confounded
  Mixing of two effects so that the data cannot separate them, whether by design or through an uncontrolled variable.
• DOEalso design of experiments, designed experiment
  Design of experiments: planning a set of runs that vary several factors at once so their effects can be separated.
• Factoralso input, X
  Input variable deliberately set at chosen levels in an experiment, such as temperature, pressure, time or supplier.
• Factorial designalso full factorial, 2^k design
  Experiment that runs every combination of the chosen factor levels, so each main effect and interaction can be estimated.
• Fractional factorial designalso fractional factorial, fraction
  Experiment that runs a chosen fraction of all factor combinations, trading some aliased effects for far fewer runs.
• Interactionalso two-factor interaction, 2FI
  Situation where the effect of one factor depends on the level of another, so their combined effect is not simply additive.
• Knobalso process knob, tuning knob
  Any adjustable process parameter on a tool, such as RF power, pressure, gas flow, temperature or time. Shop talk
• OFATalso one factor at a time, one-variable-at-a-time
  One factor at a time: changing a single input while holding the rest fixed, the habit designed experiments replace. Shop talk
• Randomizationalso random run order, randomized
  Running experimental trials in a random order so unknown time trends and nuisance effects do not bias the results.
• Replicatealso replication, true replicate
  Independent rerun of the same factor settings from scratch, which gives a true estimate of experimental error.
• Resolutionalso design resolution, Res III
  Rating of a fractional factorial design, in Roman numerals, that states which effects are aliased with which.
• Robustalso robustness
  Describes a product or process whose output stays on target despite variation in noise factors that cannot be controlled.
• RSMalso response surface methodology, response surface
  Response surface methodology: sequential experiments that fit curved models to find the settings that optimize a response.
• Split lotalso split, wafer split
  Lot of wafers divided between two or more process conditions so the comparison shares the same incoming material. Shop talk
• Sweet spotalso process window, operating window
  Region of factor settings where every response meets its target at once, found by overlaying response contour plots. Shop talk

ANOVA, regression, significance testing and the traps that turn noise into false conclusions.

• ANOVAalso analysis of variance
  Analysis of variance: splitting total variation into parts from each factor and from error, then testing which parts are real.
• Autocorrelationalso serial correlation, autocorrelated data
  Correlation between successive values in a time series, which breaks the independence that standard control charts assume.
• Confidence intervalalso CI, confidence limits
  Range calculated from sample data that brackets an unknown parameter, such as a mean, at a stated confidence level.
• Fishing expeditionalso data dredging, p-hacking
  Analysis that tests many variables or subsets in search of any significant result, almost guaranteeing a false positive. Shop talk
• Interocular trauma testalso IOTT, eyeball test
  Jokey name for an effect so obvious in a plot that it hits you between the eyes, no formal statistics needed. Shop talk
• Leveragealso hat value
  Measure of how far a data point's input values sit from the rest, which gives it outsized pull on a fitted model.
• Outlieralso wild point, anomaly
  Observation that sits far from the pattern of the rest of the data, either a genuine extreme or an error.
• p-valuealso p, significance probability
  Probability of seeing a result at least this extreme if there were truly no effect, used to judge statistical significance.
• Poweralso statistical power
  Probability that a test will detect a real effect of a given size, set by sample size, noise and alpha.
• R-squaredalso R2, coefficient of determination
  Share of the variation in a response that a regression model accounts for, on a scale from 0 to 1.
• Regressionalso regression analysis, linear regression
  Fitting an equation that predicts a response from one or more input variables, usually by least squares.
• Residualalso residuals, residual error
  Difference between an observed value and the value a fitted model predicts for it.
• Significantalso statistically significant, stat sig
  Describes a result unlikely to have come from chance alone at a stated risk level, which is not the same as important.
• t-testalso Student's t-test, two-sample t
  Test that compares a mean against a target, or two means against each other, using the t distribution.

Failure rates, life distributions, censored data and the tests that predict how long products last.

• Acceleration factoralso AF, Arrhenius acceleration
  Ratio of life under normal use conditions to life under a harsher test condition, used to turn test hours into field time.
• Bathtub curvealso bathtub, life curve
  Plot of failure rate over a product's life: falling early failures, a flat random period, then rising wear-out.
• Burn-inalso burn in, BI
  Operating products under raised stress before shipment so weak units fail in the factory instead of in the field.
• Censoringalso censored data, suspension
  Incomplete life data where a unit's exact failure time is unknown because the test ended or the unit was removed first.
• Doglegalso hockey stick, bend
  Bend in a Weibull plot where the data change slope, a sign of two failure modes or two populations mixed together. Shop talk
• FITalso failures in time, FIT rate
  Failures in time: one failure per billion device-hours, the standard unit for semiconductor failure rates.
• Infant mortalityalso early life failure, ELF
  Early-life failures caused by manufacturing flaws, giving a failure rate that starts high and then falls.
• MTBFalso mean time between failures
  Mean time between failures: average operating time between successive failures of a repairable system.
• MTTFalso mean time to failure, mean life
  Mean time to failure: expected life of a non-repairable item, the average time until its first and only failure.
• Shape parameteralso beta, Weibull slope
  Weibull beta: the slope of a Weibull plot, which shows whether failures are early-life, random or wear-out.
• Weibull distributionalso Weibull
  Flexible life distribution with a shape and a scale parameter, the standard model for fitting time-to-failure data.

Gauge studies, bias, repeatability and the reference parts that keep measurement data trustworthy.

• Biasalso offset, systematic error
  Systematic offset between the average of repeated measurements and the true or reference value.
• Gauge R&Ralso GR&R, gage R&R
  Study that measures how much observed variation comes from the measurement system's repeatability and reproducibility.
• Golden waferalso golden unit, golden sample
  Reference wafer or part kept aside and measured on a schedule to check that a tool or gauge has not drifted. Shop talk
• MSAalso measurement systems analysis, measurement system evaluation
  Measurement systems analysis: the set of studies that prove a gauge is fit for the decisions its data will drive.
• P/T ratioalso precision-to-tolerance ratio, P/T
  Precision-to-tolerance ratio: measurement system spread as a fraction of the specification width.
• Repeatabilityalso equipment variation, EV
  Scatter in the readings when one person and one gauge measure the same part over and over with nothing else changed.
• Reproducibilityalso appraiser variation, AV
  Variation in measurement results when different operators, gauges or setups measure the same items.
• Ten-to-one rulealso 10 to 1 rule, rule of ten
  Rule of thumb that a gauge should resolve one tenth or less of the tolerance or process variation it measures. Shop talk
• Tool matchingalso chamber matching, tool-to-tool matching
  Making several tools or chambers that run the same step produce the same results on the same material.
• Variance componentsalso components of variance
  Breakdown of total variation into the shares contributed by each source, such as lot, wafer, site and measurement.

Acceptance sampling plans, the normal distribution, spread and the intervals built from sample data.

• Acceptance samplingalso lot acceptance sampling, sampling plan
  Accepting or rejecting a whole lot based on inspecting a random sample from it against a predefined plan.
• AQLalso acceptable quality level, acceptance quality limit
  Acceptable quality level: the defect rate a sampling plan is built to pass most of the time, the good end of its OC curve.
• Central limit theoremalso CLT
  Result that averages of many independent values tend toward a normal distribution even when the values themselves are not normal.
• LTPDalso lot tolerance percent defective, RQL
  Lot tolerance percent defective: the poor quality level that a sampling plan should reject with high probability.
• Normal distributionalso Gaussian distribution, bell curve
  Symmetric bell-shaped distribution set by a mean and a standard deviation, the default model for measurement data.
• Operating characteristic curvealso OC curve, acceptance curve
  Graph of a sampling plan's probability of accepting a lot against the lot's true defect rate.
• Standard deviationalso sigma, s
  Typical distance of individual values from their mean, the basic measure of spread, written as sigma or s.
• Tightalso tight distribution, tight process
  Shop word for a distribution with small spread, as in a tight process or a tight spec; the opposite is wide or fat. Shop talk
• Tolerance intervalalso statistical tolerance interval
  Range expected to contain a stated share of all individual values in a population, at a stated confidence.

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