DLOG Process Capability & Deep Analytics Guide (PAT+ · MVA · Gauge R&R · Cpk/Cp · ANOVA)

Analysis Overview

1. Analytics at a Glance

Semiconductor mass production STDF V4 datalogs record thousands of parametric tests (PTR, MPR) and hundreds of thousands of parts (PRR). Simply knowing that parts passed within specification limits (LL/HL) does not reveal whether the manufacturing process is stable, whether measurements can be trusted, or whether potentially hazardous outlier parts are lurking among the good units.

DLOG provides specialized analytics screens to answer these crucial questions. Accessible from the view selector at the top of the interface, this guide explains the views dedicated to process capability, outlier screening, and measurement reliability.

Histogram, Cpk, Est ppm, and Normality statistics in DLOG Chart screen

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Figure 1. Chart screen — The mean, ±σ lines, Gaussian curve, and high limit (HL) are overlaid on the histogram. On the right, the Test Item Statistics panel displays Sigma, Cpk, Cp, Est ppm, and Normality (AD). Below, the Tests (Cpk) list color-codes the Cpk capability of all tests.

Analysis	DLOG Screen	Key Metrics	When to Use
PAT+ Outlier Screening	Wafer (PAT Data / PAT+), Chart (DPAT bands)	DPAT bands, SPAT neighbor residuals, PAT+ Flips	Screen "suspicious parts among good dies" that pass spec limits but deviate from the distribution or neighborhood.
Multivariate Outliers	MVA Explorer, Wafer (MVA-PAT)	Mahalanobis MD², PCA SPE, Isolation Forest	Detect parts whose individual tests are within spec, but whose combination of values is abnormal.
Gauge R&R	Gauge R&R	EV, AV, PV, %GRR, %P/T, ndc	Evaluate measurement system repeatability and reproducibility using repeated test runs of the same wafer.
Site Delta	SITE, Group Analysis (Group by: Site)	Per-site yield, BINs, means, η², ANOVA	Identify whether a single probe card pin, socket contact, or channel is causing systematic deviation.
Process Capability	Chart, Dashboard, Group Analysis	Cpk, Cp, Est ppm, Normality (Anderson-Darling)	Quantify spec margin, estimate ppm defect rates, and verify if normal distribution assumptions hold.
Correlation & TTO	Correlation, TTO Engine	Pearson r, Spearman ρ, Redundant test candidates	Identify duplicate tests measuring the same physical behavior to explore test time reduction.

Means and standard deviations are computed in a single pass using the Welford online algorithm. This numerically stable formulation avoids catastrophic cancellation that can occur when naively accumulating sums of squares:

$$M_1 = x_1, \quad M_k = M_{k-1} + \frac{x_k - M_{k-1}}{k}$$ $$S_1 = 0, \quad S_k = S_{k-1} + (x_k - M_{k-1})(x_k - M_k)$$ $$\mu = M_N, \quad \sigma^2 = \frac{S_N}{N - 1} \quad (N \ge 2)$$

100% On-Premise & Local Processing: All statistical computations run strictly on your local PC. Neither STDF files nor analysis results are ever uploaded to any external server.

Part Average Testing

2. PAT+ Outlier Screening (DPAT · SPAT)

PAT (Part Average Testing) is defined in the automotive semiconductor quality guideline AEC-Q001. Its purpose is to filter out parts that pass standard specification limits but fall outside the normal distribution of the population, thereby reducing early-life failures (infant mortality) in the field.

In the Wafer screen's PAT Data mode, DLOG computes and displays PAT limits (PAT LL / HL) for the selected test. When you enable PAT+ in the view settings, dies that passed test specs but are flagged as suspicious by DPAT or SPAT rules are highlighted as an overlay on the wafer map. The original test PASS/FAIL verdict is preserved.

PAT+ suspicious dies highlighted on wafer map

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Figure 2-1. Wafer screen PAT Data mode + PAT+ — The left PAT Data card displays Median, PAT LL, and PAT HL. The PAT+ Reject card shows DPAT range, SPAT settings (3x3 ×6.0), and PAT+ Flips. Suspicious dies are circled on the map.

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Figure 2-2. Tools > Studies > Yield Loss vs Quality Risk — Sweep sigma multipliers from 3 to 15 to compare yield loss against specification margin-based quality risk (DPPM) and discover recommended sigma cutoffs.

DPAT: Robust Dynamic Limits Recomputed from Data

To prevent extreme outliers from biasing the sample mean and standard deviation, DLOG uses the median instead of the mean, and a robust sigma estimated from the interquartile range (IQR):

$$\sigma_{\text{robust}} = \frac{Q_3 - Q_1}{1.35}$$ $$\text{PAT LL} = \tilde{x} - k_L \cdot \sigma_{\text{robust}}, \qquad \text{PAT HL} = \tilde{x} + k_H \cdot \sigma_{\text{robust}}$$

Dies lying outside this range are flagged as outlier candidates. The default sigma multiplier k is 6. You can configure upper and lower multipliers independently via View settings > Wafer View Options > Lower Sigma (L) / Upper Sigma (H). Smaller values of k capture more candidates.

DPAT (Dynamic PAT) dynamically re-evaluates these limits per wafer, per site, or per lot baseline rather than using static limits. Site-specific DPAT eliminates tester hardware offsets, while lot-baseline DPAT tracks inter-wafer thermal and process drift. In the Chart screen's Trend view, you can overlay the same dynamic limits using the DPAT (trend) option.

SPAT: Spatial Neighbor Residuals

Localized anomalies—such as edge clusters, scratches, or pinpoint defect clusters—may blend into the broader wafer distribution and go unnoticed without spatial context. SPAT (Spatial PAT) evaluates the residual between target die $(i, j)$ and the median of neighboring PASS dies against the neighborhood robust sigma:

$$\Delta_{\text{spatial}}(i, j) = \left| x_{i, j} - \operatorname{median}\left(\mathcal{N}(i, j)\right) \right| > k_{\text{spat}} \cdot \sigma_{\text{robust}}\left(\mathcal{N}(i, j)\right)$$

The default spatial kernel is $3 \times 3$ with a multiplier of 6.0. Near wafer boundaries or dense defect regions where valid PASS neighbors are scarce, DLOG automatically expands the kernel outward by up to 2 concentric rings until the minimum neighbor threshold is satisfied.

Choosing PAT Sigma: Yield Loss vs Quality Risk

Tightening k catches more questionable dies, but increases overkill (yield loss) by sacrificing good silicon. Tools > Studies > Yield Loss vs Quality Risk sweeps sigma values across tests to plot Reject Candidates, Yield Loss, and DPPM curves, recommending an optimal sigma balance to meet your target DPPM. Click Apply Sigma to immediately apply it.

Note on DPPM: DPPM here is not an empirically verified field escape rate; it is a risk proxy calculated from the margin between PAT limits and specification limits. Do not use it as a contractual guarantee of field reliability. You can also export a 1-page-per-test PDF report via PAT (PDF).

GDBN (Good Die in Bad Neighborhood): A rule that downgrades good dies adjacent to major defect clusters. Enabled under Convert > BIN Reclassification (PAT / GDBN / CD), it searches for defect clusters (8-way connected) exceeding your threshold size and reassigns nearby PASS dies within the designated radius to a defect BIN before writing a new converted STDF file.

Multivariate Outlier Detection

3. MVA Explorer (Multivariate Outliers)

Related parametric tests tend to vary together. A die might look perfectly normal when evaluating Test A and Test B individually, but if Test A is unusually high while Test B is unusually low, the pairing breaks normal physical correlation. While it passes individual scalar limits, it is an obvious multivariate outlier. The MVA Explorer detects these multi-dimensional anomalies.

MVA Explorer: Outlier results table and contribution breakdown

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Figure 3. MVA Explorer — Example using 15 tests with Mahalanobis Distance (MD²) at a 3.0σ threshold. The summary cards display Scored, Outliers, Threshold, and PASS part counts. Selecting a part (#0160) displays its Outlier Contribution Breakdown, highlighting the tests driving the anomaly along with their robust z-scores.

Three Outlier Detection Algorithms

Algorithm	How It Detects Outliers	Best Used When
Mahalanobis (MD²)	Statistical distance taking full covariance into account. Flags parts exceeding chi-square distribution thresholds.	Recommended general-purpose default
PCA reconstruction (SPE)	Flags parts with high reconstruction error (Q-statistic) when projected onto principal components. Captures breakdowns in normal correlation patterns.	Recommended for large test suites
Isolation Forest	Tree-based partition algorithm with no parametric distribution assumptions. Identifies easily isolatable parts, ranking the top ~1% of PASS parts as outliers.	Captures non-linear, complex multi-modal anomalies

Mahalanobis Distance (MD²)

Euclidean distance fails to account for scale differences and correlation among parameters. Mahalanobis distance resolves this by weighting deviations with the inverse of the covariance matrix ($\mathbf{\Sigma}$). DLOG computes a robust centroid and shrinkage covariance matrix, decomposing each test's contribution as $z_i \cdot (\mathbf{\Sigma}^{-1}\mathbf{z})_i$ such that the sum equals $MD^2$:

$$MD^2(\mathbf{x}) = (\mathbf{x} - \boldsymbol{\mu})^T \mathbf{\Sigma}^{-1} (\mathbf{x} - \boldsymbol{\mu})$$ $$\text{Outlier Rule}: MD^2(\mathbf{x}) > \chi^2_{r}(1 - \alpha), \qquad \alpha = 2\,(1 - \Phi(\sigma_{\text{setting}}))$$

The Threshold (Sigma) setting (3.0 / 4.0 / 5.0 / 6.0σ, default 6.0σ) is converted to a two-sided normal probability $\alpha$, which sets the critical chi-square threshold for $r$ degrees of freedom (number of selected tests). Higher sigma settings yield fewer, more severe outliers. For PCA, SPE (Squared Prediction Error, Q-statistic) scores parts based on residual variance unexplained by the principal components.

Reading the Results Table

Column	Meaning
Status	`OUTLIER` · `NORMAL` · `NOT SCORED` (missing test values among selected tests) · `EXCLUDED` (non-PASS parts)
Score	Outlier score from the selected algorithm (MD², SPE, or Isolation Forest score)
Risk	Score ÷ Threshold. Exceeding 1.0x classifies the part as an OUTLIER
Top contributor	Parametric test driving the score highest, along with its robust z-score (based on median and MAD)

Training Requirements: The baseline model is trained exclusively on complete PASS parts containing valid values for all selected tests. The sample size must be at least max(50, 5 × number of tests) (e.g., in Figure 3, 15 tests require at least 75 parts). Select physically correlated parametric tests; including unrelated tests dilutes anomaly scores. In the Wafer screen's MVA-PAT mode, you can inspect spatial scores by die coordinate and export parts flipped from PASS to MVA Outliers (MVA Flips) to CSV.

Measurement System Analysis

4. Gauge R&R Measurement System Analysis

Observed measurement variance consists of actual product variation combined with fluctuation introduced by the test system (tester instrumentation, probe card, socket contact, interface hardware):

$$\sigma_{\text{Total}}^2 = \sigma_{\text{PV}}^2 + \sigma_{\text{GRR}}^2 = \sigma_{\text{PV}}^2 + \sigma_{\text{EV}}^2 + \sigma_{\text{AV}}^2$$

Excessive measurement noise risks falsely rejecting good product or shipping defective units. The Gauge R&R screen decomposes this total variance using repeated test runs of the same wafer. By matching dies on (X, Y) coordinates, DLOG treats repeat runs as valid trials even if Lot or Wafer IDs differ between files.

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Figure 4. Gauge R&R Summary — Example with 3 repeat runs of the same wafer. Summary cards display items studied, median %repeat, median %P/T, and good / marginal / poor tallies. Below, the table lists PARTS, TRIALS, %REPEAT, %P/T, ndc, and RESULT for each test. Double-clicking a row opens Detail view showing EV, AV, and PV variance components.

Prerequisites: Requires at least 2 STDF files measuring the same wafer 2 or more times (load repeat files using Append...). Datalogs without die coordinates (such as final packaged test data) cannot be aligned.

Variance Components and Methods

Component	Description
EV (Repeatability) Equipment Variation	Fluctuation when measuring the same part repeatedly under identical conditions (tester baseline noise).
AV (Reproducibility) Appraiser Variation	Variation across different operators, files, or test sites (socket contact variation, thermal shifts).
GRR	$\sqrt{EV^2 + AV^2}$ — Total variation introduced by the measurement system.
PV	True part-to-part manufacturing variation across the wafer.

DLOG supports two computation methods: ANOVA (default, estimates variance components from Mean Squares) and Average-Range (classical AIAG worksheet method utilizing range and $d_2$ factors). ANOVA provides superior stability for large sample sizes. Two analysis modes are available: Repeatability Only (single site, AV is omitted) and Cross-Site (evaluates test sites as appraisers when all sites measure every die).

%GRR Criteria and ndc

$$\%GRR = \frac{GRR}{TV} \times 100\%, \qquad \%P/T = \frac{6 \cdot GRR}{\text{USL} - \text{LSL}} \times 100\%, \qquad ndc = 1.41 \times \frac{PV}{GRR}$$

%GRR	Verdict	Interpretation
< 10%	good	Measurement system is capable. If ndc ≥ 5, resolution is also sufficient.
10% to 30%	marginal	May be acceptable based on application importance, component cost, or repair expense.
> 30%	poor	Measurement error dominates decisions. Inspect probe contact, socket wear, and DIB noise.

The automatic verdict (RESULT) is governed by %GRR (against total variation); also check %P/T (against tolerance width) (reported as N/A if specs are single-sided). ndc must be ≥ 5 for adequate discrimination; ndc < 2 cannot distinguish product parts. Tests with identical values across all parts cannot be evaluated. Save complete tables via Export CSV.

Multi-Site Variation

5. Multi-Site Hardware Delta Analysis

In multi-site parallel testing, disparities in probe needle scrub, socket contact resistance, or relay pin wear frequently cause one specific site to systematically drift. The SITE screen compares yield, BIN composition, and parameter averages across sites to instantly identify hardware outliers.

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Figure 5. SITE screen PASS / FAIL tab — Summary cards (OVERALL YIELD, BEST SITE, WORST SITE, SITE SPREAD) and per-site yield bars. The tick mark on each bar indicates lot average yield, with the right number showing delta (e.g., Site 3 is -1.6%p).

Check Item	Screen	How to Inspect
Low yield site	SITE > PASS / FAIL	Shortest bar; highlighted in the WORST SITE card.
Defect concentration	SITE > BIN	Examine if specific Fail BINs concentrate on a single site.
Parametric shift	SITE > TEST DATA	Check site-specific PASS die mean deviation against overall mean (Δ vs overall).
Site-dominant tests	SITE > TEST MATRIX	η² (proportion of total variance explained by site differences). Below 5% indicates minimal site impact, displayed as `-`.
Statistical significance	Group Analysis (Group by: Site)	One-way ANOVA p-value and Tukey HSD pairwise contrasts.
Site reproducibility	Gauge R&R (Cross-Site)	Treat sites as appraisers when measuring identical dies to evaluate AV.

Site number 255 in STDF conventions typically represents the aggregate "ALL SITES" summary. Choose how to handle Site 255 records under Main Option > SITE 255 on part records (Auto / All Site / Physical site).

Process Capability

6. Cpk · Cp · Est ppm · Normality

Process capability indices quantify how well parameter distributions fit within specification limits (LL/HL). DLOG displays Cpk and Cp in the Chart screen's Test Item Statistics, the Tests (Cpk) sidebar list, and the Dashboard capability summary.

$$C_p = \frac{\text{USL} - \text{LSL}}{6\sigma}, \qquad C_{pk} = \min\left(\frac{\text{USL} - \mu}{3\sigma}, \; \frac{\mu - \text{LSL}}{3\sigma}\right)$$ $$\text{Est ppm} = \left[\Phi\!\left(\frac{\text{LSL} - \mu}{\sigma}\right) + 1 - \Phi\!\left(\frac{\text{USL} - \mu}{\sigma}\right)\right] \times 10^6$$

Here, $\mu$ and $\sigma$ represent sample mean and sample standard deviation within the currently selected scope. Est ppm represents the theoretical bilateral tail probability assuming a normal distribution. For single-sided limits, only the applicable tail is evaluated. In Dashboard capability grading, Cpk is categorized by default as Critical (< 1.00), Marginal (1.00 to 1.33), and Good (≥ 1.33), configurable in settings.

Cpk	Sigma Level	Normal Tail Defect Rate	Industrial Context
`1.00`	$3\sigma$	Approx. 2,700 ppm	Mean centered, 3σ margin to specification limits
`1.33`	$4\sigma$	Approx. 63 ppm	Standard industrial manufacturing acceptance benchmark
`1.50`	$4.5\sigma$	Approx. 6.8 ppm	Target for controlled high-yield lines
`1.67`	$5\sigma$	Approx. 0.57 ppm	Demanded in automotive and mission-critical semiconductors
`2.00`	$6\sigma$	Approx. 0.002 ppm	Six Sigma zero-defect objective

Values in the table are theoretical figures assuming centered data and perfect Gaussian normality. Follow customer contracts and formal product specifications for binding acceptance criteria.

Normality Testing and CDF / Probability Plots

Cpk and Est ppm are only trustworthy when the data genuinely follows a Gaussian normal distribution. DLOG computes the tail-sensitive Anderson-Darling test p-value, presented as Normality (AD). A value of p < 0.05 indicates significant departure from normality.

CDF / Probability: Empirical cumulative distribution versus theoretical normal curve

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Figure 6. CDF / Probability — Significant divergence between the empirical cumulative distribution (blue line) and the theoretical normal curve (gray dashed line) warns against uncritical reliance on Cpk. A heavy right tail signals that true out-of-spec parts far exceed Gaussian predictions.

Example from Figure 1 (IDDQ_STANDBY): Cpk displays 0.749 with Est ppm 12,602 (~1.3%), but the empirical out-of-spec count is 18 of 591 parts (~3.0%), and Normality (AD) p-value is effectively 0. Due to a pronounced right skew, the Gaussian assumption severely underestimates actual defect rates. For skewed parameters, consult quantile-based charts (Box Plot, CDF / Probability) and check Group Analysis > Distribution Fit (which fits Normal, Lognormal, and Weibull distributions ranked by Anderson-Darling scores) to review non-normal warnings.

Correlation, ANOVA & Test Time

7. Correlation Analysis · ANOVA · TTO

Root causes in semiconductor test often manifest not in a single parameter, but through interactions between multiple tests or across distinct operating groups (site, temperature, lot, test file). The Correlation screen evaluates how parameters move together, while Group Analysis verifies whether between-group differences are statistically significant.

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Figure 7-1. Correlation — Matrix heatmap (red/pink = positive correlation, blue = negative correlation), scatter plot for two selected tests (with regression line, r, and R²), and Top correlations ranking.

Group Analysis box plot and ANOVA results

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Figure 7-2. Group Analysis — Box plots across sites and bottom One-way ANOVA summary bar (Groups, N, Eta², F, Tukey HSD, p-value).

Pearson and Spearman Correlation

$$r_{xy} = \frac{\sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^N (x_i - \bar{x})^2} \sqrt{\sum_{i=1}^N (y_i - \bar{y})^2}}$$

Pearson correlation measures linear relationship strength, whereas rank-based Spearman correlation is robust against outliers and captures non-linear monotonic relationships. The Cluster sort orders strongly correlated tests adjacent to each other to expose structural blocks. Setting Parameters to Auto automatically isolates tests exhibiting strong correlation (|r| ≥ 0.70).

Redundant Tests and TTO: Test pairs with |r| ≥ 0.95 often measure the exact same physical property and are highlighted as Redundant Candidates. The TTO Engine (Test Time Optimization) groups collinear tests (|r| ≥ 0.95), selects the single test catching the most defect units per group, and suggests Drop Candidates to shorten test times. If the table's Only Drop Fails metric is greater than 0, dropping that test would allow defective parts to escape; review design specs and customer requirements before making final changes.

One-way ANOVA (Analysis of Variance)

Group Analysis segments test results by Site, File, Corner, Temp, Process, Node, Program-Rev, or Product to determine whether group means differ significantly:

$$F = \frac{MS_{\text{Between}}}{MS_{\text{Within}}} = \frac{\sum_{j=1}^k n_j (\bar{x}_j - \bar{x})^2 / (k - 1)}{\sum_{j=1}^k \sum_{i=1}^{n_j} (x_{ij} - \bar{x}_j)^2 / (N - k)}, \qquad \eta^2 = \frac{SS_{\text{Between}}}{SS_{\text{Total}}}$$

p-value < 0.05: Assuming group means are identical, the probability of observing current differences purely by chance is less than 5%. Conclude that at least one group mean differs significantly.
Eta² (η²): Proportion of total variance explained by group classification. Near 0 indicates negligible group effect; 0.40 means 40% of parameter variation originates from group differences.
Tukey HSD: Evaluates pairwise group contrasts to report the exact number of differing pairs (e.g., "0 of 6 pairs differ").

The example in Figure 7-2 displays Eta² 0.001 and p-value 0.6772, confirming no significant site variation. The green status pill No difference provides instant confirmation.

Practical Field Guide

8. Process Drift vs. Measurement Noise

When Cpk drops or yield falls, fab teams tend to suspect test hardware, while test teams suspect front-end wafer fabrication. By combining DLOG's analytical screens, you can distinguish root causes with empirical data.

Inspection Area	Fab / Process Root Cause	Tester / Measurement Root Cause
Spatial Pattern (Wafer > Signature)	Concentric rings, wafer edge falloff, center hot spots, local clusters	Low yield with near-zero cluster score (random), shot-pitch or site periodicity
Site Delta (SITE, Group Analysis)	Uniform distribution across all test sites	Single site offset, significant One-way ANOVA p-value
Measurement System (Gauge R&R)	Low %GRR, Part Variation (PV) dominates	High %GRR, Equipment (EV) or Appraiser (AV) variation dominates
Time Series Trend (Chart > Trend)	Stepwise shift aligned with wafer or lot boundaries	Continuous drift across test order, sudden shift after probe card/socket service
Corrective Action	Inspect fab equipment and recipes (litho, etch, CMP, deposition)	Clean or replace probe card / socket, verify docking, inspect DIB grounding

Setting PAT Sigma: During early production ramps with limited sample size, begin with generous k multipliers. Use Yield Loss vs Quality Risk to balance overkill against risk metrics, gradually tightening limits as volume grows. Once sufficient baseline data is collected, compare DPAT vs lot baseline alongside per-wafer DPAT.

FAQ & Report Export

9. Frequently Asked Questions & Reports

Frequently Asked Questions (FAQ)

Q1. Why do customers report field returns (RMAs) even when Cpk is high?
Cpk evaluates a single parameter assuming a standard Gaussian distribution. Non-normal distributions (bimodal distributions, heavy tails) or multi-test combinations that pass scalar limits but break physical correlations cannot be caught by Cpk alone. Combine PAT+ (DPAT · SPAT) and MVA (MVA Explorer, Wafer MVA-PAT) to catch subtle outlier escapes.

Q2. My Gauge R&R reports %GRR at 35%. Should I investigate EV or AV first?
Inspect the variance components under Gauge R&R Detail. If EV dominates, focus on tester noise, grounding, power supply ripple, and shielding. If AV dominates, investigate file or site differences (socket wear, docking alignment, calibration).

Q3. What datalog files are required to run Gauge R&R?
You need at least 2 STDF files from repeat test runs of the exact same wafer, containing die (X, Y) coordinates. Load retest files using Append.... Packaged final test data without coordinate records cannot be aligned.

Q4. Can I export analysis tables to Excel or formal engineering reports?
Yes. Click Export CSV in any screen to save tabular data. Use Export > Save Report to generate formal PDF, Excel (.xlsx), Word (.docx), or image reports. Export 1-page-per-test PAT limit charts via PAT (PDF).

Report Features: To learn how to generate customer-ready documentation with statistical charts, summary tables, and wafer maps, visit our Report Guide Page →.

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PAT+ outlier screening, MVA explorer, Gauge R&R, multi-site variance, and Cpk capability statistics.
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