Data Input
Paste your measurement data. Rows = Subgroups. Columns = Measurements. Decimals can be dots or commas.
Specification Limits
Control Charts (X-Bar & R)
Evaluated with standard Nelson Rules for out-of-control signals to distinguish normal variation from special causes.
Limits for \(\bar{X}\): \(\quad UCL_{\bar{X}} = \bar{\bar{X}} + A_2 \bar{R} \quad\) and \(\quad LCL_{\bar{X}} = \bar{\bar{X}} - A_2 \bar{R}\)
Limits for Range (\(R\)): \(\quad UCL_R = D_4 \bar{R} \quad\) and \(\quad LCL_R = D_3 \bar{R}\)
\(A_2\), \(D_3\), \(D_4\) are sample size dependent constants.
The blue dots on the X-Bar chart represent the average (mean) of each subgroup, not individual parts. For example, if you have 6 subgroups of 3 parts (18 parts total), you will only see 6 blue action points. We have overlayed your raw data as faint grey dots in the background so you can see the complete spread!
X-Bar Chart (Means)
R Chart (Ranges)
Nelson Rules Evaluation
Process Capability Indices
Cp/Cpk (Short-term capability) and Pp/Ppk (Long-term capability). Ensures your process fits within the specs.
\(C_p = \frac{\mathit{USL} - \mathit{LSL}}{6\sigma_{within}} \quad \text{(Potential Capability)}\)
\(C_{pk} = \min\left(\frac{\mathit{USL} - \mu}{3\sigma_{within}}, \frac{\mu - \mathit{LSL}}{3\sigma_{within}}\right) \quad \text{(Actual Performance)}\)
In the automotive industry, process capability is often evaluated against strict thresholds for special characteristics:
- SC (Significant Characteristic) - Target >= 1.33: Characteristics that are important for customer satisfaction.
- CC (Critical Characteristic) - Target >= 1.67: Characteristics critical for safety or regulatory compliance.
Cp/Pp measure "Potential" – they assume the mean is perfectly centered. They only look at the spread.
Cpk/Ppk measure "Actual" – they penalize you if the process is off-center. Cpk can never be > Cp. If Cpk < Cp, you just need to center your process towards the nominal target.
Cp/Cpk (Short-term) are computed using \(\sigma_{within}\) (calculated from the Ranges `R-bar` of subgroups). Represents variation inside a specific moment, ignoring long-term shifts (tool wear, temps).
Pp/Ppk (Long-term) use \(\sigma_{overall}\) (the classical standard deviation `s` of all data). Represents the total true variation the customer receives over time.
Yes! All data points across all subgroups are mathematically combined to evaluate process capability as one holistic distribution. Cpk evaluates the entire process, not just a single sample draw.
Distribution Analysis
Histogram of all individual values with normal distribution overlay.
Normal Distribution (PDF): \(f(x) = \frac{1}{\sigma_{overall}\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma_{overall}}\right)^2}\)
Skewness (Fisher-Pearson): \(G_1 = \frac{n}{(n-1)(n-2)} \sum \left(\frac{x_i - \bar{x}}{s}\right)^3\)
Measurement System Analysis (Gage R&R)
1. Parts: Select around 10 parts covering the typical process tolerance spread.
2. Appraisers: Select 2-3 operators who routinely measure these parts.
3. Trials: Each operator measures every part 2-3 times blindly (without knowing the part).
Hypothesis Tests (1-Sample T-Test)
Statistically compare your process mean against the Target/Nominal value.
1) Choose your data source (Use current / Paste / Manual).
2) Enter the Target (μ₀) and choose the hypothesis type.
3) Click Run. Read p‑value + CI + charts to interpret the result.
Uses the measurements from Module 1 (Data Entry). This is recommended so you don’t enter data twice.
\(t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}\), \(df = n-1\)
\(CI: \bar{x} \pm t_{1-\alpha/2, df} \cdot \frac{s}{\sqrt{n}}\)
Effect size (Cohen’s d): \(d = \frac{\bar{x} - \mu_0}{s}\)
Pareto Analysis
Identify the vital few defects that cause the majority of problems using the 80/20 rule.
The Pareto Principle (80/20 rule) states that roughly 80% of effects come from 20% of causes.
In quality management: a small number of defect types (“Vital Few”) typically cause the majority of all defects.
When to use: After collecting defect data, use Pareto Analysis to prioritize which defect types to tackle first for maximum impact.
Enter defect data: one defect per line, format: DefectName, Count
The Pareto Principle (Vilfredo Pareto, 1896): ~80% of effects come from ~20% of causes.
Individual %: \(\text{Pct}_i = \frac{\text{Count}_i}{\sum \text{Count}} \times 100\)
Cumulative %: \(\text{CumPct}_i = \sum_{j=1}^{i} \text{Pct}_j\)
Vital Few = categories where Cum% ≤ 80%. Trivial Many = the rest.
Report Export
Generate a professional multi-page PDF report. Select modules, add project info, and export.
1. Fill in project info (optional).
2. Select modules — green dot = has data.
3. Click Export PDF for a multi-page report.
Tip: Calculate all modules before exporting.
Project Information
Select Modules to Include
Management Dashboard
At-a-glance overview of all analysis results with actionable recommendations.
This dashboard aggregates results from all modules. Run your analyses first, then come here for a summary. The recommendation engine prioritizes actions based on industry best practices.
Correlation & Regression
Analyze the relationship between two variables with scatter plot, correlation coefficient, and linear regression.
Enter X and Y values (same number of data points). The tool calculates Pearson correlation, fits a linear regression line, and tests significance. Use this to validate cause-effect relationships (e.g. temperature vs. dimension).
Session History
Save and load sessions. Export as files for backup or sharing.
Save: Enter a name and click Save (localStorage).
Load: Click Load to restore.
Export: Download as .json for backup/sharing.
Import: Load a .json file back.
Browser storage is local — use Export for permanent backups!
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