Home / Statistical Tools / Analysis Tools / Cpkhistogram / Options
Options¶
Worked examples
The How-To pages build this chart step by step from sample data, one walkthrough per data layout the tool accepts. Start there if you would rather see a finished result than read the settings.
The Cpk/Histogram dialog has three tabs: Data for data selection and specification limits, Capability Options for statistical settings, and Display Options for chart display, distribution fitting, and binning.
Data Tab¶
- Specification Limits: a grid with one row per data column, with LSL, Target, and USL entries. Any of the three may be left blank; capability indices that need a missing limit are simply not reported.
- Overlay Datasets on a Single Chart: when multiple data columns are selected, combines them on one shared histogram grid so the distributions can be compared directly. See Plot Order for controlling the draw order.
Capability Options¶
This tab controls how the capability numbers are produced: which standard defines Cpk and Ppk, whether the data is transformed first, whether known process values replace the estimated ones, how the within standard deviation is estimated, and which normality test is run.
Process Capability Standard¶
Controls which standard deviation component the Cpk and Ppk labels use.
| Standard | Description |
|---|---|
| AIAG | Industry standard. Cpk is based on the within-subgroup StDev, Ppk on the overall StDev. Both are displayed. This is the default. |
| Boeing D1-9000 | Cpk is based on the overall StDev. No separate Ppk is displayed. |
| Custom | Full control: Cpk based on and Ppk based on each choose among Within, Overall, Between, and Within & Between. |
Sigma tolerance is the spread value used inside the Cpk/Ppk confidence interval formula. It is locked at 6 under AIAG and Boeing D1-9000 and editable only under Custom.
Transformations¶
Apply a data transformation before calculating capability indices. Useful when your data is not normally distributed.
| Option | Description |
|---|---|
| None | Use raw data as-is (default) |
| Johnson | Applies an automatic Johnson transformation (SL, SB, or SU family selected based on data shape) |
| Box-Cox | Applies a power transformation. Lambda is calculated automatically for optimal normality, or you can enter a custom lambda value between -5 and 5. Requires positive data values. |
A transformation cannot be combined with a non-normal fit distribution or with historical values. The exact transformation formulas are on Math Details.
Historical Values¶
Optionally enter known process values instead of estimating them from the data:
- Mean: Override the estimated mean
- Standard deviation (overall): Override the overall standard deviation
- Standard deviation (within): Override the within-subgroup standard deviation
Leave blank to use the values estimated from your data. Historical values cannot be combined with a transformation. When a historical mean is entered, the Cpk/Ppk confidence interval is not reported.
Estimate Sigma¶
Controls how the within standard deviation is estimated. The available methods depend on whether your data is in subgroups.
For individual observations (no subgroups):
| Method | Description |
|---|---|
| Average moving range | The average of the moving ranges, divided by the constant d2 (default) |
| Median moving range | The median of the moving ranges, divided by the constant d4; more robust to occasional large shifts |
| Square root of MSSD | The square root of half the mean squared successive difference; useful when the data has a trend |
- Moving range length: how many consecutive observations form each moving range. Default 2, allowed 2 to 100.
- Use Nelson moving-range correction: iteratively removes unusually large moving ranges before averaging. Available only with the average moving range method.
For subgrouped data:
| Method | Description |
|---|---|
| Rbar (average range) | Combines the subgroup ranges, each divided by d2 (default) |
| Sbar (average standard deviation) | Combines the subgroup standard deviations, each divided by c4 |
| Pooled standard deviation | Pools the squared deviations from all subgroups |
The exact estimator formulas are on Process Sigma Estimation.
Unbiasing Constants¶
Two independent checkboxes:
- Use unbiased constants (within sigma): applies the bias correction to the Sbar, pooled, and square root of MSSD estimates. Checked by default. It has no effect on Rbar and the moving range methods, which always apply their d2/d4 constants, so it is disabled for those.
- Use unbiased constants (overall sigma): divides the overall standard deviation by c4(N). Unchecked by default.
Confidence Intervals¶
- Show Confidence Interval: Toggle display of confidence intervals for capability indices
- Mode: Two-Sided (default), Lower Bound only, or Upper Bound only
- Confidence Level: Enter as a decimal between 0 and 1 (default 0.95 for a 95% confidence interval)
Confidence intervals are calculated for Cp, Cpk, Pp, and Ppk, plus a one-sided lower bound for Cpm when a target is given. The formulas are on Math Details. Intervals are not available for non-normal capability, and the Cpk/Ppk interval is not reported when a historical mean is entered.
Goodness of Fit¶
Tests whether your data follows a normal distribution. Select one test or None.
| Test | Description |
|---|---|
| Anderson-Darling | Emphasizes the tails of the distribution. Reports A² statistic and p-value. Default. |
| Shapiro-Wilk | Best for small to moderate sample sizes. Reports W statistic and p-value. |
| Kolmogorov-Smirnov | Uses Lilliefors correction. Reports D statistic and p-value. |
| None | Skip normality testing. |
Display Options¶
This tab controls what is drawn: the bars and curves themselves, which distribution is fitted to each column, how the bins are formed, how capability is computed when the fit is not normal, and the draw order of overlaid series.
Display Settings¶
- Display histogram bars: When checked, shows the histogram bars representing the frequency distribution. Enabled by default.
- Display PDF curve: When checked, overlays probability density function curves on the histogram. Which curves appear follows the Process Capability Standard: AIAG shows a within-subgroup StDev curve and an overall StDev curve, Boeing D1-9000 shows only the overall curve, and Custom shows a curve for each StDev component chosen in the Cpk/Ppk definitions. Enabled by default.
Distribution Fitting¶
Each data column has a Fit Type dropdown in the Chart Settings grid. Normal is the default; choosing another distribution draws that fitted curve instead of the normal curves and switches capability to the non-normal method below.
Selectable fit types:
| Distribution | Description |
|---|---|
| Normal | Standard bell curve (default) |
| Lognormal | For right-skewed positive data |
| 3-Parameter Lognormal | Lognormal with location parameter |
| Exponential | For time-to-event data |
| 2-Parameter Exponential | Exponential with location parameter |
| Weibull | Flexible shape for reliability data |
| 3-Parameter Weibull | Weibull with location parameter |
| Logistic | Similar to normal but heavier tails |
| Log-Logistic | For right-skewed data with heavy tails |
| 3-Parameter Log-Logistic | Log-Logistic with location parameter |
| Smallest Extreme Value | For minimum values (Gumbel form) |
The Distribution Fit Statistics table compares 14 distributions: the 11 selectable types above plus Largest Extreme Value, Gamma, and 3-Parameter Gamma, which appear in the comparison but cannot currently be chosen as the fitted distribution. For each, the table shows p-value, AICc, BIC, and -2ln(L). Lower AICc/BIC values and higher p-values indicate better fit.
Histogram¶
The Histogram group holds two display checkboxes and three bin settings. The same group appears on the Capability tab of the Xbar-R, Xbar-S, I-MR and I-MR-R/S control charts, so it is described here once.
- Display histogram bars: draws the bars themselves.
- Display PDF curve: draws the fitted probability density curve over them.
Each of the three bin settings is a pair of radio buttons, Auto and Manual:, with a text box that is used only under Manual:.
- Anchor: the value the bins are aligned to, which fixes where the first bin edge falls.
- Bin count: how many bins the range is divided into.
- Bin width: how wide each bin is.
Bin count and Bin width are mutually exclusive, because between them they would describe the same histogram twice. Setting either one to Manual: puts the other back to Auto for you, with no message. A manual bin count is a whole number from 1 to 250, and a manual bin width must be at least 0.001.
Non-Normal Capability Method¶
Controls how capability indices are calculated when a non-normal distribution is fitted. Only enabled when a non-normal distribution is selected in Distribution Fitting.
| Method | Description |
|---|---|
| Percentile | Uses the fitted distribution's percentiles to calculate capability (default) |
| Z-Score | Uses z-score transformation based on the fitted distribution |
Plot Order¶
Controls the draw order (Z-order) of overlaid data series when multiple data columns are combined into a single chart. Series earlier in the list are drawn first, and later series are drawn on top of them.
Use the ^ and v buttons to reorder the series. This is useful when overlaid histogram bars obscure each other: reorder so the smaller series is drawn on top and all data is visible.
Only available when multiple data columns are selected and combined into a single chart.
After Creation: the Analysis Pane¶
When the analysis finishes, a "Capability Analysis" task pane opens automatically, docked on the right. The Analysis Pane ribbon button toggles it whenever a Capability sheet is active. Changes apply to the analysis immediately. The pane offers:
- Spec Limits: an editable row per data column with LSL, Target, and USL
- Transformation: None, Use Johnson Transformation (when available), or Use Box-Cox Transformation with Use Optimal Lambda or Custom lambda
- Historical Values: Mean, Std dev (overall), Std dev (within) (disabled while a transformation is active)
- Goodness of Fit: None, Anderson-Darling, Shapiro-Wilk, or Kolmogorov-Smirnov
- Confidence Intervals: Show confidence intervals, plus Confidence level and Two-sided / Lower bound / Upper bound
- Display: Show histogram bars, Show PDF curve
These mirror the dialog options above; see each section for what the setting does.