Quality Control Edition

Process capability analysis with confidence intervals and non-normal handling Cp, Cpk, Pp, Ppk, Cpm, Z-benchmark, and sigma level — all with confidence intervals. Box-Cox and power transformations for non-normal data. Control charts in the same package to confirm stability first.

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Microsoft Excel with the Analyse-it tab selected, showing a process capability report for copper concentration: the histogram with the lower and upper specification limits and a normal curve, the normal Q-Q plot beneath, and the Process Control task pane open on the Capability section with the specification limits. Handwritten notes: Runs inside Excel: every analysis is on the Analyse-it tab; Control charts and capability: two groups on the tab; Histogram with the LSL and USL; Normal Q-Q plot; Specification limits, typed in; The report is an ordinary Excel worksheet: share it, archive it, open it on any PC with Excel.

Capability indices that mean what they say

Excel has no capability analysis. Cp and Cpk come from formulas typed by hand, with no confidence interval, no check that the process is stable and no check that the data are normal. A capability index calculated from an unstable process is a meaningless number. An index calculated from non-normal data is a misleading number. Both mistakes are common, and they happen more easily when control charts and capability analysis live in separate tools.

Is the process stable enough for an index to mean anything? Are the data normal, or do they need a transformation first? Can the process meet the specification, and how much of what it delivered actually fell outside it? What sigma level does that correspond to?

Capability indices Cp, Cpl, Cpu, Cpk and Cpm with confidence intervals

A capability index says whether the process can meet the specification when it runs in control. Cp, Cpl, Cpu, Cpk and Cpm are calculated from within-subgroup variation, so they reflect what the process can deliver rather than what it happened to deliver. A Cpk of 1.33 means the nearest specification limit is four standard deviations from the process mean; below 1.0 the process is not capable. All are reported with confidence intervals.

  • Cp, Cpl, Cpu, Cpk
  • Cpm
  • All with confidence intervals

Performance indices Pp, Ppl, Ppu and Ppk with confidence intervals

Capability and delivered performance are different questions, and the gap between them is informative. Pp, Ppl, Ppu and Ppk are calculated from total process variation, so they reflect what the process actually delivered over time. A process with a good Cpk but a poor Ppk has capability that is not being realised, which points to special-cause variation that needs investigation. All are reported with confidence intervals.

  • Pp, Ppl, Ppu, Ppk
  • All with confidence intervals
Microsoft Excel showing the Capability section of a process capability report: specification limits 7 to 11, mean and long-term sigma, the Pp, Ppl, Ppu and Ppk indices with 95% confidence intervals, observed and expected nonconforming units in PPM, and the Z benchmark table. Handwritten notes: Pp, Ppl, Ppu and Ppk with 95% CIs; Expected nonconforming units, PPM; Z-benchmark.
The Capability section for copper concentration in a plating pool: Pp, Ppl, Ppu and Ppk with 95% confidence intervals, the nonconforming unit estimates and the Z-benchmark beneath.

Z-benchmark, sigma level and nonconforming units in PPM

An index alone does not say how many units will fail. Nonconforming unit estimation gives the observed percentage, the expected percentage and the expected parts per million outside each specification limit. The practical impact on yield is quantified rather than implied. Z-benchmark, short-term and long-term, and sigma level are calculated directly from the data for Six Sigma programmes.

  • Z-benchmark (short-term and long-term)
  • Sigma level
  • Nonconforming units — observed %, expected %, expected PPM

Histogram, normal Q-Q plot with Lilliefors band and Box-Cox transformation

Indices calculated from non-normal data are misleading, and non-normal data are common in real production. A histogram with the specification limits and a normal Q-Q plot with Lilliefors confidence band are included with every analysis. The distribution is assessed before the indices are read. Where the data are non-normal, Box-Cox and other power transformations bring the distribution into a form where the indices remain valid. The Q-Q plot of the transformed data confirms the transformation worked before you report the result.

  • Histogram with specification limits
  • Normal Q-Q plot with Lilliefors confidence band
  • Box-Cox and other power transformations
Microsoft Excel showing the Normality section of a process capability report: the normal Q-Q plot, the Shapiro-Wilk test with W 0.96 and p 0.0009 and its rejected-normality footnote, and the Capability section beneath, with the task pane open on Normality. Handwritten notes: Normal Q-Q plot; Shapiro-Wilk test and its p-value; Normality test, chosen here.
The normal Q-Q plot and Shapiro-Wilk test for the copper data: p = 0.0009, so the indices beneath should not be read until the distribution is dealt with.

Shewhart control charts with WECO, Nelson and Montgomery rules

A capability index from an unstable process is a meaningless number, so stability comes first. Shewhart variable and attribute control charts with WECO, Nelson and Montgomery detection rules are in the same package. Run the control chart, confirm stability, then assess capability in the same workbook — no data transferred to a separate tool.

  • Shewhart variable and attribute control charts
  • WECO, Nelson and Montgomery detection rules
Microsoft Excel showing the Control section of a process control report for copper: the Xbar chart and R chart with 3-sigma limits, the Montgomery rules line, and the task pane open on Control Chart (Shewhart) with the rule set table. Handwritten notes: Xbar chart with 3-sigma limits; R chart; Rules applied, and any signals; Rule set: WECO, Nelson or Montgomery.
The Xbar and R charts that open the same report: Montgomery rules applied to Xbar, the process in control before capability is assessed.

Example analyses

See capability output in detail — histogram with specification limits, capability and performance indices with confidence intervals, Q-Q plot, and nonconforming unit estimation.

Capability Example 1 Process capability
Copper concentration against a 7 to 11 ppm specification. An Xbar-R chart with Montgomery rules to confirm the process is in control, then a histogram with the specification limits, box plot, Q-Q plot and Shapiro-Wilk test, Pp, Ppl, Ppu and Ppk with 95% CIs, expected nonconforming units at 216 PPM, and Z benchmarks.

Part of the Quality Control & Improvement edition

Capability analysis is one part of the complete SPC and improvement toolkit. The Quality Control & Improvement edition also includes Shewhart, CUSUM, and EWMA control charts with detection rules, phases, and stratification, and Pareto analysis for identifying the vital few defect categories, plus the full Standard edition with hypothesis tests, ANOVA, and regression. See everything in the Quality Control & Improvement edition →

Related guides in our Learn section: Cp, Cpk, Pp and Ppk explained, capability for non-normal data, and sigma level and PPM from capability.

Validated, reliable, trusted for nearly 30 years

Validated calculations Every statistic tested against published datasets and thousands of internal test-cases. No reliance on Excel’s built-in functions — Analyse-it handles all calculations internally. See how we develop and validate Analyse-it →
Data stays on your PC No cloud processing, no uploads, no third-party access. Your data never leaves your computer — essential when working with proprietary process data, customer specifications, or regulated production records.
Standard Excel workbooks Charts and results are ordinary Excel workbooks. Share with colleagues, send to auditors or customers, archive for quality records — no Analyse-it licence required to view.
No formulas to break Results contain no formulas, so they cannot be accidentally edited or corrupted. The control chart you reported will be exactly what you find when you reopen the workbook.

Free trial and pricing

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Quality Control & Improvement edition from US$ 290 per year, or US$ 760 for a perpetual licence. Every purchase carries a 30-day money-back guarantee. Need a quote for purchasing? Add the licence to the cart and save it as a PDF quote.