Skip to main content
Advantive

Process Capability Formulas Reference

Target Z, Zupper, and Zlower formulas

Target Z

Zupper

Zlower

Where:

= the mean of the X-bars
T = specification target
Sigma is an estimated sigma or sigma of the individual values, depending on how the histogram
is configured or whether you are calculating Cpk (estimated) or Ppk (actual).

Additional reference material

Additional sections from legacy actual-percent-f:

Actual percent out-of-spec formulas

Actual % out-of-spec = % above upper spec + % below lower spec

To find actual % above spec:

To find actual % below spec:

Related topic:
The formula for theoretical percent out of spec

Additional sections from legacy theoretical-f:

Theoretical percent out-of-spec formulas

To find theoretical % above spec:

Locate the value for Zupper in a standard normal table.

To find theoretical % below spec:

Locate the value for Zlower in a standard normal table.

Given:

And assuming:

In theory:

If the Z value from the standard normal table is multiplied by 100, then this process is expected to produce X% of its output outside specification.

Show me:
The standard normal table
The formulas for Target Z

Related topic:
The formula for actual percent out of spec

Reviewed by

Quality & SPC review panel

Articles on statistical process control, capability indices, control charts, and quality management are reviewed by the product teams behind InfinityQS, WinSPC, and PQ Systems (SQCpack and GAGEpack) — the SPC and quality platforms deployed across food, automotive, pharma, and CPG manufacturers.

Customers using Advantive in quality advisor

“Enact helps us quickly respond to quality issues, which saves us money.”
Jegadish Gunasagaran Quality Assurance Manager, Bakery on Main
““What sets Ben & Jerry’s apart from our competitors is not only our insistence on high-quality ingredients, but also the extra and unique flavours we use to create a euphoric customer experience. Ensuring the final product reflects the passion and quality that we put into each pint required a quality solution that emphasized the same attention to details that we do.””
Melissa Corcia, Quality Manager, Ben & Jerry’s
““By utilizing InfinityQS® ProFicient™ to implement SPC and Six Sigma best practices across our manufacturing processes, Ben & Jerry’s will continue to identify opportunities for cost savings and ensure the highest level of customer satisfaction. The result is the perfect pint for our customers.””
Nina King, Quality Supervisor, Ben & Jerry’s

Editorial standards

Fact-checking & editorial guidelines

Every article on advantive.com is written and reviewed against an internal accuracy standard before publication. Here's what that means in practice.

  • Product claims are verified by the brand team that owns the platform.

    When an article references InfinityQS, WinSPC, PQ Systems, Pinpoint, ParityFactory, ProPlanner, KiwiPlan, DDI System, VeraCore, or any of Advantive's other specialty platforms, the relevant product team checks technical statements about features, deployment, and current capability before the article goes live.

  • External statistics cite their source inline.

    When an article references industry survey results, regulatory benchmarks, or third-party research, the source is linked at the point of citation. Statements without an inline source link are first-party observations drawn from Advantive's product teams or customer base.

  • Publication and revision dates stay visible.

    The original publication date and the most recent revision date are both shown on every article. Topics that change quickly — AI capabilities, regulatory rules, product roadmaps — are revisited on a tighter cadence than evergreen reference content.

  • Corrections are issued openly.

    If a factual error is reported, the article is updated, the revision date advances, and material corrections are noted at the bottom of the article so readers can see what changed and when.

Found something wrong, or have a citation to add? Get in touch with the editorial team and we'll review it.

Subject-matter review

Reviewed by subject-matter experts

Advantive is a portfolio of 14+ specialty software platforms — each one built and maintained by a product team that has spent years inside a specific manufacturing or distribution discipline. Articles in technical channels are reviewed by the relevant team before publication.

  • Quality & SPC content

    Reviewed by the InfinityQS, WinSPC, and PQ Systems product teams — the platforms behind statistical process control, capability analysis, and gage management deployments across food, automotive, pharma, and CPG manufacturers.

  • Manufacturing operations & MES content

    Reviewed by the PINpoint, ProPlanner, ParityFactory, and VIA Information Tools teams, whose platforms run production scheduling, traceability, and shop-floor execution for discrete, automotive, and food-and-beverage manufacturers.

  • Packaging & converter content

    Reviewed by the KiwiPlan, Abaca, and AdvantZware teams, who build software specifically for corrugated, folding-carton, and packaging-converter operations.

  • Distribution, ERP & B2B commerce content

    Reviewed by the DDI System (inFORM ERP), Distribution One, VeraCore, Pepperi, and Commerce Vision teams, whose platforms run wholesale ERP, fulfillment, field sales, and B2B portals for specialty distributors and 3PLs.

Are you a practitioner with domain expertise to contribute? Get in touch — we accept guest contributions from operators in the industries we serve.