Statistical Analysis
Professional tools for capability, measurement systems, and quality control
Learn about this toolThe Sampling calculator uses simplified assumptions that may not be suitable for all applications. Sample sizes should be validated against your specific regulatory requirements and statistical methods.
The GR&R calculator follows standard MSA methodology but has not been independently validated. Results should be verified by your quality team.
Capability indices (Cp, Cpk) follow standard formulas but assume normal distribution. Verify distribution assumptions before use.
Learn about Statistics Suite
7 sections including 4 FAQs
Learn about Statistics Suite
7 sections including 4 FAQs
The Statistics Suite provides professional statistical analysis tools for packaging and quality engineers. It includes four analysis types: Descriptive Statistics for summarizing data sets, Process Capability (Cp/Cpk/Pp/Ppk) for evaluating manufacturing consistency, Gage R&R for assessing measurement system reliability, and Sampling Plan generation based on AQL/LTPD requirements. All calculations follow industry-standard formulas used in SPC (Statistical Process Control) programs.
How it works
Process Capability Analysis
Capability indices measure how well a process meets specification limits. Cp compares the specification width to the process spread: Cp = (USL - LSL) / (6σ). Cpk accounts for process centering: Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]. A Cpk of 1.33 or higher is generally considered capable. The suite also calculates Pp/Ppk (using overall standard deviation) for long-term performance assessment.
Gage R&R (Measurement System Analysis)
Gage R&R partitions measurement variation into Repeatability (within-operator variation) and Reproducibility (between-operator variation). The study calculates %GRR — the percentage of total variation attributable to the measurement system. Industry guidelines: %GRR under 10% is acceptable, 10-30% may be acceptable depending on application, and over 30% indicates the measurement system needs improvement.
Sampling Plans
The sampling plan generator creates attribute sampling plans based on your AQL (Acceptable Quality Level), lot size, and inspection level. Plans follow the methodology of ANSI/ASQ Z1.4 (formerly MIL-STD-105E), specifying sample size and accept/reject numbers. The tool can also generate plans based on LTPD (Lot Tolerance Percent Defective) for consumer-risk-focused applications.
Example: Cpk from 25 Seal-Strength Measurements
You measure peel seal strength on 25 pouches. Spec limits: LSL = 1.5 lbf/in, USL = 4.0 lbf/in. Data yields: mean (x̄) = 2.8 lbf/in, standard deviation (s) = 0.35 lbf/in.
Cp = (USL − LSL) / (6s) = (4.0 − 1.5) / (6 × 0.35) = 2.5 / 2.1 = 1.19.
Cpk = min[(4.0 − 2.8) / (3 × 0.35), (2.8 − 1.5) / (3 × 0.35)] = min[1.14, 1.24] = 1.14.
Cpk of 1.14 is below the 1.33 target — the process is marginally capable. The lower Cpk toward USL suggests the process mean should be shifted slightly lower, or variation reduced.
When to use this tool
- Evaluating whether a packaging line is capable of consistently meeting dimensional specifications
- Conducting measurement system analysis before a capability study to ensure measurement variation is acceptable
- Generating receiving inspection sampling plans based on AQL requirements from customer specifications
- Summarizing test data from compression, burst, or adhesion testing with statistical rigor
- Producing capability reports (Cp/Cpk Sixpack) for customer quality submissions
Common mistakes to avoid
- Running capability analysis on non-normal data without transformation — Cp/Cpk assume normality. Check the histogram and normality statistics first
- Confusing Cp with Cpk — Cp measures potential capability (if the process were centered), while Cpk measures actual capability accounting for process centering
- Using too few samples for capability — a minimum of 30 data points is recommended, with 50+ preferred for reliable Cpk estimates
- Setting AQL too tight for sampling plans — an AQL of 0.1% with small lot sizes may require 100% inspection, defeating the purpose of sampling
- Ignoring between-subgroup variation — Cp/Cpk use within-subgroup sigma, which may underestimate true process variation. Compare with Pp/Ppk
Frequently asked questions
What Cpk value is considered acceptable?
A Cpk of 1.33 (equivalent to 4-sigma capability) is the general industry minimum. Many automotive and aerospace specifications require Cpk of 1.67 or higher. A Cpk of 1.0 means the process just barely fits within the spec limits with no margin — about 0.27% of output will be out of spec. For packaging applications, Cpk targets between 1.33 and 1.67 are most common.
What is the difference between Cp/Cpk and Pp/Ppk?
Cp/Cpk use the within-subgroup standard deviation (short-term variation) and represent the process capability if only common-cause variation is present. Pp/Ppk use the overall standard deviation (including between-subgroup variation) and represent actual long-term performance. If Cpk is significantly higher than Ppk, it indicates the process has assignable causes of variation that shift the mean between subgroups.
How many parts should I measure for a Gage R&R study?
A standard Gage R&R study uses 10 parts, 3 operators, and 2-3 trials per operator. The parts should be selected to represent the full range of normal production variation. Using fewer parts (e.g., 5) reduces the study sensitivity, while using more operators improves the reproducibility estimate. The AIAG MSA manual recommends the 10-part, 3-operator, 3-trial design.
What AQL should I use for packaging inspection?
Common AQL values for packaging: 1.0% for minor defects (cosmetic issues, minor print defects), 0.65% for major defects (dimensional out-of-spec, seal integrity), and 0.1% for critical defects (contamination, safety issues). Your customer specification typically dictates the AQL. When no customer spec exists, AQL 1.0 with General Inspection Level II is a common starting point.