How to run a panel 01 Pick a panel from the tab bar or open its URL: /math/statpro/power, /math/statpro/spc, /math/statpro/scale or /math/statpro/reliability. 02 Power & Sample Size: choose a test and solve for power, N or the minimum detectable effect; set α, tails, effect size and any correction. The cards report power, N (split into n₁/n₂), effective α, critical value, df and noncentrality. 03 SPC Control Charts: paste subgroups, choose the chart and σ estimator, and toggle the Nelson rules. Each chart reports CL, UCL and LCL and lists flagged points by rule; the Capability view adds Cp, Cpk, Cpm, Pp, Ppk and PPM for your LSL/USL. 04 Scale Reliability: paste a respondents × items matrix for α, split-half and ICC, paired ratings for Cohen's κ, or rater-by-category counts for Fleiss κ. 05 Reliability Engineering: paste lifetimes (S marks a censored unit), choose distribution, rank method and confidence, then read the RRY, RRX and MLE fits; the System view covers series, parallel, k-out-of-n and bridge structures, availability and redundancy. Worked readouts Every figure below comes from the default inputs; the same entries reproduce them.
Panel
Input
Readout
Power
Two-sample t, solve N, d = 0.5, α = 0.05, 80% power
Two-tailed: N = 128 (64 + 64), power 80.15% , critical value 1.979 , df 126 , noncentrality 2.8284 . One-tailed: N = 101 (51 + 50), power 80.24%
SPC
5 subgroups × 5 values, X̄-R, R̄/d₂
σ̂ = 1.71974 ; X̄: CL 11 , UCL 13.3073 , LCL 8.69272 ; R: CL 4 , UCL 8.45809 , LCL 0
Scale
6 respondents × 4 items
α = 0.9419 , standardized α 0.9436 , 95% CI 0.6268 … 0.9838 , ICC(3,k) 0.9419
Reliability
6 failure times, Weibull
RRY: MTTF 69.3818 , B10 15.7721 ; MLE: MTTF 65.2114 , B10 22.9487
The power figures follow the noncentral t distribution: with 64 units per arm the test rejects at |t| > 1.979 in 80.15% of replications. The SPC run sits in control, but the panel warns that five subgroups make the limits uncertain.
Assumptions and limits
Answers inherit the design and the data. Power uses the effect size you enter; limits assume consecutive subgroups from a stable process; α, ICC and κ need complete matrices; life fits assume independent units and correct suspension marks. Small samples are flagged: five subgroups make the SPC limits uncertain, and n = 25 leaves Cpk's interval at 0.371 … 0.792 . What it does not do: it is not a general statistics package — no tests from raw sample columns, regression models or survey weights. Use Statistics for summaries and hypothesis tests from data, Verify to check a reported number independently, and the scientific calculator for one-off expression work. The two sigmas behind Cp and Pp The signature trap is that the same 25 observations carry two standard deviations. The X̄-R chart derives its limits from within-subgroup variation, σ̂ = R̄/d₂ = 1.71974 ; the capability view also reports the overall standard deviation of all 25 values, 1.58114 . Cp and Cpk use the within σ (0.5815 ), Pp and Ppk the overall σ (0.6325 ), so the long-term pair reads better here; expected PPM diverges the same way: 81,081 within versus 57,780 overall. The σ estimator is itself a choice: on unchanged data the X̄ upper limit moves from 13.3073 (R̄/d₂) to 13.2568 (s̄/c₄) to 13.148 (pooled s). Record which estimator produced the limits.
Where it fits Planning a study A two-sample t test at d = 0.5, α = 0.05 and 80% power needs N = 128 ; one-tailed it needs 101 ; Bonferroni across two comparisons raises the effective α to 0.025 and N to 155 . The A/B view adds a two-proportion z test and a Beta–binomial posterior.
Watching a production line X̄-R or I-MR charts separate special from common causes; the Capability view compares the process to specification, where the default data gives expected 81,081 PPM within, 57,780 overall and 0 observed. The Pareto view ranks defect categories.
Checking a questionnaire or rating scheme α arrives with its confidence interval, standardized α, Guttman λ₂ and item-rest correlations. The same matrix yields ICC(3,k) 0.9419 and ICC(2,1) 0.7849 , showing how much the answer depends on whether raters are treated as fixed or random; Cohen κ covers two raters, Fleiss κ many.
Setting a reliability target Three units at R = 0.9 in a 2-out-of-3 layout give 0.972000 ; MTBF 1000 h with MTTR 10 h gives availability 0.990099 , about 86.7 h of downtime per year; one-of-three redundancy at 0.8 per unit reaches 0.992000 .
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References
NIST/SEMATECH, e-Handbook of Statistical Methods , §6.1.6 What is Process Capability?, itl.nist.gov （访问日期：2026-10-01）— Cp, Cpk, Cpm and capability sample-size guidance.
NIST/SEMATECH, e-Handbook of Statistical Methods , §6.3.1 What are Control Charts?, itl.nist.gov （访问日期：2026-10-01）— 3σ control limits and the risks they carry.
Wikipedia, Cronbach's alpha , en.wikipedia.org （访问日期：2026-10-01）— coefficient α and its assumptions.
Wikipedia, Intraclass correlation , en.wikipedia.org （访问日期：2026-10-01）— one-way and two-way ICC forms.
Wikipedia, Weibull distribution , en.wikipedia.org （访问日期：2026-10-01）— shape and scale parameters, hazard reading.
G*Power, psychologie.hhu.de （访问日期：2026-10-01）— noncentral-distribution power analysis (Faul et al., 2007).
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Updated 2026-10-01