Control
4 tools in the Quality area.
SPC and Capability
Shewhart control charts and process capability from pasted measurements: X̄–R, X̄–s and I–MR charts for variables, p, np, c and u charts for attributes, with the control-chart constants and every limit's formula written out with the substituted numbers; out-of-control signals by the Western Electric or Nelson run rules; a one-pass Phase I revision that drops the flagged subgroups and recomputes the limits; and the capability study, Cp, Cpk, Cpm, Pp and Ppk with the expected and observed fraction out of specification, Z-bench and the sigma level with and without the 1.5σ shift. An optional crossed gauge R&R study (ANOVA method, AIAG MSA) reports the variance components, %Contribution, %Study Variation, %Tolerance and the number of distinct categories. The default case is the hard-bake flow-width example of Montgomery (Table 6.1), whose printed limits the page reproduces.
4 worked examples reproduced, listed on the tool page.
Acceptance Sampling
Attribute acceptance sampling by lot: the operating characteristic curve of a single plan (n, c) by the exact binomial, the Poisson approximation and the hypergeometric form for a finite lot, the producer's and consumer's risks at the AQL and the LTPD, the average outgoing quality curve with its limit (AOQL) and the average total inspection under rectifying inspection; a double plan (n1, c1, r1, n2, c2) with its OC, ASN and ATI curves; the design of a single plan from AQL, α, LTPD and β by exact binomial search and by Cameron's Poisson ratio table; and the ANSI/ASQ Z1.4 (MIL-STD-105E) lookup: lot size and inspection level to the sample size code letter, AQL and severity to n, Ac and Re from the normal, tightened and reduced master tables with the arrows followed, the double plan of Table III-A, and the OC of the plan found. The default case is Montgomery's n = 89, c = 2 plan (Chapter 15) for a lot of 2,000 at an AQL of 1 % and an LTPD of 6 %, with the Z1.4 lookup of the same lot (code letter K, n = 125, Ac 3, Re 4).
4 worked examples reproduced, listed on the tool page.
Dimensional Capability
Capability study of a whole drawing or first-article lot, every characteristic at once: paste one block per characteristic (number, name, nominal, lower and upper tolerance, type) with its measurements, or a wide table of parts against characteristics. For each characteristic the page gives n, mean, within and overall standard deviation, Cp, Cpk, Cpm (target = nominal), Pp, Ppk, the lower confidence bound on Cpk (Bissell 1990), expected and observed parts per million, the percent of tolerance used, the mean offset, a Shapiro–Wilk normality note and the verdict against the Cpk target with the AIAG PPAP bands. A true-position characteristic takes x y deviation pairs: the diametral deviation per part, the bivariate-normal yield inside the zone (quadrature, non-central χ² and the Rayleigh closed form), the equivalent Cpk from the yield (Bothe's convention), MMC bonus per part and a scatter inside the zone. The characteristics are ranked by Cpk, the assembly yield is the product of the per-characteristic yields and the table is laid out in the AS9102 Form 3 order. The default case is an illustrative six-characteristic machined part; Montgomery's flow-width data (Table 6.1, Cp = 1.192) are selectable as a check.
1 worked example reproduced, listed on the tool page.
Variables Sampling (Z1.9)
Acceptance sampling by variables after MIL-STD-414 (1957) and its descendant ANSI/ASQ Z1.9, variability unknown, standard deviation method (Section B): the sample size code letter from the lot size and inspection level (Table A-2), the sample size with the acceptability constant k (Form 1, Tables B-1 and B-2) and the maximum allowable percent defective M (Form 2, Tables B-3 and B-4) for normal, tightened and reduced inspection with the table arrows followed; the sample mean and standard deviation laid out as the standard's examples do, the quality indices Q_U = (U − x̄)/s and Q_L = (x̄ − L)/s, the estimated lot percent defective of Table B-5 computed exactly by the Lieberman–Resnikoff minimum-variance unbiased estimator (the regularised incomplete beta function), the Form 1 and Form 2 acceptability decisions for an upper, a lower or both specification limits (one AQL combined or separate AQLs), the exact operating characteristic curve of the plan by the noncentral t distribution with the AQL and LTPD points, the Z1.4 attributes plan of the same lot and AQL for comparison, the AOQL under rectifying inspection, a plan designed from two OC points, and the switching rules of Section B Part III. The default case is Example B-3 of the standard: a lot of 40 at inspection level IV, AQL 1 %, limits 180 and 209 °F, measurements 197, 188, 184, 205 and 201 (code letter D, n = 5, M = 3.32 %, p = 2.19 + 0.66 = 2.85 %, lot accepted).
1 worked example reproduced, listed on the tool page.
Other Quality sections
Measurement · Design of Experiments · Improvement · Inspection and Metrology