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MIL-STD-414 Example B-3: double specification limit, variability unknown, standard deviation method (lot of 40, level IV, AQL 1 %)

Tool	Variables Sampling (Z1.9)
Source	U.S. Department of Defense (1957). Sampling Procedures and Tables for Inspection by Variables for Percent Defective. MIL-STD-414, 11 June 1957. Section B Examples B-1 to B-4, Tables A-2, B-1, B-3 and B-5.
Level	Professional

Problem

The operating temperature of a device must lie between 180 and 209 °F. A lot of 40 is submitted at inspection level IV, normal inspection, AQL 1 % for both limits combined. Five units measure 197, 188, 184, 205 and 201 °F. Find the sampling plan, the sample mean and standard deviation, the quality indices, the estimated percent defective beyond each limit from Table B-5 and decide whether the lot meets the acceptability criterion (Form 2); also the single-limit decisions of Examples B-1 (Form 1) and B-2 (Form 2) on the upper limit alone.

Inputs to Enter

Lot size 40, inspection level IV, AQL 1.00, normal inspection, LTPD 10 % (for the OC reading)
Limits: both, U = 209, L = 180; criterion Form 2; measurements 197 188 184 205 201 (default values)
Z1.4 comparison on; design from two points off

Open the Variables Sampling (Z1.9) tool (loaded with this example)

Answers

Table A-2: code letter D; Table B-1 / B-3: n = 5, k = 1.53, M = 3.32 %
ΣX = 975, ΣX² = 190,435, CF = 190,125, SS = 310, V = 77.5, s = 8.81, x̄ = 195
Q_U = (209 − 195)/8.81 = 1.59, Q_L = (195 − 180)/8.81 = 1.70
Table B-5 (Lieberman–Resnikoff estimate, computed): p_U = 2.19 %, p_L = 0.66 %, p = 2.85 % < M = 3.32 %: the lot meets the acceptability criterion (tool at full precision of s: 2.18 + 0.62 = 2.80 %, same decision)
Example B-1 (upper limit, Form 1): 1.59 > k = 1.53, accepted; Example B-4 (AQL 2.5 % on the lower limit): M_L = 9.80 %, criteria (a) (b) (c) met
OC of the plan (n 5, k 1.53): Pa(1 %) = 0.898, Pa(10 %) = 0.422; Z1.4 level II plan for the lot: code letter C, n = 13, Ac 0 (sample-size ratio 2.6)

Notes

The tool's default inputs are this example; press Submit. Table B-5 is not transcribed: the page computes the estimate exactly and the standard's printed readings (2.19 %, 0.66 %) are reproduced when the table is entered with Q rounded to two decimals as the standard does. Switch the Limits select to 'Upper limit U only' for Examples B-1 and B-2, and set the lower-limit AQL to 2.50 for Example B-4.