Acceptance Sampling

1 Introduksi

1.1 Latar Belakang

Acceptance sampling adalah pendekatan statistical lot decision: bukan inspect 100% (mahal + destructive untuk pangan), tetapi sampel acak $n$ unit, lalu accept/reject lot berdasarkan hasil sampel (Dodge & Romig, 1959; Montgomery, 2020). Standar industri global: ANSI/ASQ Z1.4 (attribute, defect count), ISO 2859-1 (international equivalent), dan MIL-STD-105E (legacy US).

Setiap sampling plan didefinisikan oleh ($n$, $c$): sample size $n$ + maximum acceptable defects $c$. Plan dievaluasi via Operating Characteristic (OC) curve — probabilitas accept lot vs actual defect rate $p$. Acceptable Quality Level (AQL) = $p$ producer-friendly (mis. 1.0%), Lot Tolerance Percent Defective (LTPD) = $p$ consumer-protective (mis. 10%).

1.2 Tujuan Modul

Modul Acceptance Sampling di SQalytics ditujukan untuk:

Menerima inputs: lot size $N$, AQL, LTPD, $\alpha$ (producer risk), $\beta$ (consumer risk).
Memberikan sampling plan ($n$, $c$) dari ANSI/ASQ Z1.4 tables atau custom binomial calculation.
Menggambar OC curve untuk plan visualisasi.
Menjalankan lot decision dari actual count.
Audiens: QC industri, supplier audit, receiving inspection.

1.3 Posisi di Antara Alternatif

Pilih Acceptance Sampling untuk lot release/reject decision. Untuk continuous process monitoring, pakai SPC Xbar / R Charts. Untuk capability assessment, pakai Cp / Cpk Capability. Untuk HACCP safety decision, pakai HACCP Decision Tree.

2 Metode

2.1 Dasar Teoretis

Operating Characteristic (OC) function untuk single sampling plan ($n$, $c$) dengan defect rate $p$:

$$P_a(p) = \sum_{k=0}^{c} \binom{n}{k} p^k (1-p)^{n-k}$$

$P_a$ = probability accept lot. Plot $P_a$ vs $p$ memberikan OC curve — descending sigmoid dari $P_a \approx 1$ (high quality lot) ke $P_a \approx 0$ (poor quality).

Producer's risk $\alpha$ = $1 - P_a(\text{AQL})$ — probability reject good lot (defect rate at AQL).

Consumer's risk $\beta$ = $P_a(\text{LTPD})$ — probability accept bad lot (at LTPD).

Plan design — minimize $n$ subject to $\alpha \leq 0.05$ at AQL and $\beta \leq 0.10$ at LTPD:

$$\frac{n p_{\text{LTPD}}}{n p_{\text{AQL}}} = \frac{\chi^2_{1-\beta,\, 2(c+1)}}{\chi^2_{\alpha,\, 2(c+1)}}$$

(Dodge & Romig solution, iterative search atau tabel ANSI Z1.4).

ANSI/ASQ Z1.4 sampling levels:

Level I (relaxed, smaller $n$): kualitas history baik.
Level II (normal, default): standard.
Level III (tightened, larger $n$): kualitas history poor.

Lot size → code letter → sample size $n$ dari tabel:

Lot size $N$	Code (Level II)	$n$
91–150	F	20
151–280	G	32
281–500	H	50
501–1,200	J	80
1,201–3,200	K	125
3,201–10,000	L	200
10,001–35,000	M	315

AQL → acceptance number $c$:

AQL (%)	$c$ for $n = 80$
0.10	0
0.40	1
1.0	2
2.5	5
6.5	14

2.2 Persamaan Inti

OC function: $P_a(p) = \sum_{k=0}^{c} \binom{n}{k} p^k (1-p)^{n-k}$
Producer's risk $\alpha$: $1 - P_a(\text{AQL})$
Consumer's risk $\beta$: $P_a(\text{LTPD})$
Lot decision: accept bila defects observed $\leq c$; reject bila $> c$.

2.3 Asumsi & Batas Validitas

Asumsi	Konsekuensi jika dilanggar	Cara cek di SQalytics
Random sampling dari lot	Bias decision	SOP random select
Lot homogeneous	Misclassification	Stratified sampling
$n \ll N$ untuk binomial valid	Hypergeometric correction	Modul auto-detect
AQL + LTPD ratio appropriate	Plan oversized atau weak	Ratio LTPD/AQL ≈ 5–10×
Independent defects	Cluster bias	Multi-stage sampling

3 Cara Kerja

3.1 Step-by-Step di SQalytics

Buka Acceptance Sampling dari domain Mutu dan Analisis Lanjutan.
Input parameters: Lot size $N$, AQL (%), LTPD (%), $\alpha$ (default 0.05), $\beta$ (default 0.10), Inspection level (I/II/III).
Klik Design Plan — modul output ($n$, $c$) dari ANSI Z1.4 table.
Tinjau OC curve untuk visualisasi risks.
Setelah eksekusi inspection, input observed defects dalam $n$ samples.
Klik Lot Decision — modul output accept/reject.

3.2 Template Input + Contoh

Setup untuk receiving inspection finished biskuit batch:

Parameter	Value
Lot size $N$	5,000 unit
AQL	1.0% (defect = broken biskuit)
LTPD	6.5%
Inspection level	II (normal)
$\alpha$	0.05
$\beta$	0.10

SYNTHETIC Receiving inspection scenario: finished biskuit batch 5,000 unit. AQL 1.0% (acceptable quality), LTPD 6.5% (unacceptable quality). ANSI Z1.4 Level II Code L → $n = 200$, $c = 5$. Lot decision: 4 broken found → ACCEPT. CSV setara: docs/assets/example-data/id/quality-advanced/template_quality_acceptance.csv.

3.3 Contoh Luaran

Sampling plan (dari ANSI Z1.4 Level II Code L untuk $N$ 5,000):

Parameter	Value
Sample size $n$	200
Acceptance number $c$	5
Rejection number $r$	6

OC curve key points:

Defect rate $p$	$P_a$
0.5%	0.98
1.0% (AQL)	0.95 ✓ (close to $1 - \alpha$)
2.0%	0.78
3.0%	0.46
6.5% (LTPD)	0.10 ✓ ($\beta$ target)
10%	0.02

Producer's risk $\alpha = 0.05$; Consumer's risk $\beta = 0.10$. Both meet target.

Lot decision example: Inspeksi 200 biskuit, ditemukan 4 broken. Karena $4 \leq c = 5$ → ACCEPT lot.

Acceptance Sampling — figure 01 — Gambar 1. *Panel* (a) OC curve ($P_a$ vs $p$) untuk plan $n=200$, $c=5$; *panel* (b) accept/reject risk summary dengan AQL dan LTPD flagged.

Kesimpulan ringkas: "Sampling plan ANSI Z1.4 Level II untuk lot 5,000 biskuit dengan AQL 1%: $n = 200$, $c = 5$. Producer's risk 5% (akan reject 5% lot baik dengan defect rate exactly 1%). Consumer's risk 10% (akan accept 10% lot buruk dengan defect rate 6.5%). Observed 4 broken di sample 200 ≤ $c$ = 5 → ACCEPT lot. OC curve menunjukkan plan tegas: defect rate 3% sudah punya $P_a$ < 0.5 (likely reject). Recommendation untuk supplier: maintain defect rate < 1% untuk minimize rejection. Lanjut ke Cp / Cpk Capability untuk uji apakah supplier process capable terhadap broken defect spec."

4 Kesimpulan

4.1 Relevansi Real-World

Supplier receiving inspection — material incoming lot decision.
Finished product release — final lot decision sebelum shipping.
Returned goods evaluation — accept/reject decision.
Contract quality — AQL formal di Purchase Order.
Audit verification — internal vs external audit consistency.

4.2 Where to Go from Here

SPC Xbar / R Charts — preventive monitoring during production.
Cp / Cpk Capability — verify process capable terhadap AQL.
HACCP Decision Tree — safety-critical decision logic.
ANSI/ASQ Z1.4-2018 untuk tabel lengkap.

⚙ Troubleshooting Cepat

OC curve terlalu steep. Plan ekonomis tetapi rejecting border-OK lots; consider double sampling.

OC curve terlalu shallow. Plan lemah; consider tightened inspection.

Defects clustered di sample. Lot non-uniform; pakai stratified sampling.

i Riwayat Revisi

Tanggal	Revisi	Penulis
2026-05-12	Draft v2 publikasi (KaTeX OC curve + ANSI Z1.4 + producer/consumer risk + APA Dodge-Romig/Montgomery)	Claude
2026-05-12	Konversi MD → HTML (W5 quality-advanced batch)	Claude

4 Referensi

Dodge, H. F., & Romig, H. G. (1959). Sampling inspection tables: Single and double sampling (2nd ed.). John Wiley & Sons.
American Society for Quality. (2018). ANSI/ASQ Z1.4-2018: Sampling procedures and tables for inspection by attributes. ASQ.
International Organization for Standardization. (1999). ISO 2859-1: Sampling procedures for inspection by attributes. ISO.
Montgomery, D. C. (2020). Introduction to statistical quality control (8th ed.). John Wiley & Sons.
Schilling, E. G., & Neubauer, D. V. (2017). Acceptance sampling in quality control (3rd ed.). CRC Press.