Thinning — modified reliability calculator

Modified reliability methodology (paper §4.1.3–4.1.4): your equipment data → A_rt (Eq. 2) → FS → SR_p → β → Bayes-updated D_fB → D_f,thin → P_f. All damage factors are calculated from Eqs. (2.13)–(2.20).

Metal loss = a × r

Reliability calc only — A_rt → FS → SR_p → β → D_f,thin → P_f

Equipment data & assumptions (steps 1–11)

Item

Reference

Data

UnitsEntry and displaymetric (US in brackets)

Meaning: Enter all data in metric in the Data column (unit label beside each field). Imperial equivalents appear in brackets on hints and calculated outputs only.

Typical: mm (in), mm/yr (mpy), MPa (ksi), MPa (psi) for pressure, yr for age, dimensionless for E and COV.

All entries metric — US in brackets on results

1 — Calculation of A_rt

Eq. (2): max[1−(t_rdi−C_r,bm×age)/(t_min+CA), 0] — paper worked example

1t_rdiReference thickness1–100 mm (0.04–4 in)

Meaning: Furnished or last-known wall thickness — denominator in A_rt = (a×r)/t, Eq. (2.12).

Typical: 3–25 mm (0.12–1 in) shells; large vessels to ~50 mm. Range 1–100 mm (0.04–4 in).

1C_r,bmBase corrosion rate0–3 mm/yr (0–120 mpy)

Meaning: Base-metal corrosion rate r. Enter mm/yr in Data; mpy shown in brackets on hints and outputs.

Typical: 0.05–0.25 mm/yr (2–10 mpy) active corrosion; 0–0.13 mm/yr when inhibited. Range 0–3 mm/yr (0–120 mpy).

mm/yr

1ageTime in service0–50 yr

Meaning: Years in service used as a in Eq. (2.12) (time × rate → metal loss).

Typical: 5–30 yr at assessment; new equipment 0–2 yr. Range 0–50 yr.

1t_minMinimum thickness1–80 mm (0.04–3 in)

Meaning: Code or FFS minimum/retirement thickness for design-based strength ratio, Eq. (2.14).

Typical: Often 60–85% of original t; examples ~9–13 mm. Range 1–80 mm (0.04–3 in). If t_c is entered, conversion line under Data shows max(t_min, t_c).

1CACorrosion allowance0–10 mm (0–0.4 in)

Meaning: In denominator of A_rt with t_min (paper Eq. 2). Enter actual CA — not assumed 25% of t.

Typical: 1.5–6 mm (1/16–1/4 in) per design. Range 0–10 mm (0–0.4 in).

2 — Calculation of flow stress

FS_Thin = (YS+TS)/2 × 1.1 × E

2YSYield strength200–550 MPa (30–80 ksi)

Meaning: Yield strength at assessment temperature; with TS and E forms flow stress FS_Thin, Eq. (2.13).

Typical: Carbon steel 205–345 MPa (30–50 ksi). Range 200–550 MPa (30–80 ksi).

MPa

2TSTensile strength350–700 MPa (50–100 ksi)

Meaning: Tensile strength at temperature; averaged with YS for FS_Thin, Eq. (2.13).

Typical: ~1.2–1.5× YS; carbon steel 380–550 MPa. Range 350–700 MPa (50–100 ksi).

MPa

2EJoint efficiency0.6–1.0

Meaning: Weld joint efficiency in FS_Thin and design SR_p path.

Typical: 1.0 seamless; 0.85–1.0 welded per code. Range 0.6–1.0.

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3 — Strength ratio calculation

Eq. (2.14) and Eq. (2.15)

3SAllowable stressfor Eq. (2.14)

Meaning: Code allowable stress at temperature for Eq. (2.14) design ratio.

Typical: From ASME/API tables at T; often 100–200 MPa (15–30 ksi) carbon steel.

MPa

3PPressure0–20 MPa (0–3000 psi)

Meaning: Internal design/operating pressure for hoop-stress SR_p, Eq. (2.15).

Typical: 0.3–4 MPa (50–600 psi) process vessels; up to ~20 MPa. Range 0–20 MPa (0–3000 psi).

MPa

3DInside diameter25–3000 mm (1–120 in)

Meaning: Inside diameter for hoop-stress geometry in Eq. (2.15).

Typical: 300–3000 mm (12–120 in) vessels; piping from ~25 mm. Range 25–3000 mm (1–120 in).

3Shape αGeometry factor1.13–4

Meaning: Shape factor α in P·D/(α·FS·t) — cylinder, sphere, or head.

Typical: Cylinder α=2; sphere α=4; formed head α=1.13. Range 1.13–4.

3SR_p methodEq. 2.14 / 2.15—

Meaning: Which strength-ratio equation(s) govern SR_p,Thin (design vs hoop stress).

Typical: Max both shows both results and uses the higher for β. Use 2.14 or 2.15 only only when you deliberately exclude the other limit state.

3t_cStructural minimum (opt.)—

Meaning: Optional structural minimum; Eq. (2.14) uses max(t_min, t_c) when entered.

Typical: Leave blank if not in FFS. When entered, appears under t_min Data as t_c … mm (…) in the max(t_min, t_c) line for Eq. (2.14).

5 — Damage states (rate uncertainty)

D_S = 1, 2, 4 — fixed per API

5Damage statesRate uncertaintyD_S=1,2,4

Meaning: Three corrosion-rate states (expected, 2×, 4× rate). Each has β_n and POF_n; inspection updates posterior PoP_n.

Typical: Fixed per API Eq. (2.18).

State 1: D_S=1 · State 2: D_S=2 · State 3: D_S=4

6 — Bayesian inspection updating

Posterior ∝ Prior × Conditional (Tables 4.5–4.6)

6Inspection N_A–N_DEffectiveness counts0–6 total

Meaning: Count of past thickness inspections in each API Table 4.6 effectiveness class (A best → D poorest). Feeds Eq. (2.16) before β and POF.

Each field: N_A highly effective · N_B usually · N_C fairly · N_D poor (UT method, coverage, access per API 581).

Typical: No history: 0,0,0,0. Light program: 1–2 total (often B or C). Mature RBI: 2–4 total mixed A–C. Each box 0–6; sum of all four ≤ 6.

N_A

N_B

N_C

N_D

Total inspections: 0 (max 6)

6Prior probabilitiesTable 4.5sum = 1

Meaning: Prior confidence in the corrosion-rate estimate (Table 4.5) before inspection update.

Typical: Low = little data; Medium = some history; High = good rate data or recent confirmatory inspection.

6Conditional prob.Table 4.6fixed

Meaning: Table 4.6 conditional probabilities P(inspection | damage state); fixed by API, revised with priors on Calculate.

Typical: Read-only — updates when N_A–N_D or confidence changes.

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7 — Reliability index β_n

Eq. (2.18)

7COV′_tThickness scatter0.05–0.30

Meaning: Coefficient of variation for thickness / A_rt uncertainty in β, Eq. (2.18).

Typical: 0.15–0.25 default; 0.05–0.10 with many A-class UT points; 0.25–0.30 sparse D-class. Range 0.05–0.30.

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7COV_SfFlow-stress scatter0.05–0.30

Meaning: COV on flow stress FS_Thin (material scatter) in Eq. (2.18).

Typical: 0.10–0.20 with mill certs; up to 0.25–0.30 if properties uncertain. Range 0.05–0.30.

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7COV_PStrength-ratio scatter0.05–0.30

Meaning: COV on strength ratio SR_p (analysis scatter) in Eq. (2.18).

Typical: 0.05–0.10 well-defined FFS; 0.15–0.25 screening. API default ~0.05. Range 0.05–0.30.

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10 — Final thinning damage factor

D_f,thin with modifiers

10Management FEq. (2.20)1 or 3

Meaning: D_f,thin=max[(D_fB×F_IP×F_DL×F_WD×F_AM×F_SM)/F_OM, 0.1]. F_OM in denominator.

Typical: 1 = no issue; 3 = significant concern per API. Only 1 or 3.

F_OM

F_IP

F_DL

F_WD

F_AM

F_SM

11 — Final probability of failure

P_f = gff × F_MS × D_f,thin

11gffGeneric failure frequency/yr

Meaning: Equipment GFF (API Table 3.1). Used in P_f(t)=gff×F_MS×D_f^total.

Typical: Vessel small hole ~3×10⁻⁵ /yr; from GFF library.

/yr

11F_MSManagement systems0.1–10

Meaning: Management systems factor; scales P_f with program effectiveness.

Typical: 1.0 default.

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Calculated results (steps 1–11)

Item

Reference

Data

1A_rtWall-loss fraction0–1

Step 1 — A_rt from Eq. (2) and your t_min+CA.

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1Metal lossa × r—

Intermediate thickness loss.

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2FS_ThinFlow stress250–800 MPa (35–115 ksi)

Step 2 — Eq. (2.13) flow stress.

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3SR_p Eq. (2.14)Design / code path(S·E/FS)·(t_lim/t)

Meaning: Strength ratio from allowable stress and retirement thickness.

Needs: t_min, S, YS, TS, E, t_rdi.

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3SR_p Eq. (2.15)Hoop / pressure pathP·D/(α·FS·t)

Meaning: Strength ratio from internal pressure and geometry.

Needs: P, D, shape α, YS, TS, E, t_rdi.

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4 — Final strength ratio

SR_p^Thin = max(2.14, 2.15)

4SR_p,Thin usedGoverning valuemax(2.14, 2.15) unless method restricts

Meaning: Value passed to β and POF (Eq. 2.18) — higher of 2.14 and 2.15 when both exist and method is Max both.

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6PoP_1–3Posterior weightssum = 1

Step 6 — Bayesian posterior after inspection (Eq. 2.16).

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7β₁Reliability indexstate 1× rate

Step 7 — Eq. (2.18), D_S=1.

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7β₂Reliability indexstate 2× rate

Step 7 — D_S=2.

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7β₃Reliability indexstate 4× rate

Step 7 — D_S=4.

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8 — Probability of failure (each state)

POF_n = Φ(−β_n)

8POF₁Φ(−β₁)0–1

Step 8 — Φ(−β₁).

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8POF₂Φ(−β₂)0–1

Step 8 — state 2.

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8POF₃Φ(−β₃)0–1

Step 8 — state 3.

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9 — Base thinning damage factor

D_fB = Σ PoP_nΦ(−β_n) / 1.56×10⁻⁴

9D_fBBase damage factor—

Step 9 — Eq. (2.19).

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Σ PoP·Φ(−β) / 1.56×10⁻⁴

10D_f,thinFinal thinning D_f0.1–6410

Step 10 — max[(D_fB×F_IP×F_DL×F_WD×F_AM×F_SM)/F_OM, 0.1].

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11P_f(t)Probability of failure/yr

Step 11 — P_f=gff×F_MS×D_f^total; thinning only → D_f^total=D_f,thin.

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Audit

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