RBI Methodology - Probability Of Failure

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Newton RDMS’ Risk Based Inspection (RBI) module implements, and it’s certified on the American Petroleum Institute (API) recommended practice 580, which defines it as a risk assessment and management process that is focused on loss of containment of pressurized equipment in processing facilities, due to material deterioration. These risks are managed primarily through equipment inspection.

Simply, we assess the likelihood that an asset will fail (events per year) with predefined risk models for the most common damage mechanisms that consider:

  • The equipment type
  • Unique asset characteristics: age, usage, environment, installation, design vs. operating conditions, distinctive attributes, such as the presence of an injection point for a piping circuit
  • Asset condition (based on past and future maintenance and condition monitoring)

And then we assess the magnitude of the consequence if the asset fails (impact per event, measured in $) for several categories:

  • Safety, Health, or Environmental impact (EPA Dispersion Models)
  • Monetary loss such as Maintenance cost, Production loss or Disruption to use

The result of this analysis is a prioritized list of equipment based on their risk profile visualized by a configurable risk matrix like the one below:

Damage Mechanisms

The RBI methodology determines probability of failure from a damage factor for wall thinning (i.e., corrosion), environmental cracking and creep. The damage factor is converted to a Probability Category based on Table1.  Other Damage Mechanisms can be included in the risk assessment if the Probability Category is determined by a subject matter expert and then manually entered for each damage mechanism.

Table 1        Probability Category
Damage Factor Range Probability Category
1000 + 1
100 to 999 2
10 to 99 3
1 to 9 4
1 to 9 and additional criteria (see note) 5

NOTE:  The Probability Category for Internal or External Corrosion (i.e., Thinning) is reduced one level (i.e., 4 to 5, 3 to 4, etc.) when Wall Ratio is greater than 1.50 and corrosion rate is less than 0.005 inches per year.  This reduction does not apply to Environmental Cracking so the lowest Probability Category for cracking is 4.


Wall Thinning

Newton RDMS method to determine wall thinning damage factor applies to both internal corrosion and external corrosion. The only differences are how corrosion rate and age are established.

Fractional Wall Loss: Newton RDMS calculates the Fractional Wall Loss for internal corrosion and external corrosion using the following equation based on API 581 2nd Edition.

``FLW = frac{a * cr}{iwt}``


FWL = internal or external fractional wall loss

a = internal or external years in service (yrs.)

cr = internal or external corrosion rate (in/yr.)

iwt = Newton RDMS uses the Nominal Thickness from the component data sheet as Initial Wall Thickness in Criticality. 

NOTE: There are some cases when a measured thickness value is used as the Initial Wall Thickness, but the Date in Service should also be changed to align with the date of the thickness reading.  One such case is when an equipment item has been successfully operating for more than 20 years while the confirmed measured corrosion rate is less than 0.0001 inches/year. Since 0.0001 in/year is the smallest corrosion rate that can be entered in Criticality, the initial thickness might need to be adjusted so the POF does not indicate high likelihood of leak from corrosion when inspection data confirms the equipment is fit for continued service.

Age is the External years in service minus a time delay determined by Coating type and Circuit complexity. 

  • The External years in service is the years between the Criticality Analysis Date and the External date in service.  The External date in service should correspond to the date when external condition of equipment was “like-new” (i.e., cleaned and re-coated). 
  • The Coating type is an optional field that provides a qualitative measure of how well the coating can delay the onset of external corrosion.
    • Best coating delays onset by 10 years (i.e., External years in service minus 10).
    • Average coating delays onset by 5 years (i.e., External years in service minus 5).
    • None delays onset by 1 year (i.e., External years in service minus 1).  This is the default.  “None” should be used for either no coating applied or only a primer applied.
  • Circuit complexity is an optional field that only applies to piping.
    • In Criticality for piping on the External corrosion tab, enter number of barrier penetrations, insulation terminations and vertical runs.  Also enter total piping length.
    • Calculate a complexity factor by summing the number of penetrations, terminations and vertical runs and divide by the total length.
    • The complexity factor determines the time delay:
      • If complexity factor is less than 0.01, delay is 10 years (i.e., External years in service minus 10).
      • If complexity factor is greater than or equal to 0.01 but less than or equal to 0.05, delay is 5 years (i.e., External years in service minus 5).
      • If complexity factor is greater than 0.05, delay is zero.

Corrosion Rate is the Adjusted external corrosion rate.

Initial Wall Thickness is the nominal thickness.

Internal years in service: Newton RDMS calculates internal years in service by taking the year from Date of Analysis and subtracting the year from Date in Service.

External years in service: Newton RDMS either calculates external years in service or the user enters an override value to represent the time for external corrosion.  The calculated age is determined by taking the year from Date of Analysis, subtracting the year from Date in Service and subtracting a time delay. The delay is by default 1 year because mill scale or a primer is expected to delay onset of external corrosion. Additional delay is provided if the optional field for coating type is entered resulting in a 5-year delay for an "average" coating or 10-year delay for a "best" coating.

Internal corrosion rate: Newton RDMS provides three options for internal corrosion rate; expected, short term average and long term average.

    • Expected rate is manually entered and usually contains the value assigned during the Corrosion Study. 
    • Short-term and long-term values are calculated by the Thickness Inspections module. Short term average is the average of all short-term corrosion rates calculated for all Active locations.  Long term average is the average of all long-term corrosion rates for Active locations. The application allows negative corrosion rates to be ignored in the average and this is the recommended setting. The system requires the user to select which of the three options should be used for calculating fractional wall loss.

External corrosion rate: The system provides three options for external corrosion rate; calculated, expected and measured.

  • Calculated rate only applies when three conditions are true; insulated Yes; susceptible to external corrosion Yes; and operating temperature between 0 °F and 350 °F. These conditions represent the special case of Corrosion Under Insulation (CUI). The figure below is used to estimate the CUI rate and the three lines represent Area Humidity.  This method was developed by Capstone with input from customers. If additional information is provided, this rate is adjusted by factors that may increase or decrease the CUI rate looked up from this chart.  Additional information for CUI includes insulation material type, insulation jacket condition and external wetting (i.e. presence of additional source of moisture like down-wind of a cooling tower).
  • Expected rate is manually entered and usually contains the value assigned during the Corrosion Study. 
  • Measured rate is also manually entered to represent direct measurements of external corrosion rate.


Damage Factor: The system looks up the damage factors for internal corrosion and external corrosion using the table below based on the respective Fractional Wall Loss (first column; ar/t) and the number/confidence of inspections (across the top). The number and confidence of inspection are manually entered to represent inspection history.



ar/t = fractional wall loss (FWL)

l, m, h, vh = inspection confidence; respectively Low, Medium, High, Very High

Wall Ratio: Newton RDMS calculates the wall ratio for internal corrosion and external corrosion using the following equation. The Wall Ratio is used to determine if the Probability Category can be reduced one level (i.e., lower probability of failure)

`` WR = frac{rt}{t}``


WR = Wall Ration. Internal or external wall ratio.

rt = Remaining Thickness. Internal or external remaining wall thickness (in) calculated using the following equation:

`` RT = iwt - (a *cr)``


iwt = Initial Wall Thickness. Wall thickness at the time of Date in Service (in).

a = Age. Internal or external years in service (yrs.).

cr = Corrosion Rate. Internal or external corrosion rate (in/yr.).

t = Required Thickness. Estimated minimum wall thickness (in). Required thickness is the greater of structural minimum thickness (i.e., lookup value based on equipment type) or pressure minimum thickness calculated using the appropriate design code equation. The user can also override the estimated minimum thickness to match design calculations.

Probability Category: The Probability Categories for internal corrosion and external corrosion are based on the Damage Factors using Table 1 unless the Wall Ratio is greater than 1.5 and corrosion rate is less than 0.005 in/yr.  When these criteria are true, the Probability Category is reduced one level so a 4 becomes a 5, 3 becomes a 4, etc. The use of Wall Ratio and low corrosion rates was a method developed by Capstone.


Environmental Cracking

Newton RDMS considers environmental cracking an optional damage mechanism because it does not apply to all equipment items. To activate the Environmental Cracking module, the user selects a cracking mechanism and enters an initial potential.  This module is designed for cracking that initiates on the inside surface of process-containing equipment and is based on methodology developed by Capstone.

Environmental Cracking mechanism: Newton RDMS includes the following cracking mechanisms, and each is assigned to one of three levels of severity (i.e., aggressiveness).  If the box is checked for "Calculate with Higher Severity" then the Non-Severe or Special Case mechanism will be treated as Severe, so this check box does not affect mechanism that are already categorized as Severe.

  • Severe cracking mechanisms: Amine Cracking (ASCC), Carbonate Cracking, Caustic Cracking, Chloride Stress Corrosion Cracking (Cl SCC), Hydrofluoric Acid (SOHIC, HIC, HSC), Polythionic Acid SCC (PTA), and Deaerator Cracking.
  • Non-severe cracking mechanisms:  NH3 (ammonia) Cracking and Wet H2S (Blistering, SOHIC, HIC, SSC).
  • Special case: NH3 (ammonia) Cracking in API 620 Tanks (i.e., low temperature ammonia storage).

Initial Potential: The Initial Potential (Low, Medium or High) is manually entered and assigned during the Corrosion Study.

Updated Potential: Newton RDMS determines the updated potential as follows based on the number and confidence of inspections as well as whether cracking damage was found at the last inspection:

  • Use Initial Potential for the following:
    • Zero inspections and No cracking damage found.
    • Any number of Low confidence inspections and No cracking damage found.
    • Only 1 Medium or High confidence inspection and No cracking damage found.
  • Increase Initial Potential one level (e.g., Low to Medium) for the following:
    • Cracking damage found by any number of Low confidence inspections.
    • Cracking damage found by only 1 Medium or High confidence inspection.
  • Increase to High Potential if cracking damage found by more than 1 Medium or High confidence inspection.
  • Decrease Initial Potential one level (e.g. Medium to Low) if No cracking damage found by more than 1 Medium or High confidence inspection.

Cracking Potential Factor: The system determines the Cracking Potential Factor as follows based on the cracking severity and Updated Potential:

    • Severe cracking mechanisms: Low (10), Medium (5), High (2.5).
    • Non-Severe cracking mechanisms: Low (15), Medium (10), High (5).
    • Special case cracking mechanism: Low (20), Medium (15), High (10).

Environmental Cracking Age (EC Age): Date of Analysis minus environmental cracking Date in Service

  • Time before Last Inspection (T1) - Date of Last Inspection minus environmental cracking Date in Service.
  • Time since Last Inspection (T2) - Date of Analysis minus Date of Last Inspection.

Adjusted Years: Newton RDMS determines the adjusted years in service as follows based on the environmental cracking age (EC Age), Time before Last Inspection (T1), Time since Last Inspection (T2), confidence of inspection and whether cracking damage was found at the last inspection:

  • Use Environmental Cracking Age for zero inspections or any number of Low confidence inspections.
  • Use T2 + ½* T1 if cracking damage found by Medium confidence inspection.
  • Use lesser of T2 + 10 yrs. or EC Age if No cracking damage found by Medium confidence inspection.
  • Use T2 + ¼ * T1 if cracking damage found by High confidence inspection.
  • Use lesser of T2 + 5 yrs. or EC Age if No cracking damage found by High confidence inspection.

Damage Factor: The model calculates the damage factor using the following equation.

``DF = 10^(frac{ay}{cpf})``


DF = Cracking damage factor.

ay = Adjusted years in service.

cpf = cracking potential factor.

Probability Category: The Probability Category for Environmental Cracking is based on the Damage Factor using Table 1. Probability Category "5" is not possible for Environmental Cracking.



Creep is the slow deformation of a continuously-stressed metal.  It is strongly influenced by time and temperature.  Creep may lead to wall thinning and deformation, and eventually to metal failure.

The RBI model for creep is based on methods and analysis developed for API RP-581 Base Resource Document for Risk-Based Inspection (Appendix J), with enhancements based on MPC Project Omega from API RP-579 Fitness for Service.  The model for creep examines the effects of long-term creep on metals at high temperatures.  Short term creep should be addressed on an as-needed basis using more advanced analysis techniques, such as Level III Fitness for Service.

Data required for the creep model. 

The data required to complete the Creep Damage Model of the RBI Probability of Failure Analysis for fixed equipment items are defined below:

Required Data Definition
Date of Analysis The date the last creep analysis was performed on the current equipment item.
Date in Service This is the date the equipment went into creep service, which usually corresponds to the date the equipment went into the current service.
Pressure Internal pressure inside the furnace/boiler tube, psig.
Temperature Maximum average temperature in the tubes, °F.
Diameter Outer diameter of the tubes, inches.
Thickness Nominal thickness of the tubes.
Expected Corrosion Rate The current estimate of the rate of thinning, inches per year.
Material Spec and Grade The ASTM or API material specification of the material used to fabricate the equipment item.
Number of Inspections This is the number of times the equipment has been inspected for Creep Damage.
Inspection Confidence An input from the following categories: Very High (VH), High (H), Medium (M), or Low (L). The inspection confidence describes how effective the prior inspections were to correctly identify the presence and extent of Creep Damage.

Initial Potential for Creep Damage

Before launching into a detailed assessment of creep failure probability, the model checks to see if there is a potential for creep, based on the maximum average temperature in the tubes, and on the type of material.  The reference table used is Table 10.1 of API RP-579 Fitness for Service.   

If the maximum average temperature in the tubes is below the threshold value for the metal, the Creep Damage Factor is set to 1.0.

Number of Inspections

An equipment item is given credit for each inspection performed to detect a particular mechanism.  The total number of inspections is the number of times the equipment's internal surface was monitored for cracking.

Inspection Confidence

The confidence level given for an inspection to depends on the method used and the percent of the weld area covered.

Years In Service

The number of years an equipment item has been in creep service is measured from the initial date in creep service to the time the Probability of Failure Analysis is performed.  The age-clock resets only when an entire section of tubes is replaced.  If individual tubes have been replaced, the age does not reset to zero.

Creep Damage Factor

The Creep Damage Factor is found by determining the Creep Damage Potential and multiplying that by the Inspection Reduction Factor for Creep.

The Creep Damage Potential is found by first finding the Percent of Tube Life Consumed, and then using a lookup table to determine the Potential.  The correlation of percent life consumed to Creep Damage Potential was established according to the following table:

% Life Consumed Creep Potential % Life Consumed Creep Potential % Life Consumed Creep Potential
1% 1 34% 26 68% 125
2% 1 36% 28 70% 145
4% 2 38% 31 72% 172
6% 2 40% 33 74% 207
8% 3 42% 36 76% 252
10% 4 44% 39 78% 313
12% 5 46% 42 80% 400
14% 6 48% 45 82% 600
16% 7 50% 49 84% 700
18% 9 52% 53 86% 800
20% 10 54% 57 88% 900
22% 13 56% 62 90% 1000
24% 15 58% 69 92% 2000
26% 17 60% 76 94% 3500
28% 19 62% 90 96% 5000
30% 21 64% 100 98% 7500
32% 23 66% 110 100% 10000

The Percent Life Consumed at a given time, t, is estimated based on MPC Project Omega remaining life in API-579 Fitness for Service, June 2016, Annex 10B, according to the following method:

Steps used to determine the percent life consumed (PLC):

  • Establish the time-step size for iterations, 730 hours is recommended.
  • Find N, the number of time steps in the calculation.

Perform the following steps for each n, where n runs from 1 to N.

  • Find thickness at step n, w(n) = original thickness – (corrosion rate) * (time step)/8760.
  • Find σ1, σ23eff, given that P = pressure (ksi), OD = outer diameter (in)

``sigma_1 = P[frac{OD - w(n)}{2x(n)}]``

``sigma_2 = frac{sigma_1}{2}``

``sigma_3 = -P``

``sigma_(eff) = sqrt frac{(sigma_1-sigma_2)^2 + (sigma_2 - sigma_3)^2 + (sigma_1 - sigma_3)^2}{2}``

  • Check to ensure that σeff< yield stress, if not, end the calculation.

``S_(iota) = log_(10)(sigma_(eff))``

``delta = 0.33 xx [frac{sigma_1 + sigma_2 + sigma_3}{sigma_(eff)}-1]``

  • Look up the necessary coefficients for the material of interest from Table F.12 of API-579 (unknown edition, but same as Table F.30 in 2nd Edition, June 5, 2007 (p. 1062) or Table 10B.1 June 2016 edition (p. 998).

``eta = -{frac{1}{T - 460} xx [A_2 + 2A_3S_(iota) + 3A_4S_(iota)^2]}``

``epsilon = 10^-{A_0-0.5+(frac{1}{T+460}) xx [A_1+A_2S_(iota)+A_3S_(iota)^2+A_4S_(iota)^3]}``

``Omega = 10^{B_0+(frac{1}{T+460}[B_1+B_2S_(iota)+B_3S_(iota)^2+B_4S_(iota)^3]}``

``Omega(n) = max[Omega - eta),3]``

``Omega_m = Omega(n)^(delta+1) + 2eta``

``L(n) = frac{1}{Omega_(m^epsilon)}``

``PLC = frac{730}{L(n)}``

``sum_(n=1)^N PLC``

The Total PLC is then used in the table above to determine the Creep Potential.

The Inspection Effectiveness Reduction Factor is found from the following table:

  Number of Inspections
Effectiveness (Confidence) 0 1 2 3 4 5
High (Very High) 1 0.169 0.105 0.066 0.052 0.0625
Usually (High) 1 0.249 0.175 0.116 0.072 0.0425
Fairly (Medium) 1 0.400 0.272 0.179 0.121 0.0975
Poorly (Low) 1 0.839 0.563 0.367 0.251 0.215
Ineffective 1 1 1 1 1 1


Determining the creep damage probability category

Similar to the internal and external corrosion probability categories, the Creep Damage Probability Category is calibrated in order of magnitude steps.  The Creep probability category ranges in value from 4, low, to 1, very high and is determined using only the Creep Damage Factor.  The Creep Corrosion Probability Category is assigned using the corresponding Creep Corrosion Factor from the table below.

Creep Damage Factor (CDF) Creep Probability Category
1 <= CDF < 10 4
10 <= CDF < 100 3
100 <= CDF <1000 2
1000 <= CDF 1


Other Damage Mechanisms

Newton RDMS uses the term "other damage mechanism" for mechanisms such as Mechanical Damage (e.g., thermal fatigue, cyclic fatigue) and Material Property Degradation (e.g., high temperature hydrogen attack, low temperature embrittlement).  The Corrosion Study identifies "other" damage mechanism to be included in the risk assessment and assigns the Probability Category to be entered in Newton RDMS.