1 Module 8 UNIT III " Copyright 2002, Information Spectrum, Inc. All Rights Reserved." HOW TO PERFORM RCM ANALYTICAL METHODS

2 Module Preview: Introduction Interval Calculations Interval Calculations IntroductionIntroduction Cautions and Warnings Cautions and Warnings Review and Summary Cost Calculations Cost Calculations Spreadsheet Exercise Spreadsheet Exercise ANALYTICAL METHODS

3 Module Objective: This module will provide information on different analytical methods that may be used in RCM analysis: 1.Introduce some methods of determining task intervals 2.Demonstrate the cost equations used by the IRCMS software 3.Discuss limitations and cautions associated with these methods IntroductionIntroduction ANALYTICAL METHODS

4 Interval Calculations Inspection Interval (I) (Ref: NAVAIR ): Inspection Interval (I) (Ref: NAVAIR ): I = PF/n I = PF/nWhere: PF = interval from potential failure to functional failure n = number of inspections during PF interval Where: Using Pacc (safety or non-safety) Using Pacc (safety or non-safety) n = ln (Pacc) / ln (1-theta) Using Cost optimization (non-safety) Using Cost optimization (non-safety) n = ln [ (-MTBF*Ci/PF)/((Cnpm-Cpf)*ln(1-theta)) ] n ln(1-theta) On-condition Task: ANALYTICAL METHODS

5 Interval Calculations Derivation:n = ln (Pacc) / ln (1-theta) Theta = probability of detecting a Potential Failure in one inspection assuming it exists (1-theta) = probability of not detecting a Potential Failure in one inspection assuming it exists (1-theta) n = probability of not detecting a Potential Failure in “n” inspections assuming it exists Goal of inspection is (1-theta) n < Pacc Goal of inspection is (1-theta) n < Pacc Longest inspection meeting this criteria would occur at (1-theta) n = Pacc Longest inspection meeting this criteria would occur at (1-theta) n = Pacc Solving for n: Solving for n: n = ln (Pacc) / ln (1-theta) On-condition Task: ANALYTICAL METHODS

6 Interval Calculations If an inspection may require deferral of the corrective action when found the inspection interval should allow for the deferral time (Tc) If an inspection may require deferral of the corrective action when found the inspection interval should allow for the deferral time (Tc) Applicable in continuously operating equipment or processes or where repair deferred and use continues Applicable in continuously operating equipment or processes or where repair deferred and use continues Mathematically: Mathematically: I = (PF/n)-Tc where: Tc = Time needed to perform corrective action On-condition Task: ANALYTICAL METHODS

7 LIMITATIONS Method is conservative Method is conservative Based on assumption that potential failure always exists Based on assumption that potential failure always exists If more precise interval is desired, actual failure rate and distribution needs to be considered in more detail If more precise interval is desired, actual failure rate and distribution needs to be considered in more detail As more precision is pursued, loss of conservatism must be weighed against confidence in the data sources to ensure adequate levels of protection As more precision is pursued, loss of conservatism must be weighed against confidence in the data sources to ensure adequate levels of protection On-condition Task: Interval Calculations ANALYTICAL METHODS

8 Interval Calculations n = ln [ (-MTBF*Ci/PF)/((Cnpm-Cpf)*ln(1-theta)) ] n ln(1-theta)Where: Ci = Cost of one inspection Cnpm = Cost of No PM = Cost of Corrective Maint + Cost Lost Op time Cpf = Cost of repairing a PF See NAVAIR On-condition Task: ANALYTICAL METHODS

9 Interval Calculations Statistical (Weibull) or empirical (Test or sampling) methods Statistical (Weibull) or empirical (Test or sampling) methods Beyond the scope of this course Beyond the scope of this course Hard-Time Task: ANALYTICAL METHODS

10 Interval Calculations Failure Finding Task Failure Finding Task: Inspection Interval (I) (Ref: NAVAIR ): Inspection Interval (I) (Ref: NAVAIR ): Determine by setting P mf = P acc Determine by setting P mf = P accWhere: P mf = P hidden x P additional P mf = Probability of multiple failure occurring P hidden = Probability of the hidden failure occurring P additional = Probability of an additional failure occurring ANALYTICAL METHODS

11 Interval Calculations Failure Finding Task: Assuming a constant failure rate for each term: P = 1 - e -t / MTBF (1) P mf = P hidden x P additional = (1 - e -t / MTBF hidden ) x (1 - e -t / MTBF additional ) (2) P mf = P acc (t) = (1 - e -t / MTBF acceptable ) ANALYTICAL METHODS

12 Interval Calculations Failure Finding Task: Combining equations (1) and (2) (3) (1 - e -t / MTBF acceptable ) = (1 - e -t / MTBF hidden ) x (1 - e -t / MTBF additional ) Two unknowns: MTBF acceptable and t To determine MTBF acceptable solve (1 - e -t / MTBF acceptable ) for a known Pacc and t For example using a program established Pacc(at t=1) = Finally Equation (3) can be solved for t which is used for I Note: equation (3) can only be solved iteratively (use the spreadsheet) For economic/operational consequences, must be cost-effective ANALYTICAL METHODS

13 Interval Calculations Failure Finding Task: LIMITATIONS Method assumes hidden and additional failures are random and independent Method assumes hidden and additional failures are random and independent Assumption of randomness is usually conservative Assumption of randomness is usually conservative If failures are dependent method may NOT be conservative! If failures are dependent method may NOT be conservative! If hidden failure is not random to a high degree another task option such as Hard time may be more appropriate If hidden failure is not random to a high degree another task option such as Hard time may be more appropriate ANALYTICAL METHODS

14 Overview:Overview: Cost Calculations IRCMS Cost Analysis provides a means to compare relative cost of each task and other failure management options IRCMS Cost Analysis provides a means to compare relative cost of each task and other failure management options Normalized to one unit of operating time Normalized to one unit of operating time Typical Cost per Unit Op time Typical Cost per Unit Op time = Cost of one task / task interval + Cost of repairs associated with task/period between repairs ANALYTICAL METHODS

15 Service/Lube:Service/Lube: Cost Calculations Service/Lube Task Service/Lube Task SL OP = Service/lubrication task cost per operating time SL OP = C SL / I SL Where: C SL = Cost Of One SL Task = ( MHs to perform task) x (cost per MH) + material cost I SL = Task Interval ANALYTICAL METHODS

16 On-Condition:On-Condition: Cost Calculations On-condition TaskOn-condition Task OC OP = On-condition task cost per operating time OC OP = ((C OC / I OC ) *(L - (I I -I OC )) / L) + C R / MTBF Where: C OC = Cost of one OC Task (Not including repair costs) (MHs to perform task) * (cost per MH) + cost of materials L = Item Design Life I I = Initial Inspection Interval (Inspection Threshold) I OC = Task Interval MTBF = Mean time between failures (both potential and functional with task in place) C R = Average Repair Cost. Include all failures (potential and functional failures) Include secondary damage Include the cost of multiple failures in the functional failure portion of the cost Include operational impact if it has been converted to a "cost" ANALYTICAL METHODS

17 Hard-Time:Hard-Time: Cost Calculations Hard-Time Task Hard-Time Task HT OP = Hard time task cost per operating time HT OP = [C HT (S) + C R (1-S)] / [(S) I HT + (1-S) K I HT ] Where: C HT = Cost Of One HT = (MHs to perform task) x (cost per MH) + cost of materials S = Percentage of items that survive to the hard time limit I HT = Task Interval K = Premature Failure Factor = Average age of premature failures as a percentage of I HT. (Note: K I HT is used to estimate MTTF of premature failures.) C R = Average Repair Cost if HT not accomplished. Ensure secondary damage is included For hidden functions include the cost of multiple failures. Include operational impact if converted to a "cost" ANALYTICAL METHODS

18 Failure Finding: Cost Calculations Failure Finding Failure Finding FF OP = Failure Finding task cost per operating time FF OP = C FF / I FF + C R / MTBF Where: C FF = Cost Of One Inspection = ( MHs to perform task) x (cost per MH) + cost of materials I FF = Task Interval MTBF = Mean time between failures (with task in place) C R = Average Repair Cost. Average cost of repairing the functional failures found by the inspection and those that become evident by multiple failures not prevented. Average cost of repairing the functional failures found by the inspection and those that become evident by multiple failures not prevented. Include operational impact if it has been converted to "cost". Include operational impact if it has been converted to "cost". ANALYTICAL METHODS

19 Overview:Overview: Cost Calculations No PM (Run to Failure) No PM (Run to Failure) NO OP = “No PM” cost per operating time NO OP = C R / MTBF Where: C R = Average Repai r Cost Average cost to repair the functional failure and secondary damage. Average cost to repair the functional failure and secondary damage. For hidden functions, include the cost of multiple failures. For hidden functions, include the cost of multiple failures. Include operational impact if it has been converted to "cost". Include operational impact if it has been converted to "cost". MTBF = Mean time between failures (with no task in place) ANALYTICAL METHODS

20 Overview:Overview: Cost Calculations Other Action Other Action OA OP = “Other action” cost per operating time OA OP = C OA / L R Where: C OA = Total cost to develop and implement “Other Action” L R = Total remaining life of system/fleet ANALYTICAL METHODS

21 Overview:Overview: Cautions and Warnings All methods are approximations All methods are approximations Subject to changes in data Subject to changes in data Consider sensitivity Consider sensitivity Schedule follow-up validation of assumptions (Age Exploration) Schedule follow-up validation of assumptions (Age Exploration) User is responsible for understanding the limits and applicability of each method User is responsible for understanding the limits and applicability of each method Not every failure mode requires in depth analytical analysis (pick your battles) Not every failure mode requires in depth analytical analysis (pick your battles) Estimates can be used in many cases Estimates can be used in many cases Note: Equations discussed on the following slides describe the current methods provided in NA Users should stay abreast of differences between latest NA methods and those used in IRCMS Note: Equations discussed on the following slides describe the current methods provided in NA Users should stay abreast of differences between latest NA methods and those used in IRCMS ANALYTICAL METHODS

22 Overview: Spreadsheet Exercise Exercise Exercise ANALYTICAL METHODS

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24 Overview: Analytical Methods Spreadsheet Exercise Exercise Exercise

25 Review and Summary Module Objective Module Objective Review and Summary Review and Summary Introduction Interval Calculations Interval Calculations Cautions and Warnings Cautions and Warnings Cost Calculations Cost Calculations Spreadsheet Exercise Spreadsheet Exercise ANALYTICAL METHODS

26 End of Module up next…….. Unit IV Module 1 Packaging End of Module up next…….. Unit IV Module 1 Packaging