Quantitative analysis of a conceptual system dynamics maintenance performance model using multi-objective optimisation

Figures & data

Table 1. Overview of the modelling process.

Problem articulation	Understand the problem and articulate it and select the boundary	Regular meetings during a one year period with experts and managers of the clients resulted in using SD. The modelling aim was to contain maintenance behaviour in order to answer questions such as: what are the dynamic effects from more or less planned maintenance in a production line, in the long and the short-term? And, the question: what are the optimum levels of maintenance in terms of maximising benefits from invested resources, led to exploring the application of MOO. The model boundary selection is further treated in the next section
Dynamic hypothesis	Formulate a dynamic hypothesis regarding how the problem dynamics are endogenously generated from the feedback structure within the selected boundaries. Such formulation includes studying the relevant literature on problem phenomena and investigating the situation at the studied companies	The model focused on the relation between more developed PM work and its assumed effects on a more proactive behaviour in operations, favouring planned maintenance interventions resulting in higher efficiency. Yet, requiring the accurate levels of resources in order to realise such change, where an initial inertia is present requiring higher levels of resources initially to tip the reactive behaviour into a more proactive future behaviour. Hence, applying MOO could support searching the solutions leading to best trade-off performance according to presented experiments
Formulation	Build a simulation model based on the dynamic problem and test the hypothesis. This is a highly intuitive process (Sterman, 2000) and there are no formal descriptions of how to implement system dynamics projects (Linnéusson, 2009). The model includes specifications of structure and decision rules, parameter estimation, behavioural relationships, initial conditions, and tests for consistency with the aim of the model	The model was created with an interacting decision-maker in mind with the purpose to generate learning of connections between aspects of the modelled system. The model includes existing ideas from the literature and tacit real-world descriptions based on above-mentioned meetings with client and interviews among people with different roles in a relatively unstructured and open-ended character to understand their experiences. Searching literature, see Linnéusson et al. (2018), resulted in identifying qualitative sub-structures to create the basic structures. Simplicity to exemplify maintenance dynamics has been searched, which, for example, led to the inclusion of only one continuous improvement mechanism; learning from breakdowns
Testing	Examine whether the model reproduces adequately, with respect to its purpose. SD models are causal-descriptive as well as “statements as to how real systems actually operate in some aspects” (Barlas, 1996; p. 185). The internal structure validation of the model, together with its capacity to explain how the behaviour arises, is therefore crucial. While correlational black-box models are validated using statistical tests, this is not applicable for validating behaviours in an SD model, due to the problems of autocorrelations and multicollinearity (Barlas, 1996). Moreover, judging the validity of the internal structure of a model is very problematic and most methods are informal and qualitative in nature (Barlas, 1996) (see, for instance, Luna-Reyes & Andersen, 2003). Therefore, it is largely the usefulness of the model in explaining problem phenomena that determines its validation (Sterman, 2000). In other words, if the model can be considered acceptable, relevant and its usage may assist managers’ decision-making in the real world, it supports validation (Bertrand & Fransoo, 2002)	Tests for consistency were applied continuously during modelling where each sub-structure and equation formulation have been carefully processed. As soon as all feedback loops were closed and units checked, the manual and automated parameter testing identified improvements of consistency. Direct structure tests to confirm structure and parameter estimations were made during modelling and a set of four model walk-through workshops was carried out with an expert group from the partner companies. Moreover, simulation allowed extreme condition and behaviour sensitivity tests in the Vensim software
		The process of applying MOO to the developed SD model strengthened the testing substantially by multiple evaluations of trade-off solutions of the conflicting objectives. Numerous attempts and model improvements to assure viable evaluations were iterated until satisfying output was achieved. It required improvements of formulations and changing some minor structures from the model presented in Linnéusson et al. (2018). The presentation of the experiments here furthermore makes explicit the resulting near-optimal trade-off solutions, showing the performance of the SD model. Besides assuring the capacity of the model to represent valid solutions the process of applying MOO did not change any parameter settings from the previous presentation of the SD model
Policy formulation and evaluation	Apply the model to explore possible “what if” scenarios, test their sensitivity to implementation and examine synergy policies and so on	A set of “what if” scenarios were presented in Linnéusson et al. (2018) to illustrate the application of the SD model as a vehicle for support understanding the dynamics of the maintenance behaviour. As presented in the subsequent analysis section, the effective search of the objective landscape using MOO mainly supports the policy formulation and evaluation step

Figure 1. Overview of the maintenance performance SD model.

Figure 2. The general SBO process, adapted from (Aslam, 2013).

Figure 3. The general procedure for an MOO + SD analysis.

Table 2. Input parameter data for the MOO.

Input parameter in SD model	Notation	Range	Step	Note
numberRepairWorkers	S R	4–50	1	Total work pool of repair staff
numberMaintenanceEngineers	S E	0–30	1	Staff dedicated to develop new PM work
fractionPMiFromRCA	F PM	0–1	0.05	These two parameters control the distribution between PMfi, CBMi, and CBMs
fractionCBMiFromRCAhelp	F CBM	0–1	0.05
goalFractionCBMoverPM	PMFCBM	0–1	0.05	Goal for CBMi + CBMs over all PM work
inspectionInterval	I I	4–52	2	Interval for inspections for CBMi
goalCBMsensors	PMCBMs	0–500	25	Goal for CBMs

Figure 4. Scatter plots for the three scenarios.

Figure 5. 2D scatter plot for the three scenarios.

Figure 6. PCHM for scenario 1.

Figure 7. PCHM for scenario 2.

Figure 8. PCHM for scenario 3.

Table

Variable name	Expression	Unit
AccCompanyResults	INTEG (profit or loss,0)	$
AccMaintBudgetMargin	INTEG (diffCostOverBudget, 0)	$
analytic capabilities	1-fractionEquipmentHealthOverPossibleDefects	Dmnl
Availability	EquipmentInFullFunctionality/number of equipment	Dmnl
average CBM interval	avgMaintIntCBMs/(fractionEquipmentHealthOverPossibleDefects/fractionNormalHealthStatus)	Week
average reliability	52	Week
avgMaintIntCBMs	104	weeks
breakdown report demand	unscheduled repairs*policy fraction report per breakdown	info/Week
breakdown report done	Breakdown reports Backlog/delaytime breakdown report	info/Week
Breakdown reports Backlog	INTEG ( breakdown report demand-breakdown report done, 0)	info
BreakdownAnalysisRCAWIP	INTEG (RCAUsefulData-RCAcountermeasureToBreakdown, 0)	info
breakdownRate	EquipmentInFullFunctionality/delayBreakdowns + breakdownsLateWO	equipment/Week
breakdowns due to unperformed takedowns	breakdownsLateWO	equipment/Week
breakdownsLateWO	riskLateWO*EquipmentInFullFunctionality/Week	equipment/Week
capacity inspections	MAX(max capacity scheduled repairs – scheduled repairs , 0) * productivity inspections	equipment/Week
capital cost spare part inventory	interest rate spare part inventory/Week * capitalInSparePartInventory	$/Week
capitalInSparePartInventory	(spare part per equipment breakdown strategy*(number of equipment-SumPM preparations) + spare part per equipment takedown strategy*((1-fractionCBMoverPM) + 0.5*fractionCBMoverPM) * SumPMpreparations) * cost per spare part	$
CBMi	(EquipmentToInspect + EquipmentWithCBMinspectionPlans)/SumPMpreparations	Dmnl
CBMifaktorRiskReduction	0.8	Dmnl
CBMpreparation	MIN(ImplementedRCA*fractionCBMiFromRCA/delay convert to CBM , max capacity implement CBM inspections)	info/Week
CBMs	EquipmentWithCBMsensors/SumPMpreparations	Dmnl
CBMsensorPreparation	MIN(ImplementedRCA*fractionCBMsFromRCA/delay convert to CBM sensors , max capacity implementing CBM sensors)	info/Week
collateral damage	breakdownRate*probability collateral damage*possible defects per equipment	defects/Week
consequential breakdown costs	4*cost per stop * breakdownRate	$/Week
convertPMToCBM	MIN(MAX(0,(goalFractionCBMoverPM*EquipmentWithPMpreparations-fractionCBMoverPM* EquipmentWithPMpreparations)/delay convert to CBM), CBMpreparation*PM preparation release)	equipment/Week
corrective takedowns	Defective equipment/delay planning defective equipment work order	equipment/Week
cost breakdowns	cost per stop*breakdownRate	$/Week
cost man hours	man hour cost per Week*sumStaff	$/Week
cost per spare part	2000	$/equipment
cost per stop	1.25*cost per spare part	$/equipment
cost takedowns	cost per stop*takedownRate	$/Week
decisionDelayRole	12	weeks
decisionDelayRoleReactiveTo Proactive	4	weeks
defect elimination per repair	MAX(max fixed defects per repair* fractionEquipmentHealthOverPossibleDefects , 1)	defects/equipment
defectCreation	operations + collateral damage	defects/Week
defectEliminationPM	MIN(scheduled repairs*defect elimination per repair, EquipmentHealth/repairDelay)	defects/Week
defectEliminationRepairs	MIN(unscheduled repairs*defect elimination per repair, EquipmentHealth/repairDelay)	defects/Week
Defective equipment	INTEG (identified defective equipment-corrective takedowns, 1)	equipment
delay convert to CBM	26	Week
delay convert to CBM sensors	52	Week
delay plan PMwo	time to plan PMwo/(MIN(fractionPMwork , 0.5)*2)	Week
delay planning defective equipment work order	time to plan corrective actions/(MIN(fractionPMwork , 0.5)*2	Week
delay PM preparation	13	Week
delay RCA	time to implement/(MIN(fractionPMwork , 0.8)*2)	weeks
delay scheduled repairs	0.05	Week
delay scheduling takedowns	1	Week
delay unscheduled repairs	0.1	Week
delayBreakdowns	tbl risk effect on reliability(riskFactorBreakdowns) * average reliability	Week
delayOldPMremoval	26	weeks
delaytime breakdown report	1	weeks
diffCostOverBudget	maintenance budget –maintenanceCost	$/Week
discretionary inspections	IF THEN ELSE(ratioLatePlannedWO> = 0.1, 0, IF THEN ELSE(capacity inspections> = 2* (EquipmentToInspect/inspection delay), MIN(2*EquipmentToInspect/inspection delay, capacity inspections), MIN(EquipmentToInspect/inspection delay, capacity inspections)))	equipment/Week
effect breakdown frequency on capacity	tbl breakdown frequency and stop effect(breakdownRate/normal breakdown rate)	Dmnl
equipment per machine	25	equipment/machine
EquipmentHealth	INTEG (defectCreation-defectEliminationPM-defectEliminationRepairs, initial value of Hidden defects*number of equipment)	defects
EquipmentInFullFunctionality	INTEG (scheduled repairs + unscheduled repairs-breakdownRate-takedownRate, 0.622*number of equipment)	equipment
EquipmentToInspect	INTEG (planned inspections-descretionary inspections, 0)	equipment
EquipmentWithCBMinspectionPlans	INTEG (convertPMToCBM-newCBMsensors-planned inspections + descretionary inspections, initial library of inspection plans)	equipment
EquipmentWithCBMsensors	INTEG (newCBMsensors, initial library of CBMs)	equipment
EquipmentWithPMpreparations	INTEG (newPMpreparations + start PMwo-convertPMToCBM-planned repairs, initial library of PM preparations)	equipment
FINAL TIME	520	Week
fixedInterval	52	Week
fraction available data RCA	useful info in reports * analytic capabilities	Dmnl
fractionCBMiFromRCA	(1-fractionPMiFromRCA)*fractionCBMiFromRCAhelp	Dmnl
fractionCBMiFromRCAhelp	0.45	Dmnl
fractionCBMoverPM	(EquipmentToInspect + EquipmentWithCBMinspectionPlans + EquipmentWithCBM sensors)/(PMreplacementBacklog + EquipmentToInspect + EquipmentWithCBM inspectionPlans + EquipmentWithCBMsensors + EquipmentWithPMpreparations)	Dmnl
fractionCBMsFromRCA	1-fractionCBMiFromRCA-fractionPMiFromRCA	Dmnl
fractionEquipmentHealthOverPossibleDefects	EquipmentHealth/(number of equipment*possible defects per equipment)	Dmnl
fractionInitPMfi	0.5	Dmnl
fractionNormalHealthStatus	0.7	Dmnl
fractionPMiFromRCA	0.5	Dmnl
fractionPMwork	PM work/number of equipment	Dmnl
goal availability	0.9	Dmnl
goal PM preparations	number of equipment*goalPMwork	equipment
goalCBMsensors	25	equipment
goalFractionCBMoverPM	0.3	Dmnl
goalPMwork	1	Dmnl
identified defective equipment	identifiedDefectiveEquipmentInspections + identifiedDefectiveEquipmentCBMsensors	equipment/Week
identifiedDefectiveEquipment CBMsensors	EquipmentWithCBMsensors/average CBM interval	equipment/Week
identifiedDefectiveEquipment Inspections	discretionary inspections * fractionEquipmentHealthOverPossibleDefects * quality of inspections	equipment/Week
ImplementedRCA	INTEG (RCAcountermeasureToBreakdown-CBMpreparation-CBMsensorPreparation-PMpreparation,1)	info
initial library of CBMs	initLibraryofCBMs*number of equipment	equipment
initial library of inspection plans	initLevelofInspPlans * number of equipment	equipment
initial library of PM preparations	initLevelofPMfi*number of equipment	equipment
INITIAL TIME	0	Week
initial value of Hidden defects	initRatioEquipmentHealth*possible defects per equipment	defects/equipment
initLevelofInspPlans	0.001	Dmnl
initLevelofPMfi	fractionInitPMfi	Dmnl
initLibraryofCBMs	0.001	Dmnl
initRatioEquipmentHealth	0.7737	Dmnl
inspection delay	2	Week
inspectionInterval	4	Week
inspectionInterval	4	Week
interest rate spare part inventory	0.4	Dmnl
investCBMs	newCBMsensors*priceCBMs	$/Week
limit takedown rate	0.05	Dmnl
MaintCostOverNetMargin	maintenanceCost/Net contribution margin production	Dmnl
maintenance budget	100,000	$/Week
maintenanceConsequentialCost	consequential breakdown costs + capital cost spare part inventory	$/Week
maintenanceCost	cost man hours + cost breakdowns + cost takedowns + investCBMs	$/Week
maintenanceTotalCost	maintenanceConsequentialCost + maintenanceCost	$/Week
man hour cost per Week	2400	$/(Person*Week)
max capacity implement CBM inspections	(max capacity PM preparations-PMpreparation) * productivity PM to CBM	info/Week
max capacity implementing CBM sensors	(max capacity implement CBM inspections-CBMpreparation) * productivity CBM to sensor	info/Week
max capacity PM preparations	(max capacity RCA – RCAcountermeasureToBreakdown)*productivity PM preparations	info/Week
max capacity RCA	numberMaintenanceEngineers*productivity engineers RCA analysis and PM preparations	info/Week
max capacity schedued repairs	resSchRep*productivity scheduled repairs	equipment/Week
max capacity unscheduled repairs	resUnsRep*productivity unscheduled repairs/effect breakdown frequency on capacity	equipment/Week
max contribution margin per week	600,000	$/Week
max fixed defects per repair	8	defects/equipment
MTTF	EquipmentInFullFunctionality/breakdownRate	Week
Net contribution margin production	Availability * max contribution margin per week * tblContributionMarginOverAvailability(Availability)	$/Week
NetProfit	Net contribution margin production – maintenanceTotalCost	$/Week
newCBMsensors	IF THEN ELSE(goalCBMsensors > EquipmentWithCBMsensors, MIN( CBMsensor Preparation*PM preparation release, MIN((goalCBMsensors-EquipmentWithCBM sensors)/delay convert to CBM sensors, MAX(0 , EquipmentWithCBMinspectionPlans/delay convert to CBM sensors))) , 0)	equipment/Week
newPMpreparations	MIN((goal PM preparations-SumPMpreparations)/delay PM preparation, PMpreparation*PM preparation release) – IF THEN ELSE(goal PM preparations < SumPMpreparations, EquipmentWithPMpreparations/delayOldPMremoval, 0)	equipment/Week
normal breakdown rate	18	equipment/Week
number of equipment	number of machines in line*equipment per machine	equipment
number of machines in line	20	machines
numberMaintenanceEngineers	3	people
numberRepairMen	10	people
operations	Availability * wear and tear operations	defects/Week
planned inspections	EquipmentWithCBMinspectionPlans/inspectionInterval	equipment/Week
planned repairs	EquipmentWithPMpreparations/fixedInterval	equipment/Week
PlannedTakedowns	INTEG (corrective takedowns + PMworkOrder-breakdowns due to unperformed takedowns-takedown rate p – breakdowns due to unperformed takedowns, 4)	equipment
PM preparation release	1	equipment/info
PM work	EquipmentWithCBMinspectionPlans*CBMifaktorRiskReduction + EquipmentWithCBM sensors + EquipmentWithPMpreparations*PMfaktorRiskReduction	equipment
PMbacklog	PMreplacementBacklog + EquipmentToInspect + Defective equipment + PlannedTakedowns	equipment
PMfaktorRiskReduction	0.5	Dmnl
PMfi	(EquipmentWithPMpreparations + PMreplacementBacklog)/SumPMpreparations	Dmnl
PMpreparation	MIN(ImplementedRCA*fractionPMiFromRCA/delay PM preparation , max capacity PM preparations)	info/Week
PMreplacementBacklog	INTEG (planned repairs-start PMwo, 0)	equipment
PMtotal	SumPMpreparations/number of equipment	Dmnl
PMworkOrder	start PMwo	equipment/Week
policy fraction report per breakdown	IF THEN ELSE(numberMaintenanceEngineers > 0 :AND: resourcesScheduledRepairs > 0, 1, 0)	info/equipment
possible defects per equipment	20	defects/equipment
pressure per breakdown report	1	1/info
pressure scheduling delay	(delay scheduling takedowns*pressure to produce)	Week
pressure to produce	MIN(MAX(1, goal availability/Availability) , 4)	Dmnl
priceCBMs	10,000	$/equipment
probability collateral damage	0.25	Dmnl
probability wear and tear	0.015	1/Week
productivity CBM to sensor	0.5	Dmnl
productivity engineers RCA analysis and PM preparations	10	info/(Week*people)
productivity inspections	2*0.8	Dmnl
productivity PM preparations	0.5	Dmnl
productivity PM to CBM	0.1	Dmnl
productivity scheduled repairs	36 * 0.2	equipment/(Week*people)
productivity unscheduled repairs	9 * 0.5	equipment/(Week*people)
profit or loss	NetProfit	$/Week
quality of inspections	1	Dmnl
ratioLatePlannedWO	PlannedTakedowns/SumPMpreparations	Dmnl
RCAcountermeasureToBreakdown	MIN(BreakdownAnalysisRCAWIP/delay RCA , max capacity RCA)	info/Week
RCAUsefulData	breakdown report done*fraction available data RCA	info/Week
repairDelay	1	Week
resourcesScheduledRepairs	0.2*numberRepairMen	people
resourcesUnscheduledRepairs	0.8*numberRepairMen	people
resSchRep	INTEG (roleToProactive-roleToReactive, resourcesScheduledRepairs)	people
resUnsRep	INTEG (roleToReactive-roleToProactive, resourcesUnscheduledRepairs)	people
risk delayed work	2	Dmnl
riskFactorBreakdowns	fractionEquipmentHealthOverPossibleDefects * (risk delayed work/riskFactorReductionDueToPMwork)	Dmnl
riskFactorReductionDueToPMwork	tbl reduced risk due to PM work(fractionPMwork)	Dmnl
riskLateWO	ratioLatePlannedWO/riskFactorReductionDueToPMwork	Dmnl
roleToProactive	IF THEN ELSE(resUnsRep < 1, 0, IF THEN ELSE(resUnsRep > 4:AND:usage reactive staff < 0.75, 1, IF THEN ELSE(resUnsRep < 4:AND:usage reactive staff < 0.5, 1, 0)))/decisionDelayRoleReactiveToProactive	people/Week
roleToReactive	IF THEN ELSE(resSchRep < 1, 0, IF THEN ELSE(resSchRep > 4:AND:usage preventive staff < 0.75, 1, IF THEN ELSE(resSchRep > 2:AND:usage preventive staff < 0.5, 1, 0)))/decisionDelayRole	people/Week
SAVEPER	13	Week [0,?]
scheduled repairs	MIN(ScheduledMaintenance/delay scheduled repairs , max capacity schedued repairs)	equipment/Week
ScheduledMaintenance	INTEG ( takedownRate-scheduled repairs, 0)	equipment
spare part per equipment breakdown strategy	5	Dmnl
spare part per equipment takedown strategy	2	Dmnl
start PMwo	IF THEN ELSE(ratioLatePlannedWO>=0.1, 0, PMreplacementBacklog/delay plan PMwo)	equipment/Week
SumPMpreparations	PMreplacementBacklog + EquipmentToInspect + EquipmentWithCBMinspectionPlans + EquipmentWithCBMsensors + EquipmentWithPMpreparations	equipment
sumStaff	numberMaintenanceEngineers + resourcesScheduledRepairs + resourcesUnscheduledRepairs	people
takedown rate p	IF THEN ELSE(ScheduledMaintenance > limit takedown rate*number of equipment/pressure to produce, 0, PlannedTakedowns/pressure scheduling delay)	equipment/Week
takedownRate	takedown rate p	equipment/Week
tbl breakdown frequency and stop effect	([(0,0)–(4,9)],(0,1),(1,1),(2,3),(4,9))	Dmnl
tbl pressure to close gap	([(0,0)-(100,000,1)],(0,1),(1,1),(5,0.9),(10,0.7),(20,0.5),(100,0.2),(100,000,0))	Dmnl
tbl reduced risk due to PM work	([(0,0.8)-(1,2)],(0,1),(0.3,1.05),(0.6,1.4),(0.75,1.9),(1,2))	Dmnl
tbl risk effect on reliability	([(0,0)-(2.1,4)],(0,4),(0.3,3.6),(0.38,3),(0.45,1.5),(0.5,1),(0.65,0.72), (1.05,0.36),(2.1,0.1))	Dmnl
tblContributionMarginOverAvailability	( [(0,0)-(1,1)],(0,1),(0.7,1),(1,0.85))	Dmnl
TIME STEP	0.015625	Week [0,?]
time to implement	13	Week
time to plan corrective actions	1	Week
time to plan PMwo	2	Week
unscheduled repairs	MIN(UnscheduledMaintenance/delay unscheduled repairs , max capacity unscheduled repairs)	equipment/Week
UnscheduledMaintenance	INTEG (breakdownRate-unscheduled repairs, 0.378*number of equipment)	equipment
usage engineers	IF THEN ELSE(max capacity implementing CBM sensors = 0, 1, ZIDZ( CBMsensorPreparation, max capacity implementing CBM sensors))	Dmnl
usage preventive staff	ZIDZ(descretionary inspections, capacity inspections)	Dmnl
usage reactive staff	ZIDZ(unscheduled repairs, max capacity unscheduled repairs)	Dmnl
useful info in reports	tbl pressure to close gap(Breakdown reports Backlog*pressure per breakdown report)	Dmnl
wear and tear operations	tbl probability wear and tear EqpmtAge(EqpmtAge)*probability wear and tear * MIN(EquipmentHealth, 9000)	defects/Week
Week	52	Week

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