EffectOfFatigueModeling the influence of excessive workloads on productivity or quality 
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Fatigue is modeled as a smooth of the normalized input u which is indicating the current workload with regard to capital equipment or workers. The current workload will be normalized by dividing the input u by a constant or a variable reference workload (referenceWorkload
or u_ref
, respectively). The timeToGetFatigued
describes the time constant for the smooth and indicates the lag between beginning to work at an excessive level and the onset of the full effect on productivity (or quality).
Janoscheks growth curve is used to model the nonlinear effect of a prolonged work intensity. It describes a negatively sloping sshaped curve that will pass through the reference point (1,1). The upper bound of the effect (effectMax
) must be given slightly above 1.0 as the curve will collapse in all other cases. If the effect is to be clipped at 1.0 then the parameter clipEffect
should be set to true
.
hours worked per month
, output per hour
etc.).init
in the Advanced tab allows to select →InitializationOptions:initialFatigue
to determine the initial output of the smoothed, normalized workload.fatigue
using initialFatigue
as an initial guess.timeToGetFatigued 
Value: Type: Time (s) Description: Time constant for the exponential smooth of overtime in periods 

referenceWorkload 
Value: 1 Type: Rate (1/s) Description: Constant reference workload (optinal) 
delayOrder 
Value: 1 Type: Integer Description: Delay order of the smooth for workload 
effectMax 
Value: 1.1 Type: Real Description: The upper bound for the effect of less work than normal on PDY (MAX >= 1) 
effectMin 
Value: 0 Type: Real Description: The lower bound for the effect of fatigue on PDY (MIN >= 0) 
steepness 
Value: 10 Type: Real Description: High values indicate a steep gradient for the lookup curve (JanoschoekNegative.growthRate) 
hasConstantReference 
Value: true Type: Boolean Description: = true, if the reference workload is given by a constant parameter 
clipEffect 
Value: false Type: Boolean Description: = true, if the maximum effect is to be 1.0 
initialFatigue 
Value: 1 Type: Real Description: Initial Output (fatigue.initialValue) 
init 
Value: modelSettings.init Type: InitializationOptions Description: Provide InitializationOptions (Free, FixedValue, SteadyState) 
strict 
Value: true Type: Boolean Description: = true, if strict limits with noEvent(..) (clippedEffect.strict) 
u 
Type: RealInput Description: Input of workload 


u_ref 
Type: RealInput Description: Input for the reference workload (optional) 

y 
Type: RealOutput Description: Effect on Productivity given as a multiplier 
modelSettings 
Type: ModelSettings Description: Setting important global variables within a model 


normalizedWorkload 
Type: DmnlInput Description: Workload divided by the normal workload 

parRef 
Type: ConstantConverter Description: Constant reference value for the workload (optional) 

effectOnOutcome 
Type: JanoschekNegative Description: The multiplicative effect of fatigue on productivity or quality 

fatigue 
Type: SmoothN Description: Fatigue is an nth order smooth of overtime 

clippedEffect 
Type: Clip Description: Clip Effect to only allow values within the closed unit interval 

unchangedEffect 
Type: PassThrough Description: Leave the effect unchanged 