DYNAMICS LAB · OPERATIONS TWIN · SCIENTIFIC REPORT

OTE-002 · Digital Twin Calibration & Validation

Study context

Problem addressed
Which empirical model reproduces historical duration and route frequencies on a later period?
Contribution relative to existing methods
The study compares two trace bootstraps and a semi-Markov model on independent time periods and reports missed thresholds.
Potential commercial use
Set acceptance tests for a process twin before trialing it on internal data.

Market context and value assumptions on the engine page

OTE-002

Experiment conclusions

Pooled bootstrap, selected on the validation set, estimated mean test durations with 12.2% relative error. The distance between variant distributions was 0.372, above the 0.30 threshold. All three models exceeded that threshold: the twin reproduced timings better than process paths.

Study limits. Validation is partial and retrospective, with observed arrival times given to the simulator. The two-way match category had only one test case.

Model-by-model results
Pooled bootstrap
Best on validation. In the test, variant distance was 0.372.
Category bootstrap
Test distance was 0.369, slightly lower but still above the threshold.
Semi-Markov
Low median-duration error of about 2%, but variant distance was 0.781.

COMPUTED RESULT. Observed elapsed time, simulated service assumptions and business outcomes are distinct. This report does not assess individual employees or calculate monetary savings.

Objective and dataset

BPI Challenge2019 · public Purchase-to-Pay log · Boudewijn van Dongen · 4TU.ResearchData · version1 · CC BY4.0. Original input:728,558,522bytes, checked against official MD5.

Official dataset and attribution

Method and parameters

Preregistered core projection excludes SRM administrative activities only from the twin. Eligible core cases begin Create Purchase Order Item, end Clear Invoice, remain entirely in one2018quarter, and exclude Consignment/unknown categories. This is an observed endpoint proxy, not proof of closure. Q1+Q2calibration, Q3validation,Q4test; documents crossing sets excluded. SHA-selected heldoutsamples are capped3000cases per set. Pooled trace bootstrap, category trace bootstrap and category semi-Markov elapsed-time models use identical observed arrival schedules and fixed92day windows.20seeded replicas per model/set. Seven unweighted validation errors select one model before independent testing. All model test metrics are reported.90percent marginal duration intervals derive only from calibration; actual heldoutcoverage is measured.95percent Student-t intervals quantify independent MC mean uncertainty conditional on the model;499whole-document bootstrap repetitions quantify observed sample uncertainty separately. Experimental acceptance tolerances and minimum100cases are preregistered engineering bounds, not official standards. Quarter/end-point selection and retrospective arrival conditioning preclude prospective prediction claims.

Independent test and validation

Selected only on validation: pooled_bootstrap. PARTIAL OR NO VALIDATION; see per-category checks

validation · 3000cases · 1467documents

modelmean_relative_errormedian_relative_errorp90_relative_errorthroughput_relative_errorwasserstein_over_observed_meanvariant_total_variationproxy_rework_rate_absolute_differencevalidation_lossmean_signed_error_daymedian_signed_error_dayp90_signed_error_dayactivity_total_variation
pooled_bootstrap0.07618810.04969450.03787990.18440.07774650.1795330.01011670.087937-4.05407-2.64019-3.031470.0141322
category_bootstrap0.07915870.05134080.04123690.183250.08075950.177250.009666670.0889518-4.21213-2.72766-3.300130.0159345
semi_markov0.08203980.1500050.02383970.2085830.1322280.7731830.015450.197904-4.36544-7.969511.907860.0150347

test · 1757cases · 654documents

modelmean_relative_errormedian_relative_errorp90_relative_errorthroughput_relative_errorwasserstein_over_observed_meanvariant_total_variationproxy_rework_rate_absolute_differencevalidation_lossmean_signed_error_daymedian_signed_error_dayp90_signed_error_dayactivity_total_variation
pooled_bootstrap0.1216130.1024270.2251910.1527890.1314040.3723390.005520770.1587555.321784.6846214.16380.0586728
category_bootstrap0.1172390.09973430.2167560.1506550.1278510.3688670.006232210.1553345.130364.5614613.63320.0521212
semi_markov0.1156560.01964930.3080910.1820150.1742660.7809330.007029030.2268065.0611-0.70805619.37790.0513515

Per-category acceptance · independent test

modelcategoryobserved_casesmean_metricsfailed_acceptance_checksstatus
pooled_bootstrap2-way match1{"mean_relative_error": 0.36301030347634095, "median_relative_error": 0.36301030347634095, "p90_relative_error": 0.36301030347634095, "throughput_relative_error": 0.0, "wasserstein_over_observed_mean": 0.36301030347634095, "variant_total_variation": 1.0, "proxy_rework_rate_absolute_difference": 1.0, "validation_loss": 0.49314874484362337, "mean_signed_error_day": -21.400000000000002, "median_signed_error_day": -21.400000000000002, "p90_signed_error_day": -21.400000000000002, "activity_total_variation": 0.2976061776061777}["mean_relative_error", "median_relative_error", "p90_relative_error", "wasserstein_over_observed_mean", "variant_total_variation", "proxy_rework_rate_absolute_difference", "minimum100independent_cohort_cases"]NOT VALIDATED
pooled_bootstrap3-way match, invoice after GR104{"mean_relative_error": 0.1421504967343082, "median_relative_error": 0.19670151006298092, "p90_relative_error": 0.28150491892019114, "throughput_relative_error": 0.14375, "wasserstein_over_observed_mean": 0.1864759339667361, "variant_total_variation": 0.6307692307692307, "proxy_rework_rate_absolute_difference": 0.052403846153846155, "validation_loss": 0.23339370522961328, "mean_signed_error_day": 6.111305755876069, "median_signed_error_day": 8.317673611111113, "p90_signed_error_day": 16.612309027777776, "activity_total_variation": 0.47642376411345727}["p90_relative_error", "variant_total_variation"]NOT VALIDATED
pooled_bootstrap3-way match, invoice before GR1652{"mean_relative_error": 0.12074736644269697, "median_relative_error": 0.09597406126855192, "p90_relative_error": 0.22313326051940607, "throughput_relative_error": 0.15345036319612593, "wasserstein_over_observed_mean": 0.12864221651916313, "variant_total_variation": 0.3696428571428571, "proxy_rework_rate_absolute_difference": 0.005962469733656175, "validation_loss": 0.1567932278317796, "mean_signed_error_day": 5.288250773473227, "median_signed_error_day": 4.414340277777776, "p90_signed_error_day": 14.04530902777778, "activity_total_variation": 0.04142795820803251}["variant_total_variation"]NOT VALIDATED
category_bootstrap2-way match1{"mean_relative_error": 0.5227499025931859, "median_relative_error": 0.5227499025931859, "p90_relative_error": 0.5227499025931859, "throughput_relative_error": 0.0, "wasserstein_over_observed_mean": 0.5227499025931859, "variant_total_variation": 0.0, "proxy_rework_rate_absolute_difference": 0.0, "validation_loss": 0.29871423005324915, "mean_signed_error_day": -33.541666666666664, "median_signed_error_day": -33.541666666666664, "p90_signed_error_day": -33.541666666666664, "activity_total_variation": 0.0}["mean_relative_error", "median_relative_error", "p90_relative_error", "wasserstein_over_observed_mean", "minimum100independent_cohort_cases"]NOT VALIDATED
category_bootstrap3-way match, invoice after GR104{"mean_relative_error": 0.1457476735090982, "median_relative_error": 0.15023730734174726, "p90_relative_error": 0.33449475158276254, "throughput_relative_error": 0.15673076923076923, "wasserstein_over_observed_mean": 0.2105821088671625, "variant_total_variation": 0.5370192307692309, "proxy_rework_rate_absolute_difference": 0.01923076923076923, "validation_loss": 0.2220060872187914, "mean_signed_error_day": 6.265954861111114, "median_signed_error_day": 6.335572916666669, "p90_signed_error_day": 19.739371527777774, "activity_total_variation": 0.20367038731392345}["p90_relative_error", "wasserstein_over_observed_mean", "variant_total_variation"]NOT VALIDATED
category_bootstrap3-way match, invoice before GR1652{"mean_relative_error": 0.11604434857006984, "median_relative_error": 0.09527425905515377, "p90_relative_error": 0.21002035480240971, "throughput_relative_error": 0.15036319612590796, "wasserstein_over_observed_mean": 0.12390983752993978, "variant_total_variation": 0.3643765133171913, "proxy_rework_rate_absolute_difference": 0.0061440677966101715, "validation_loss": 0.15230465388532607, "mean_signed_error_day": 5.082277437281405, "median_signed_error_day": 4.382152777777778, "p90_signed_error_day": 13.219906250000014, "activity_total_variation": 0.027188751038910858}["variant_total_variation"]NOT VALIDATED
semi_markov2-way match1{"mean_relative_error": 0.5272928481752457, "median_relative_error": 0.5272928481752457, "p90_relative_error": 0.5272928481752457, "throughput_relative_error": 0.0, "wasserstein_over_observed_mean": 0.5272928481752457, "variant_total_variation": 0.0, "proxy_rework_rate_absolute_difference": 0.0, "validation_loss": 0.3013101989572833, "mean_signed_error_day": -33.83315972222223, "median_signed_error_day": -33.83315972222223, "p90_signed_error_day": -33.83315972222223, "activity_total_variation": 0.0}["mean_relative_error", "median_relative_error", "p90_relative_error", "wasserstein_over_observed_mean", "minimum100independent_cohort_cases"]NOT VALIDATED
semi_markov3-way match, invoice after GR104{"mean_relative_error": 0.12714736399370535, "median_relative_error": 0.051639391376464706, "p90_relative_error": 0.3874998234837253, "throughput_relative_error": 0.1745192307692308, "wasserstein_over_observed_mean": 0.20612361480678895, "variant_total_variation": 0.8740384615384615, "proxy_rework_rate_absolute_difference": 0.019230769230769225, "validation_loss": 0.26288552217130656, "mean_signed_error_day": 5.466294070512822, "median_signed_error_day": 1.9316319444444467, "p90_signed_error_day": 22.867333333333338, "activity_total_variation": 0.18837335473091013}["p90_relative_error", "wasserstein_over_observed_mean", "variant_total_variation"]NOT VALIDATED
semi_markov3-way match, invoice before GR1652{"mean_relative_error": 0.11551602555947102, "median_relative_error": 0.022166820165174468, "p90_relative_error": 0.3056925597405178, "throughput_relative_error": 0.1825968523002421, "wasserstein_over_observed_mean": 0.17373449436217128, "variant_total_variation": 0.7766646489104116, "proxy_rework_rate_absolute_difference": 0.007415254237288135, "validation_loss": 0.22625523646789664, "mean_signed_error_day": 5.059139006591335, "median_signed_error_day": -0.90890625, "p90_signed_error_day": 19.24207291666668, "activity_total_variation": 0.027803163763415368}["p90_relative_error", "variant_total_variation"]NOT VALIDATED

Nominal90%duration coverage · not implied by mean fit

categorycasesmodelinterval90_daynominal_coveragecalibration_generated_samplescapped_draws_excludedobserved_coverageobserved_cases
2-way match1pooled_bootstrap[21.26388888888889, 80.1859375]0.923886011
2-way match1category_bootstrap[8.529097222222223, 52.71534722222222]0.92001
2-way match1semi_markov[5.907638888888889, 55.33680555555555]0.94096001
3-way match, invoice after GR104pooled_bootstrap[21.26388888888889, 80.1859375]0.92388600.932692104
3-way match, invoice after GR104category_bootstrap[21.26388888888889, 82.90208333333334]0.9106200.932692104
3-way match, invoice after GR104semi_markov[17.739583333333332, 94.0032986111111]0.9409600.942308104
3-way match, invoice before GR1652pooled_bootstrap[21.26388888888889, 80.1859375]0.92388600.9255451652
3-way match, invoice before GR1652category_bootstrap[21.26388888888889, 80.1388888888889]0.92282200.9255451652
3-way match, invoice before GR1652semi_markov[17.166319444444444, 94.6045138888889]0.9409600.9449151652

Calculated figures

OTE-002 computed research figure
Generated from the result JSON. No manually inserted scientific values.

Uncertainty and limitations

Evidence and reproducibility

Acquisition: 2026-11-06T11:24:17.701083+00:00 · Execution: 2026-11-06T12:20:23.643683+00:00.

Scientific fingerprint 5947b4bc8b35778d6c4735b21e43849dcb9ea17767bf8ca53dc7114a4cb5e4cd

Results JSON · Manifest

Complete computed result
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  "experiment": "OTE-002",
  "title": "Digital Twin Calibration & Validation",
  "kind": "COMPUTED RESULT",
  "model_version": "ote-twin-1.0",
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    "3-way match, invoice after GR": 1062,
    "3-way match, invoice before GR": 22822
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  "selected_on_validation_only": "pooled_bootstrap",
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      "documents": 1467,
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          "category": "3-way match, invoice after GR",
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      "models": {
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            "median_relative_error": {
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              "assumption": "Independent seeded simulation replicates conditional on fixed data/model; not total epistemic uncertainty"
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            "p90_relative_error": {
              "mean": 0.037879877821261544,
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      },
      "origin_us": 1538352000000000,
      "horizon_day": 92.0
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  },
  "nominal_interval_coverage": 0.9,
  "split_method": "Q1+Q2calibration,Q3validation,Q4test; entire core case inside quarter; cross-split purchase documents excluded; max3000SHA-selected heldoutcases",
  "time_model": "Observed elapsed transitions; no claim to identified service or waiting durations",
  "arrival_conditioning": "Heldout sampled-cohort arrival times are conditioned on; fixedquarter completions are simulated. This is retrospective distributional validation, not a prospective demand forecast.",
  "limits": [
    "Observed invoice endpoints and quarter containment create selection bias; results do not validate all251734cases or future periods.",
    "Only2calibration and1test 2-way matching cases: insufficient evidence, regardless of numerical fit.",
    "A semi-Markov model may lose path dependence and perform worse than whole-trace bootstrap; all results are reported.",
    "Simulation CIs condition on fitted model and fixed data; separate purchase-document bootstrap assumes cluster exchangeability.",
    "A90percent marginal duration interval is evaluated for coverage; a successful mean fit does not imply individual case prediction calibration.",
    "Administrative SRM events excluded only from the model projection; complete observed reconstruction remains unchanged."
  ],
  "results_sha256": "5947b4bc8b35778d6c4735b21e43849dcb9ea17767bf8ca53dc7114a4cb5e4cd"
}