Inspection cell virtual operating trial
Executed 800 synthetic operating shifts and 500 independent holdout shifts with batching, absence, slower service and overtime clearance. Every refused, carried and unfinished job remains counted.
Methods and declared inputs
The original workload is reused with five conditions: reference; five-minute arrival batches; a two-hour worker-0 absence; service times increased 40%; and all three stressors combined. Forty seeds, 8100 through 8139, are generated independently. The four staffing/dispatch policies within a condition receive identical pre-generated jobs.
Batches move each arrival to the beginning of its five-minute interval. This preserves the offered job count and service draws but deliberately changes the temporal pattern. It is a stress input, not an inferred factory distribution.
WIP remains 24 jobs, including work in process, waiting and rework delay. Two or three inspectors use FIFO or shortest estimated service. Class estimates do not see actual sampled durations. Absence starts after any active job finishes, just like the existing deferred-break semantics; it is not an abrupt interrupted-service model.
Arrivals stop after eight hours. Staff continue for at most two hours to clear admitted backlog. The study records completion by eight hours, backlog, refusal, overtime and uncleared work. If work remains at ten hours, clearance is censored at two hours and fails the service screen.
Selected operating policy is FIFO with three inspectors for reference or batched arrivals, four for a known two-hour absence or 40% slower service, and five for the combined case. This is a capacity reserve policy, not a minimum-cost staffing claim. It was evaluated on 100 new seeds per condition, disjoint from policy-selection runs. The acceptance criterion is a two-sided exact 95% upper bound of at most 10% on a shift missing the declared service screen.
The illustrative service screen requires <=1% refused arrivals, <=30 minutes clearance overtime, no uncleared work and <=15 minutes empirical 95th-percentile waiting among detailed jobs. This is an analyst-defined comparison criterion, not a customer service agreement. A policy can raise total completions while making long-job waiting worse.
Mean intervals are Student-t nominal 95% intervals across 40 shifts. Paired differences use the same seed before computing intervals. Exact binomial intervals describe a shift missing the full screen. These intervals capture Monte Carlo variation under the stated inputs, not uncertainty about real demand or service distributions.
Executed cases
| condition | policy | mean_done_8h | mean_backlog_8h | mean_refused | screen_failures | screen_risk_95pct |
|---|---|---|---|---|---|---|
| reference | 2 FIFO | 254.88 | 1.15 | 0.12 | 26/40 | 48.3% to 79.4% |
| reference | 3 FIFO | 255.22 | 0.93 | 0.0 | 0/40 | 0.0% to 8.8% |
| reference | 2 estimated SPT | 255.03 | 1.12 | 0.0 | 36/40 | 76.3% to 97.2% |
| reference | 3 estimated SPT | 255.22 | 0.93 | 0.0 | 4/40 | 2.8% to 23.7% |
| five_minute_batches | 2 FIFO | 255.7 | 0.33 | 0.12 | 29/40 | 56.1% to 85.4% |
| five_minute_batches | 3 FIFO | 256.02 | 0.12 | 0.0 | 0/40 | 0.0% to 8.8% |
| five_minute_batches | 2 estimated SPT | 255.9 | 0.25 | 0.0 | 38/40 | 83.1% to 99.4% |
| five_minute_batches | 3 estimated SPT | 255.97 | 0.17 | 0.0 | 2/40 | 0.6% to 16.9% |
| two_hour_absence | 2 FIFO | 244.18 | 1.15 | 10.82 | 40/40 | 91.2% to 100.0% |
| two_hour_absence | 3 FIFO | 255.22 | 0.93 | 0.0 | 3/40 | 1.6% to 20.4% |
| two_hour_absence | 2 estimated SPT | 252.0 | 1.12 | 3.02 | 40/40 | 91.2% to 100.0% |
| two_hour_absence | 3 estimated SPT | 255.22 | 0.93 | 0.0 | 12/40 | 16.6% to 46.5% |
| service_plus_40pct | 2 FIFO | 248.6 | 3.3 | 4.25 | 40/40 | 91.2% to 100.0% |
| service_plus_40pct | 3 FIFO | 254.7 | 1.43 | 0.03 | 5/40 | 4.2% to 26.8% |
| service_plus_40pct | 2 estimated SPT | 251.12 | 4.15 | 0.88 | 40/40 | 91.2% to 100.0% |
| service_plus_40pct | 3 estimated SPT | 254.72 | 1.43 | 0.0 | 21/40 | 36.1% to 68.5% |
| combined_stress | 2 FIFO | 221.25 | 2.58 | 32.33 | 40/40 | 91.2% to 100.0% |
| combined_stress | 3 FIFO | 254.38 | 0.45 | 1.32 | 33/40 | 67.2% to 92.7% |
| combined_stress | 2 estimated SPT | 229.78 | 5.33 | 21.05 | 40/40 | 91.2% to 100.0% |
| combined_stress | 3 estimated SPT | 255.38 | 0.4 | 0.38 | 39/40 | 86.8% to 99.9% |
Acceptance checks
| id | description | expected | observed | passed | method |
|---|---|---|---|---|---|
| replications | Full virtual operations experiment executed | 800 | 800 | True | 5 conditions x 4 policies x 40 independent matched seeds |
| balances | All jobs and time-area identities remain accounted for | True | True | True | Check every simulation for job count, queue-area, WIP-area and capacity balances |
| backlog | End-of-shift backlog is carried into clearance | 8 h completed + backlog = admitted for all runs | True | True | Inspect each job finish time, not just the final aggregate |
| stress | Combined adverse inputs increase regular-shift backlog | Mean combined-stress backlog > reference for 2 FIFO | {'reference': 1.15, 'stress': 2.575} | True | Same declared policy; batch arrivals, 40% slower service and a 2 h absence |
| third-worker | Additional staff reduces stress backlog | 3 FIFO mean backlog < 2 FIFO | {'two': 2.575, 'three': 0.45} | True | Matched arrival/service/rework streams, same WIP limit |
| service-screen | Screen identifies adverse operational conditions | At least one shift misses declared screen | 488 | True | Reject >1% arrivals, >30 min clearance, >15 min detailed-job tail wait or unfinished at horizon |
| selected-policy | Selected FIFO staffing plan passes independent holdout risk criterion | Each condition upper 95% risk <= 10% | [{'condition': 'reference', 'staff': 3, 'misses': 0, 'shifts': 100, 'lower': 0.0, 'upper': 0.03621669264517641, 'meets_10pct_upper_bound': True}, {'condition': 'five_minute_batches', 'staff': 3, 'misses': 0, 'shifts': 100, 'lower': 0.0, 'upper': 0.03621669264517641, 'meets_10pct_upper_bound': True}, {'condition': 'two_hour_absence', 'staff': 4, 'misses': 0, 'shifts': 100, 'lower': 0.0, 'upper': 0.03621669264517641, 'meets_10pct_upper_bound': True}, {'condition': 'service_plus_40pct', 'staff': 4, 'misses': 0, 'shifts': 100, 'lower': 0.0, 'upper': 0.03621669264517641, 'meets_10pct_upper_bound': True}, {'condition': 'combined_stress', 'staff': 5, 'misses': 0, 'shifts': 100, 'lower': 0.0, 'upper': 0.03621669264517641, 'meets_10pct_upper_bound': True}] | True | 100 disjoint seeds per condition; 3 regular, 4 for absence or slow service, 5 for combined stress |
| zero-failure-risk | Zero observed failures do not imply zero probability | 0 < upper bound < 0.1 | 0.08809730287880237 | True | Two-sided exact binomial 95% interval for 0/40 failures |
| capacity-bound | One nominal inspector has insufficient mean work budget | Offered-work fraction > 1 for one, < 1 for two | [{'staff': 1, 'expected_arrivals': 253.33333333333334, 'expected_service_per_job_s': 124.784, 'available_regular_service_s': 25200, 'nominal_offered_work_s': 31611.94666666667, 'offered_work_fraction': 1.2544423280423282}, {'staff': 2, 'expected_arrivals': 253.33333333333334, 'expected_service_per_job_s': 124.784, 'available_regular_service_s': 50400, 'nominal_offered_work_s': 31611.94666666667, 'offered_work_fraction': 0.6272211640211641}] | True | Independent expected workload = arrivals * mean service * sum p^visit; excludes randomness/burst penalty |
Scope of the evidence
This completes a synthetic operating trial. No actual production shift, time study, staffing decision or throughput gain is claimed.
The experiment includes one deferred absence and a two-hour clearance window. It does not model multi-day carryover, skill differences, inspection errors, physical space or economic cost.
The service screen is deliberately explicit and can fail. Monte Carlo confidence does not certify input realism, and repeated scenario comparisons are not adjusted for multiple testing.
Reproduce
python -m pip install -r requirements.txt python run.py
Acceptance matrix · Evidence record and source hashes · Original analysis
Selected FIFO policy and staffing reserves
Independent selected-policy acceptance
500 independent holdout shifts
Exact service-screen failure intervals
Matched two-versus-three inspector comparison