You are the safety lead for a crew of six on an eight-hour shift. One area is loud — a maintenance job or a machine — and the rest of the plant hums at lower levels. Every ten minutes the model adds each worker's noise dose by the OSHA permissible-exposure rule and the NIOSH recommended limit, counts the protection their hearing protectors really give, and tallies what the crew produces. Educational simulation only — not legal, compliance or medical advice.
What you will learn
How a noise dose adds up: every 5 dB (OSHA) or 3 dB (NIOSH) more halves the time a person may stay.
Why a protector's label overstates its protection, and why a few unworn minutes in loud noise cancel most of it.
The hierarchy of controls in practice: quiet the source first, then limit time by rotation, then protect the ear.
Simulator
Time 0 min
·Worker, dose below 50 %
!Worker, dose 50–100 %
‼Worker, dose over 100 %
◉Has a hearing protector
≋Area at 95 dBA or more
▭Enclosure (installed / being installed)
Controls
Who fills the loud posts. Fixed = the same people all shift; hourly = the loud posts pass along the crew every hour; dose-based = each hour the lowest-dose workers take them.
A maintenance job progresses with at most two people at the work face; a machine produces per operator. Everyone there is exposed.
Each worker spends 10 minutes per hour in the quiet room, staggered. Less exposure, fewer hands.
Raises the share of time protectors are actually worn from about 80 % to about 97 %.
Stops the source at once. The loud crew moves to the line; the job or the machine's output waits.
Panels around the source cut it by 10 dB after a 60-minute installation; work inside runs about 10 % slower.
Arrives 30 minutes later with a fresh dose. Crew up to eight.
Indicators
Highest OSHA PEL dose
0%
normal
Highest NIOSH dose at the ear
0%
normal
Loud job completed
100%
normal
Production vs. shift plan
0%
critical
Highest 8-h TWA (OSHA, 80-dB threshold)
40.0 dBA
Highest 8-h TWA at the ear (NIOSH)
40.0 dBA
Projected end-of-shift PEL dose (current pace)
0 %
Workers over 100 % PEL dose
0
Level at the loud task
85.0 dBA
Level at the line
82.0 dBA
Output rate
0 units/h
Crew on shift
6
Workers with protectors
0
Enclosure installation left
-1 min
Trend
Crisis scenarios
Level 1 · Loud maintenance job
At 07:30 a hopper lining must be chipped out and replaced: three worker-hours at 104 dBA, done this shift, and only two people fit at the work face. Enclosure panels cannot be set up inside the hopper, and no hearing protectors have been issued yet this morning. The line must keep running. Nobody may end the shift above 100 % of the OSHA dose, and the ears must stay inside the NIOSH limit too.
Highest OSHA PEL dose ≤ 100 % at the end
Highest NIOSH dose at the ear ≤ 100 %
Maintenance job finished this shift
Production ≥ 95 % of the shift plan
Level 2 · Hearing-protector shortage
The earplug delivery did not arrive and there are only two pairs of earmuffs on site. The forming press runs all shift at 96 dBA with two operators, and the enclosure panels are on another job. Plan the shift so that nobody exceeds the OSHA dose or the NIOSH ear limit — and production still meets plan.
Highest OSHA PEL dose ≤ 100 % at the end
Highest NIOSH dose at the ear ≤ 100 %
Production ≥ 95 % of the shift plan
Level 3 · Production push, new loud machine
A new cut-off machine starts at 07:30 to meet a raised plan. It measures 103 dBA at the operator position and needs two operators. Foam earplugs are on hand. Meet the plan without anyone exceeding the OSHA dose or the NIOSH ear limit.
Highest OSHA PEL dose ≤ 100 % at the end
Highest NIOSH dose at the ear ≤ 100 %
Production ≥ 95 % of the raised plan
Basis — the model behind the numbers
Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.
Sound levels add as energies: two equal sources are 3 dB louder than one. Each area hears its own background plus the loud source, reduced by distance and walls.
L_area = 10·log10(10^(L_bg/10) + 10^((L_src − spill − IL)/10)) + N(0, 1 dB)[6]Assumption: area backgrounds, spill-over, enclosure insertion loss and lead time, wearing compliance, production rates and level variation are illustrative values for a generic plant; the dose rules themselves are the published ones.
OSHA dose: each period C at level L uses up C/T of the day, where T halves every 5 dB above 90 dBA. A total of 100 % is the permissible exposure limit.
T = 8 / 2^((L − 90)/5) h; D = 100·Σ Cᵢ/Tᵢ (levels ≥ 90 dBA for the PEL, ≥ 80 dBA for the action level)[1][2][3]
Dose and 8-hour time-weighted average are the same information: 50 % = 85 dBA (action level for a hearing conservation program), 100 % = 90 dBA.
NIOSH recommended limit: 85 dBA for 8 hours, halving the time every 3 dB — the equal-energy rule. At 100 dBA that is 15 minutes.
T = 8 / 2^((L − 85)/3) h (80–140 dBA integrated); TWA_NIOSH = 10·log10(D/100) + 85[4]
Protector labels are laboratory values. OSHA subtracts 7 dB for A-weighted readings and then halves the rest; wearing plugs and muffs together adds only about 5 dB to the better one.
Unworn minutes count at the full level. Because energy adds, a protector worn 80 % of the time in 100 dBA gives far less than its rating.
ear dose per tick = w·r(L − A) + (1 − w)·r(L); w ~ N(c, 0.05) clipped to [0,1], c = 0.80 (0.97 enforced)[7][4]Assumption: area backgrounds, spill-over, enclosure insertion loss and lead time, wearing compliance, production rates and level variation are illustrative values for a generic plant; the dose rules themselves are the published ones.
An enclosure lowers the level for everyone near the source; rotation and breaks only share or shorten the time spent there.
enclosure: L_src − 10 dB after 60 min, task productivity × 0.9; rotation/breaks change Cᵢ, not L[5][6]Assumption: area backgrounds, spill-over, enclosure insertion loss and lead time, wearing compliance, production rates and level variation are illustrative values for a generic plant; the dose rules themselves are the published ones.
Production follows crew placement: posts on the line and at the machine produce, the quiet room does not.
output = Σ workers rate(area)·(1 + 0.1·z); loud job progress = min(n_loud, 2) × 10 minAssumption: area backgrounds, spill-over, enclosure insertion loss and lead time, wearing compliance, production rates and level variation are illustrative values for a generic plant; the dose rules themselves are the published ones.
Other operating constants used by the model.
backgrounds: loud area 85, line 82, assembly 78, quiet room 62 dBA · source spill −20 dB at the line, −26 dB at assembly, −45 dB in the quiet room · line 3 posts at 1 unit per 10 min, assembly 0.5 · 10-min quiet break per hour, staggered · extra worker arrives after 30 min, crew ≤ 8Assumption: area backgrounds, spill-over, enclosure insertion loss and lead time, wearing compliance, production rates and level variation are illustrative values for a generic plant; the dose rules themselves are the published ones.
Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.
D. A. Bies, C. H. Hansen, C. Q. Howard — Engineering Noise Control (decibel addition, enclosures and barriers, insertion loss) — CRC Press, 5th ed., 2017
E. H. Berger et al. (eds.) — The Noise Manual, 5th ed. (hearing protector field performance; effect of wearing time on effective attenuation) — American Industrial Hygiene Association, 2003