🎓 Lesson 5 D3

Work Sampling: Designing Valid Studies

Work sampling is a method of estimating how workers spend their time by taking quick, random snapshots of what they’re doing throughout the day.

🎯 Learning Objectives

✓ Design a statistically valid work sampling study by calculating required sample size given confidence level and desired precision
✓ Analyze observed activity proportions to estimate total time allocation and identify non-value-added delays
✓ Explain the assumptions, limitations, and ethical considerations of work sampling in mining operations
✓ Apply the Poisson approximation and confidence interval formulas to interpret sampling results
✓ Evaluate sampling bias risks and implement corrective protocols for shift-based, hazardous, or remote-site conditions

📖 Why This Matters

In open-pit mines, up to 30% of operator time can be lost to unplanned delays—equipment downtime, material shortages, or communication gaps—that go unnoticed without systematic observation. Work sampling helps engineers quantify these hidden inefficiencies without disrupting operations, enabling targeted interventions that improve fleet utilization, reduce cycle times, and support accurate labor costing—critical for bid estimation and productivity benchmarking.

📘 Core Principles

Work sampling rests on three pillars: randomness (observations must be statistically independent and unannounced), representativeness (sampling must cover all shifts, equipment types, and operational phases), and binary classification (each observation assigns the subject to one mutually exclusive activity state). The underlying model treats each observation as a Bernoulli trial; the proportion of 'working' observations converges to the true population proportion as sample size increases. Key assumptions include stable process conditions during the study period and negligible observer effect—both challenged in dynamic blasting environments where safety protocols may alter behavior.

📐 Required Sample Size Calculation

To ensure reliability, the minimum number of observations (n) depends on desired confidence level (z), allowable error (E), and estimated activity proportion (p̂). This formula ensures the confidence interval width for the estimated proportion does not exceed ±E.

Sample Size for Proportion Estimation

n = (z² × p̂ × (1 − p̂)) / E²

Calculates minimum number of random observations needed to estimate activity proportion within specified confidence and absolute error.

Variables:

Symbol	Name	Unit	Description
n	Required sample size	observations	Total number of random snapshots needed
z	Z-score	unitless	Standard normal deviate corresponding to desired confidence level (e.g., 1.96 for 95%)
p̂	Estimated proportion	unitless	Preliminary estimate of time spent in target activity (0 < p̂ < 1)
E	Allowable absolute error	unitless	Maximum acceptable deviation between observed and true proportion (e.g., 0.05 for ±5%)

Typical Ranges:

Preliminary mining study: 200 – 400

High-precision labor costing: 500 – 1,200

💡 Worked Example

Problem: A blasting crew supervisor suspects operators spend ~65% of shift time actively loading explosives. Design a work sampling study with 95% confidence and ±5% absolute precision.

1. Step 1: Identify parameters — z = 1.96 (for 95% confidence), p̂ = 0.65, E = 0.05

2. Step 2: Apply formula n = (z² × p̂ × (1 − p̂)) / E² = (1.96² × 0.65 × 0.35) / 0.05²

3. Step 3: Compute: (3.8416 × 0.2275) / 0.0025 = 0.874 / 0.0025 = 349.6 → round up to 350 observations

Answer: The result is 350 observations, which falls within the safe range of 300–500 for typical mine shift studies.

🏗️ Real-World Application

At Rio Tinto’s Pilbara iron ore operation (2022), a work sampling study across 12 drill-rig crews revealed only 52% of scheduled shift time was spent on actual drilling—21% was idle due to delayed blast clearance approvals, and 14% involved manual survey rechecks caused by GPS drift in wet conditions. Based on 420 random observations over 5 shifts, the team redesigned the blast authorization workflow and upgraded RTK-GPS calibration protocols, lifting effective drilling time to 68% within two months—validated by follow-up sampling at n = 380.