Question 6 of 7: Computerized Work Sampling, Operator Acceptance, and Required Sample Size

Question 6: Computerized Work Sampling, Operator Acceptance, and Required Sample Size (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) Applications of Computerized Work Sampling

Computerizing work sampling removes the two biggest practical costs of a manual study — a dedicated observer and hand-tallied data — and opens applications a manual study could not economically reach: continuous, unattended monitoring of machine or operator utilization across an entire shop floor (or multiple shifts and sites) from a single system, automatic generation of statistically randomized observation timings so the schedule is genuinely unpredictable to the operator, real-time dashboards of utilization and downtime causes feeding directly into ERP/production-planning systems, simultaneous sampling of many stations that a single human observer could never cover, automatic computation of running confidence intervals so the study can be stopped exactly when the required accuracy (part iii) is reached rather than over- or under-sampling, and extension of work sampling into office, service and administrative settings where a visible human observer would be impractical or intrusive.

(ii) Selling Work-Sampling Validity to the Operator

An operator unfamiliar with statistics is likely to distrust a technique that infers a full-shift percentage from a handful of instantaneous snapshots, so the case is best made with demonstration and analogy rather than formulas. A useful analogy is the opinion poll or quality-control sample the operator already implicitly trusts: just as a pollster does not need to ask every voter to estimate an election result within a known margin of error, work sampling does not need to watch every second of the shift to estimate a percentage within a stated accuracy — the mathematics (part iii) is the same in both cases. Concretely: (1) run a short pilot study together and show the operator that the sampled percentage tracks what they themselves report about their idle/working time; (2) explain, plainly, that individual instantaneous observations are not being used to judge or discipline them, only pooled statistically; (3) involve the operator (or their representative/union) in agreeing the random observation schedule and idle/working categories in advance, so nothing about the method feels imposed; and (4) present the final results with their stated confidence level and accuracy openly, so the claim being made (“idle time is X% ± the stated accuracy, 95% of the time”) is transparent rather than presented as an unquestionable number.

(iii) Required Sample Size for ±10% Accuracy at 95% Confidence

Given.

Find. The total number of random observations $n$ needed to estimate the idle-time percentage to ±10% accuracy at 95% confidence.

Approach. Use the trial proportion as the best estimate of $p$, then solve the work-sampling sample-size relation $n=z^2(1-p)/(s^2p)$, which sets the standard error of the estimated proportion so that $z$ standard errors equal the required absolute accuracy $sp$.

1. Trial proportion idle. $p=30/150=\boxed{0.20}$ (20% idle).
2. Sample-size relation. Requiring $z\sqrt{p(1-p)/n}=sp$ and solving for $n$ gives $n=\dfrac{z^2(1-p)}{s^2p}$.
3. Substitute. $n=\dfrac{(1.96)^2(1-0.20)}{(0.10)^2(0.20)}=\dfrac{3.8416(0.80)}{0.01(0.20)}=\dfrac{3.0733}{0.002}=\boxed{1536.6}$.
4. Round up. A sample size must be a whole number of observations and must at least meet the accuracy requirement, so round up: $n=\boxed{1537\text{ observations}}$ — 1387 more than the 150 already taken.