Question 6 of 7: Work Sampling — Purpose, a Standard-Time Application, and Sampling Accuracy

Question 6: Work Sampling — Purpose, a Standard-Time Application, and Sampling Accuracy (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) Basic Purpose and Applications of Work Sampling

Work sampling estimates the proportion of time spent by a worker, machine, or group in defined activity categories (working, idle, on allowance, waiting for material) by taking a large number of instantaneous, randomly timed observations, rather than by continuously timing a single cycle with a stopwatch. Its basic purpose is to obtain a statistically reliable estimate of an activity proportion at a fraction of the observer cost and worker intrusion of continuous stopwatch study, and it applies well precisely where continuous timing is impractical.

Its applications include: (1) measuring machine or labour utilization across a shift or department; (2) determining the empirical size of personal, fatigue and delay allowances directly from observed idle categories, rather than assuming a traditional fixed percentage; (3) establishing time standards for long-cycle, irregular or group work by combining the observed working proportion with a performance rating and an output count, exactly as done in part (ii) below; (4) measuring the percentage of time spent on each of several jobs in a mixed-work or indirect-labour environment; and (5) auditing existing standards for method drift without the cost of a full re-study.

(ii) Standard Time by Work Sampling — Lathe Operation

Given.

Find. The standard time for the operation, in min./pc.

Approach. Convert the idle-observation count to a working percentage, apply it and the average rating to the day’s total time to get the day’s normal time, divide by output to get normal time per piece, then apply the 15% allowance.

1. Percentage of time working. $\%\text{working}=\dfrac{N-\text{idle}}{N}=\dfrac{150-50}{150}=\boxed{66.67\%}$.
2. Normal time per piece. $NT=\dfrac{(\text{total time})\times(\%\text{working})\times(\text{rating})}{\text{pieces produced}}=\dfrac{480(0.6667)(1.50)}{250}=\dfrac{480}{250}=\boxed{1.92\text{ min/pc}}$ (the working-time fraction and the rating multiply to exactly 1.0 here: $0.6667\times1.50=1.0$, so normal time per piece reduces to total time / pieces).
3. Standard time. $ST=NT(1+A)=1.92(1.15)=\boxed{2.208\text{ min/pc}}$.

(iii) Relative and Absolute Accuracy of Operator Idle Time (99% Confidence)

Given. Day-2 observations $N_2=300$; operator found idle 75 times; confidence level 99% ($z=2.576$).

Find. The absolute and relative accuracy of the estimated proportion of idle time.

Approach. Each observation is a Bernoulli trial (idle / not idle), so the count of idle observations is binomial; with $N_2p$ and $N_2(1-p)$ both well above 5, the normal approximation applies and the standard proportion confidence-interval formula gives the absolute accuracy directly, with the relative accuracy obtained by dividing by $p$.

1. Sample proportion idle. $p=\dfrac{75}{300}=\boxed{0.25}$ (25%).
2. Absolute accuracy. $S_{abs}=z\sqrt{\dfrac{p(1-p)}{N_2}}=2.576\sqrt{\dfrac{0.25(0.75)}{300}}=2.576\sqrt{0.000625}=2.576(0.025)=\boxed{0.0644}$, i.e. $\pm 6.44$ percentage points.
3. Relative accuracy. $S_{rel}=\dfrac{S_{abs}}{p}=\dfrac{0.0644}{0.25}=\boxed{0.2576}$, i.e. $\pm 25.76\%$ of the estimated idle proportion itself.