23-Ind-A2 Analysis and Design of Work · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2017 — 98-Ind-A2 Analysis and Design of Work. Three-hour, closed-book exam (approved Casio/Sharp calculator only); any five of the seven questions constitute a complete paper and only the first five answered in the answer book are marked — all seven are solved below for completeness. The source prints Question 3's second and third sub-parts both labelled “(iii)”; they are answered here in the marking-scheme order (i)/(ii)/(iii), 8/6/6 marks.
Reference texts: Niebel & Freivalds, Niebel’s Methods, Standards, and Work Design (13th ed.) — operations analysis, workplace/tool design and motion economy, stopwatch time study, performance rating and allowances, predetermined time systems (MTM/MOST), work sampling, wage-incentive and job-evaluation systems.
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.
Work sampling estimates the proportion of time spent by a worker, machine, or group of workers/machines in defined categories of activity (e.g. working, idle, on personal 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 statistically reliable estimates of activity proportions — machine or labour utilization, the empirical size of delay and personal allowances (Question 3(iii)), or the percentage of time spent on each of several different jobs in a mixed-work environment — at a fraction of the observer cost and worker intrusion of continuous stopwatch study, and for situations (long or irregular cycles, group operations, indirect labour) where continuous timing is impractical or prohibitively expensive.
Each individual observation in a work-sampling study is a Bernoulli trial: at the randomly chosen instant, the worker is either in the category of interest (success, probability $p$) or not (failure, probability $1-p$), and the observations are taken independently of one another. The count of “in-category” observations across $n$ independent trials is therefore a binomial random variable, and it is this binomial model — not a continuous-time model — that underlies every work-sampling formula, including the standard sample-size and confidence-interval equations built from $p(1-p)/n$.
The binomial distribution approaches the normal distribution, by the De Moivre–Laplace / Central Limit approximation, once the sample is large enough and $p$ is not too close to 0 or 1 — the conventional rule of thumb is $np\ge5$ and $n(1-p)\ge5$ (some texts use the stricter $np\ge10$). Once that condition holds, work-sampling practitioners can use the familiar normal-based confidence-interval formula $p\pm z\sqrt{p(1-p)/n}$ to state a required sample size for a target precision, or to report the precision actually achieved by a completed study, instead of working with the exact (and much less convenient) binomial distribution directly.
Advantages of work sampling: (1) substantially lower observer cost per study, since observations are brief and can be spread over the analyst’s day rather than requiring continuous attendance; (2) one observer can study several workers or machines simultaneously, which continuous stopwatch timing cannot do; (3) far less worker resistance and “watch consciousness,” because a worker is not visibly being timed continuously; (4) well suited to long-cycle, irregular, or non-repetitive work (maintenance, indirect labour, group activities) where a stopwatch cycle time is hard to even define; and (5) it directly and empirically measures delay/personal/idle percentages instead of relying on a traditionally assumed allowance figure.
Disadvantages of work sampling: (1) it produces a proportion of time in broad categories, not a detailed breakdown of individual therbligs or fine motion elements, so it cannot drive a methods-improvement redesign the way a detailed stopwatch/motion study can; (2) achieving tight precision on a low-frequency category requires a very large number of observations, which can make the total observer-hours comparable to, or exceed, a stopwatch study for that category; (3) results depend on truly random observation times and on correct, consistent category judgement at each instant — a poorly randomized schedule (e.g. always sampling at convenient round times) reintroduces bias; and (4) the analyst still needs training in both the statistical method and the activity-classification scheme to produce a defensible study.
