23-Ind-A2 Analysis and Design of Work · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2016 — 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.
Reference texts: Niebel & Freivalds, Niebel’s Methods, Standards, and Work Design (13th ed.) — operations analysis and process/flow charting, motion economy, multiple-machine assignment, stopwatch time study, performance rating and allowances, predetermined time systems (MTM/MOST), work sampling, and 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 a worker, machine, or group of workers/machines spends in defined categories of activity — working, idle, on personal allowance, waiting for material, and so on — 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 these activity proportions — machine or labour utilization, the empirically observed size of delay and personal-allowance time (feeding directly into Question 3(i)'s allowance discussion), 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 or non-repetitive 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 or machine is either in the category of interest (a "success," probability $p$) or not (probability $1-p$), and successive 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 confidence-interval and required-sample-size equations built from $p(1-p)/n$, directly analogous to the $s^2/n$ term used for the continuous-time stopwatch calculation of Question 3(ii).
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 use the familiar normal-based interval $p\pm z\sqrt{p(1-p)/n}$ to state a required sample size for a target precision, or to report the precision actually achieved by a completed study, rather than working with the exact (and far less convenient) binomial distribution directly.
Advantages of work sampling: a single observer can study several operators or machines simultaneously, since only an instantaneous glance is needed at each round; it is far less intrusive and fatiguing for the worker than being continuously followed with a stopwatch, reducing behaviour changes caused by observation itself; it is well suited to long-cycle, irregular, or non-repetitive work (indirect labour, maintenance crews, group operations) where continuous stopwatch timing is impractical; observations can be spread over days or weeks, averaging out day-to-day variability that a short continuous study might miss; and it typically requires less specialized analyst training than rating an operator's pace in real time.
Disadvantages of work sampling: it does not directly provide an element-by-element breakdown of a cycle the way a stopwatch study does, and is therefore less suited to setting a fine-grained standard for a short, repetitive job; achieving a tight confidence interval requires a very large number of observations (per the work-sampling sample-size formula $n=z^2p(1-p)/\ell^2$, the categorical counterpart of the stopwatch formula used in Question 3(ii)(b)), which can make the total observation effort, and the calendar time to collect it, larger than a stopwatch study would need; it does not itself measure performance rating, so an additional rating step is still required if the study is used to set a time standard; and because observations are spread over an extended period, the study is more exposed to conditions or method changes occurring mid-study, which can bias the result if not controlled for.
