Question 5 of 8: Time Standards and Incentive Pay from a Short Study

Question 5: Time Standards and Incentive Pay from a Short Study (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.

Given. An observation period of 45 minutes yielding 30 finished units; performance rating 90 percent; allowance for rest and personal time 12 percent; base wage rate $6.00 per hour; an eight-hour day in which 300 units were produced; a 100-percent-participation premium plan.

Find. (a) the normal time per unit, (b) the standard time per unit, and (c) the day's earnings of a worker who produced 300 units in eight hours.

Approach. Reduce the study to an observed time per unit, rate it to normal, add the allowance to reach standard, then convert the day's output into standard hours earned and pay the larger of the guaranteed day rate and the earned amount.

1. Part (a) — reduce the study to an observed time per piece. The study is a production study rather than an element-by-element time study, so the observed time is simply the observation period divided by the output: $$OT=\frac{45\ \text{min}}{30\ \text{units}}=1.50\ \text{min per unit}$$ This is the pace of the particular worker on the particular day, and it cannot be used as a standard until it has been rated.
2. Apply the performance rating. Normal time is the observed time multiplied by the rating, $NT=OT\times R$, so a worker judged to be moving at 90 percent of normal pace should have taken proportionally less time at normal pace: $$NT=1.50\times0.90=\boxed{1.35\ \text{min per unit}}$$ The direction matters. Rating below 100 percent reduces the standard, because the observed operator was working more slowly than a qualified operator would.
3. Part (b) — add the allowance. The firm's 12 percent covers rest and personal time, so the standard time is $$ST=NT\,(1+A)=1.35\,(1.12)=\boxed{1.512\ \text{min per unit}}$$ equivalent to a standard output of $60/1.512=39.7$ pieces per hour, or 317.5 pieces in an eight-hour day. If the firm instead defines its allowance as a percentage of the working day rather than of normal time, the equivalent standard is $ST=NT/(1-A)=1.35/0.88=1.534$ min per unit, about 1.5 percent higher; the plant's own convention governs and should be recorded with the standard.
4. Part (c) — convert the day's output into standard hours. Under a measured-daywork or premium plan, output is paid in the standard hours it represents: $$H_{e}=\frac{300\times1.512}{60}=\frac{453.6}{60}=7.56\ \text{standard hours}$$ against 8.00 clock hours worked. The worker's performance index is therefore $300/317.5=94.5$ percent of standard, so the day fell just short of the standard pace.
5. Pay the plan. A 100 percent premium plan credits the operator with the whole of the time saved, so earnings are the standard hours earned at the base rate, subject to the guaranteed base day that every such plan carries: $$E=\max\left(H_{w}r,\;H_{e}r\right)=\max\left(8.00\times\$6.00,\;7.56\times\$6.00\right)=\max\left(\$48.00,\;\$45.36\right)$$ The earned amount of $45.36 falls below the guaranteed day, so the worker is paid $$\boxed{\$48.00\ \text{for the day}}$$ and no premium is earned. Had the plan carried no guarantee — which is unlawful in every Canadian jurisdiction, since employment-standards legislation requires at least the minimum wage for hours worked — the pay would have been the earned $45.36. Had the worker instead produced 350 units, 8.82 standard hours would have been earned and the day's pay would have risen to $52.92.