22-Mec-B4 Integrated Manufacturing Systems · May 2015

Question 2 of 7: Time Study, Standard Time and Incentive Earnings

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Exams, May 2015 — 07-Mec-B4 Integrated Manufacturing Systems. Three hours, open book, any non-communicating calculator permitted. Seven questions are printed; any five constitute a complete paper and only the first five appearing in the answer book are marked, each of equal value (20 marks). All seven are solved here, because the complete set is the study resource. Questions 5, 6 and 7 are explicitly essay questions, in which the examiners award marks for clarity and organisation as well as content.

Reference texts. E. S. Buffa and R. K. Sarin, Modern Production / Operations Management, 8th ed. (requirements schedules, economic lot size, economic order interval, part-period balancing, production planning); R. B. Chase and F. R. Jacobs, Operations and Supply Chain Management, 16th ed. (demand components, adaptive forecasting, aggregate planning, statistical quality control); B. W. Niebel and A. Freivalds, Methods, Standards, and Work Design, 13th ed. (time study, performance rating, allowances, wage incentive plans); D. C. Montgomery, Introduction to Statistical Quality Control, 8th ed. (Shewhart charts, process capability); M. P. Groover, Automation, Production Systems, and Computer-Integrated Manufacturing, 5th ed. (process planning, CAPP, machinability data systems, maintenance); S. Nahmias and T. L. Olsen, Production and Operations Analysis, 7th ed. (forecasting, aggregate planning).

Question 2: Time Study, Standard Time and Incentive Earnings (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. One continuous observation period, the output achieved in it, the analyst’s pace rating, the firm’s allowance, and the day’s output and wage terms used in part (c).

Given data
Quantity	Symbol	Value
Observation period	t	45 min
Units produced in that period	N	30
Performance rating	R	90 per cent
Rest and personal allowance	A	12 per cent
Day’s output, part (c)	N_d	300 units in 8 h
Base wage rate	w	$6.00 per hour
Incentive plan	—	100 per cent premium

Find. The normal time and the standard time per unit, and the worker’s gross pay for a day on which 300 units were produced under a 100 per cent premium plan.

Figure 2.1 — the two adjustments that turn a stopwatch reading into a time standard. Rating (90 per cent) pulls the observed time down because this operator was working slower than normal pace; the 12 per cent allowance then pushes it back up to cover rest and personal time. The two nearly cancel here, which is coincidence, not a rule.

Approach. Convert the observation to an observed time per unit, level it to normal pace with the rating, inflate it by the allowance to obtain the standard time, and then use the standard time to convert the day’s output into standard hours earned, which is the quantity a 100 per cent premium plan actually pays for.

Observed (select) time per unit. The whole observation is one continuous run, so the observed time per unit is simply the period divided by the output:$$OT=\frac{t}{N}=\frac{45\ \text{min}}{30\ \text{units}}=1.500\ \text{min/unit}$$
Part (a) — normal time. Rating levels the observed time to the pace of a qualified operator working without incentive. A rating below 100 per cent means this operator was working more slowly than normal, so the observed time is reduced:$$NT=OT\times R=1.500\times 0.90=\boxed{1.350\ \text{min per unit}}$$
Part (b) — standard time. The allowance adds back the unavoidable non-productive time. Applying it as a percentage of normal time, which is the convention the phrase “allowances in the firm are 12 percent” carries in Niebel’s treatment:$$ST=NT(1+A)=1.350(1.12)=\boxed{1.512\ \text{min per unit}}$$equivalently 39.7 pieces per hour, or 317.5 pieces in an eight-hour day.

Before turning to pay it is worth stating the standard as a daily output, because that is the number the incentive plan is measured against:$$N_{std}=\frac{480\ \text{min}}{1.512\ \text{min/unit}}=317.5\ \text{units per eight-hour day}$$The worker in part (c) produced 300 units, which is $300/317.5=94.5$ per cent of standard — a fair day’s work, but below the standard the plan pays a premium for.

Part (c) — standard hours earned. Under a 100 per cent premium plan the operator is credited with one hour of pay for each standard hour of work produced, so output is first converted to standard hours:$$H_{e}=\frac{N_{d}\times ST}{60}=\frac{300\times 1.512}{60}=7.56\ \text{standard hours}$$
Apply the plan, including its guaranteed base. Every 100 per cent premium plan guarantees the base day rate to a worker who does not reach standard, so the day’s pay is the greater of the guaranteed day and the standard hours earned:$$\text{Pay}=\max\left(8w,\;H_{e}w\right)=\max\left(8(\$6.00),\;7.56(\$6.00)\right)=\max(\$48.00,\;\$45.36)=\boxed{\$48.00}$$

The interpretation matters as much as the arithmetic. The worker missed standard by 17.5 units and therefore earns no premium at all; the day’s pay is the guaranteed base of $48.00, and the firm absorbs $2.64 of unearned wage. Had the same worker produced 340 units, standard hours earned would be 8.57 and the day’s pay $51.42, the extra $3.42 being the premium the plan exists to pay.

Final results — Question 2
Quantity	Value
Observed (select) time	1.500 min per unit
(a) Normal time	1.350 min per unit
(b) Standard time	1.512 min per unit
Standard output, eight-hour day	317.5 units
Performance on 300 units	94.5 per cent of standard
Standard hours earned	7.56 h
Incentive earnings alone	$45.36
Guaranteed base day	$48.00
(c) Day’s pay	$48.00

Check: two conventions are declared here, per the paper’s Note 1. First, the 12 per cent allowance is applied as a percentage of normal time, giving 1.512 min. The alternative convention treats the allowance as a fraction of the total workday, $ST=NT/(1-A)=1.350/0.88=1.534$ min per unit, which lowers standard output to 313.0 units and standard hours earned to 7.67 h — still below the guaranteed day, so part (c) is unchanged at $48.00. Second, the 100 per cent premium plan is taken to guarantee the base day rate, which is both the textbook form of the plan and the minimum permitted under Canadian employment-standards legislation. Without a guarantee the answer to (c) would be $45.36.

Concept & Theory

Topic. Stopwatch time study: rating, allowances and the wage incentive that rides on the resulting standard.

Key relations. Observed time $OT=t/N$; normal time $NT=OT\times R$; standard time $ST=NT(1+A)$ (allowance on normal time) or $ST=NT/(1-A)$ (allowance on the workday); standard hours earned $H_{e}=N_{d}\,ST/60$; earnings under a 100 per cent premium plan $E=\max(H_{\text{shift}}w,\;H_{e}w)$.

Why this works. A stopwatch measures one operator on one day, and neither the operator’s pace nor the day’s interruptions are properties of the job. Rating removes the first by scaling the reading to a defined normal pace, so that a slow operator and a fast one studied on the same job converge to the same normal time. The allowance restores the second, because a standard that assumed continuous work would be unattainable over a shift. Only after both corrections is the number a property of the method rather than of the study, which is what makes it fair to pay against and legitimate to use for capacity planning and costing.

Common pitfall. Applying the rating in the wrong direction. A 90 per cent rating means the operator was slower than normal, so the observed time must come down, not up; dividing by 0.90 instead of multiplying inflates the standard by 23 per cent and would hand this worker an unearned premium. The second trap is forgetting the guaranteed base in part (c) and reporting the raw incentive earnings.

Source. Niebel & Freivalds, Methods, Standards, and Work Design, 13th ed., §§9–11 (time study, performance rating, allowances) and ch. 17 (wage payment and premium plans); Chase & Jacobs, Operations and Supply Chain Management, 16th ed., appendix on job design and work measurement.

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