9.3 Time Study Fundamentals, Performance Rating & Allowance Factors

9.3 Time Study Fundamentals, Performance Rating & Allowance Factors

Work measurement is the industrial engineering discipline tasked with determining the time required by a qualified, well-trained operator, working at a normal pace under standard operating conditions, to complete a specified task. Establishing robust labor standards is fundamental to capacity planning, assembly line balancing, production scheduling, labor cost accounting, and employee incentive compensation.

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1. Direct Stopwatch Time Study Methodology

Direct time study utilizes a stopwatch (electronic or mechanical) to observe and record the elapsed time of operational elements directly on the factory floor.

Element Breakdown Principles

An operation cannot be timed as a single monolithic block. It must be partitioned into distinct elements—short, homogeneous segments of work that have clear beginnings and endpoints. Dividing operations into elements serves critical engineering functions:

1. Isolates Operational Variability: Distinguishes between highly consistent elements and variable, error-prone elements.
2. Separates Operator and Machine Durations: Allows manual handling time (subject to pace rating) to be evaluated separately from machine processing time (fixed by feeds, speeds, and controllers).
3. Facilitates Standard Data Synthesis: Elemental times can be archived into a standard data repository to predict times for future operations.
4. Enhances Rating Accuracy: An observer can evaluate operator pace more objectively over a 15-second element than across a 5-minute cycle.

Guidelines for Establishing Element Boundaries

• Elements should be as short as can be reliably timed by the observer (typically between 0.04 minutes / 2.4 seconds and 0.50 minutes / 30 seconds).
• Breakpoints (Terminal Points): The transition between successive elements must be marked by an unambiguous, sensory breakpoint—preferably an audible or distinct visual event (e.g., the sharp metallic sound of a clamp locking, or the instant fingers release a workpiece).
• Elements must be categorized as regular elements (occurring every cycle) or irregular / periodic elements (occurring once every $N$ cycles, such as changing a deburring blade every 50 parts or clearing chips every 20 parts).

Continuous Timing vs. Snapback Timing

Two classical timing techniques exist for direct stopwatch studies:

Foreign Elements and Outlier Management

A foreign element is an unexpected, non-cyclical event that occurs during the study (e.g., dropping a component, answering a supervisor question, or untangling power cords). The observer logs the foreign element with a letter code, records its duration, and excludes it from the calculation of the regular cycle's average observed time ($OT$).

Outliers must not be deleted arbitrarily. An observation may only be discarded if an identifiable, documented operational abnormality occurred (e.g., raw material defect, tool chatter). If statistical filtering is required, tests such as Dixon's Q-test or Chauvenet's criterion should be applied and documented.

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2. Performance Rating (Pace Rating)

Because operators do not work at the identical pace during an observation, the recorded Average Observed Time ($\bar{x}_{OT}$) must be calibrated to represent the time required by an operator working at a standard, normal pace. This adjustment is termed Performance Rating ($PR$).

Calculating Normal Time ($NT$)

The Normal Time ($NT$) represents the duration an experienced operator requires to execute the element when working at 100% standard pace:

$NT = OT \times PR = \bar{x}_{OT} \times \left( \frac{\text{Rating Percentage}}{100} \right)$

For a multi-element task with $m$ discrete manual elements:

$NT_{\text{cycle}} = \sum_{j=1}^m NT_j = \sum_{j=1}^m \left( \bar{x}_{OT, j} \times PR_j \right)$

The Standard Benchmark Pace (100% Pace)

Methods engineering texts (for example Niebel and Freivalds, Methods, Standards, and Work Design) use classic physical benchmarks to define 100% normal pace:

• Walking Benchmark: Walking unburdened on smooth, level ground at exactly 3.0 miles per hour (4.4 ft/s or 4.83 km/h).
• Card Dealing Benchmark: Dealing a standard 52-card playing deck into four distinct piles (located at the corners of a 1-foot square) in exactly 0.50 minutes (30.0 seconds).
• Pegboard Benchmark: Assembling 30 cylindrical pins into a standard two-handed pegboard in exactly 0.41 minutes (24.6 seconds).

An operator working at 120% pace moves 20% faster than the benchmark, requiring a normal time adjustment of $NT = OT \times 1.20$. Conversely, an operator moving at 80% pace has an adjustment of $NT = OT \times 0.80$.

The Westinghouse Rating System

Developed by the Westinghouse Electric Corporation, this system reduces observer subjectivity by evaluating performance across four independent behavioral categories:

1. Skill: Facility in following a given method, coordination, and rhythm (+0.15 Superskill A1 to -0.22 Poor F2).
2. Effort: The will to work, energy expenditure, and mental focus (+0.13 Excessive A1 to -0.17 Poor F2).
3. Conditions: Temperature, lighting, ventilation, and physical environment affecting the operator (+0.06 Ideal A to -0.07 Poor F).
4. Consistency: Regularity of successive cycle times (+0.04 Perfect A to -0.04 Poor F).

The composite performance rating is computed additively relative to the 1.00 baseline:

$PR = 1.00 + \Delta_{\text{Skill}} + \Delta_{\text{Effort}} + \Delta_{\text{Conditions}} + \Delta_{\text{Consistency}}$

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3. Allowance Factors (PFD Allowances)

An operator cannot sustain 100% normal pace continuously across an entire 8-hour shift without experiencing fatigue, attending to bodily needs, or encountering minor operational delays. Therefore, industrial engineers add Allowances to Normal Time to compute Standard Time ($ST$).

Allowances are partitioned into three primary components, collectively termed PFD (Personal, Fatigue, and Delay) Allowances:

PFD Allowance Architecture
├── Personal Needs Allowance (A_p) [~5% constant; restroom, hydration, hygiene]
├── Basic Fatigue Allowance (A_f) [~4% constant; basic physiological recovery]
├── Variable Fatigue Allowance (A_vf) [Task-dependent ergonomics]
│   ├── Working posture (standing, crouching, awkward bending)
│   ├── Muscular force exerted / weight of lifted objects
│   ├── Atmospheric heat stress (WBGT) and high humidity
│   ├── Visual optical strain and glare
│   └── Excessive ambient noise and mental concentration
└── Unavoidable Delays (A_d) [Minor machine adjustments, material transit waiting]

Total Allowance Percentage

The total allowance fraction ($A_{\text{total}}$) is the algebraic sum of the individual allowance categories:

$A_{\text{total}} = A_p + A_f + A_{vf} + A_d$

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4. Standard Time Calculations and Production Rates

In industrial engineering practice, allowances are mathematically incorporated using one of two distinct conventions. Candidates must verify how the examination question states allowances.

Method 1: Allowances Based on Normal Time (Industry Standard)

In the vast majority of manufacturing operations, allowances are expressed as a direct percentage multiplier applied to the Normal Time:

$ST = NT \times (1 + A_{\text{total}}) = NT \times (1 + A_p + A_f + A_{vf} + A_d)$

Method 2: Allowances Based on the Total Working Day (Shift Basis)

Under this convention, allowances are established as a percentage of the total working shift ($T_{\text{shift}}$, e.g., 480 minutes). The total working shift is partitioned into productive standard time and allowance downtime ($T_{\text{allowance}} = A_{\text{day}} \times T_{\text{shift}}$):

$ST = \frac{NT}{1 - A_{\text{day}}}$

Standard Production Rate ($R$)

Once the Standard Time ($ST$) per unit is determined, the standard production output rate is the mathematical inverse:

$R = \frac{1}{ST} \quad \left[ \frac{\text{units}}{\text{minute}} \right] \qquad \text{or} \qquad R_{\text{hour}} = \frac{60}{ST} \quad \left[ \frac{\text{units}}{\text{hour}} \right]$

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5. Statistical Sample Size Determination

Because time study is an inductive sampling procedure, a finite sample of $n$ cycles is used to estimate the true population mean cycle time $\mu$. To guarantee that the sample mean $\bar{x}$ estimates $\mu$ within an allowable relative error percentage $k$ (e.g., $\pm 5\%$) at a specified confidence level $(1 - \alpha)$ (e.g., 95%), the sample size must satisfy statistical rigor.

Derivation from Confidence Interval Formulation

The half-width margin of error $e$ is expressed as:

$e = k \cdot \bar{x} = z_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$

Solving explicitly for the required number of observations $n$:

$n = \left( \frac{z_{\alpha/2} \cdot s}{k \cdot \bar{x}} \right)^2 = \left( \frac{z_{\alpha/2} \cdot s}{e} \right)^2$

Where:

• $n$ = Minimum required sample size (number of cycles).
• $z_{\alpha/2}$ = Standard normal distribution critical value corresponding to confidence level $1 - \alpha$ ($z = 1.96$ for 95% confidence; $z = 2.576$ for 99% confidence).
• $s$ = Sample standard deviation computed from a preliminary pilot study: $s = \sqrt{\frac{\sum_{i=1}^n (x_i - \bar{x})^2}{n - 1}}$.
• $\bar{x}$ = Sample mean observed time from the pilot study: $\bar{x} = \frac{\sum x_i}{n}$.
• $k$ = Desired relative precision percentage expressed as a decimal (e.g., $\pm 5\% \implies k = 0.05$).
• $e$ = Absolute precision margin of error ($e = k \cdot \bar{x}$).

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6. Comprehensive Worked Numerical Problem

Problem Statement

An industrial engineer conducts a time study on a semi-automated medical device assembly operation consisting of three distinct manual elements. The preliminary pilot study evaluates 10 cycles for each element.

Data gathered from the pilot study:

• Element 1 (Pick up base housing and secure into fixture): $\bar{x}_1 = 0.24$ min, $s_1 = 0.024$ min, Performance Rating $PR_1 = 110\%$.
• Element 2 (Insert PCB, attach ribbon cable, and drive 4 micro-screws): $\bar{x}_2 = 0.75$ min, $s_2 = 0.060$ min, Performance Rating $PR_2 = 90\%$.
• Element 3 (Inspect optical alignment, release clamp, drop into tote): $\bar{x}_3 = 0.31$ min, $s_3 = 0.031$ min, Performance Rating $PR_3 = 100\%$.

Company policy requires a 95% confidence level ($z = 1.96$) with a relative precision of $\pm 5\%$ ($k = 0.05$) across all elements.

Allowances applied to the operation are established as follows:

• Personal needs allowance: $A_p = 5\%$
• Basic fatigue allowance: $A_f = 4\%$
• Variable fatigue (standing posture + fine visual strain): $A_{vf} = 3\%$
• Unavoidable delays: $A_d = 2\%$

Step-by-Step Calculation

Step 1: Verify Sample Size Adequacy

Calculate the required sample size for each element using $n = \left( \frac{1.96 \cdot s}{0.05 \cdot \bar{x}} \right)^2$:

• Element 1: $n_1 = \left( \frac{1.96 \times 0.024}{0.05 \times 0.24} \right)^2 = \left( \frac{0.04704}{0.012} \right)^2 = (3.92)^2 = 15.37 \implies 16 \text{ observations}$

• Element 2: $n_2 = \left( \frac{1.96 \times 0.060}{0.05 \times 0.75} \right)^2 = \left( \frac{0.1176}{0.0375} \right)^2 = (3.136)^2 = 9.83 \implies 10 \text{ observations}$

• Element 3: $n_3 = \left( \frac{1.96 \times 0.031}{0.05 \times 0.31} \right)^2 = \left( \frac{0.06076}{0.0155} \right)^2 = (3.92)^2 = 15.37 \implies 16 \text{ observations}$

Conclusion: While Element 2 satisfies the precision requirement with the initial 10 cycles, Elements 1 and 3 require at least 16 observations to guarantee the desired statistical precision.

Step 2: Compute Normal Time ($NT$)

Using the full sample data where average observed times remain stable:

• $NT_1 = \bar{x}_1 \times PR_1 = 0.24 \times 1.10 = 0.264 \text{ minutes}$
• $NT_2 = \bar{x}_2 \times PR_2 = 0.75 \times 0.90 = 0.675 \text{ minutes}$
• $NT_3 = \bar{x}_3 \times PR_3 = 0.31 \times 1.00 = 0.310 \text{ minutes}$

Total Cycle Normal Time: $NT_{\text{cycle}} = NT_1 + NT_2 + NT_3 = 0.264 + 0.675 + 0.310 = 1.249 \text{ minutes}$

Step 3: Compute Total Allowance Percentage ($A_{\text{total}}$)

$A_{\text{total}} = 5\% + 4\% + 3\% + 2\% = 14\% = 0.14$

Step 4: Compute Standard Time ($ST$) under Both Methods

• Method 1 (Allowance on Normal Time): $ST_1 = NT_{\text{cycle}} \times (1 + A_{\text{total}}) = 1.249 \times (1 + 0.14) = 1.249 \times 1.14 = 1.42386 \approx 1.424 \text{ minutes}$

• Method 2 (Allowance on Working Shift): $ST_2 = \frac{NT_{\text{cycle}}}{1 - A_{\text{day}}} = \frac{1.249}{1 - 0.14} = \frac{1.249}{0.86} = 1.45233 \approx 1.452 \text{ minutes}$

Step 5: Compute Standard Hourly Production Rates

• Under Method 1: $R_1 = \frac{60 \text{ min/hr}}{1.42386 \text{ min/unit}} = 42.14 \text{ units per hour}$

• Under Method 2: $R_2 = \frac{60 \text{ min/hr}}{1.45233 \text{ min/unit}} = 41.31 \text{ units per hour}$