18.1 Methods Engineering, Process Charting, and Principles of Motion Economy

Methods engineering—originally pioneered by Frederick Winslow Taylor and Frank and Lillian Gilbreth—is the systematic branch of industrial engineering charged with designing, improving, and standardizing human work systems. It focuses on the human-machine interface, workstation kinematics, material flows, and operation sequences to eliminate waste, enhance physical safety, reduce musculoskeletal fatigue, and optimize unit production costs. On the FE Industrial and Systems exam, methods engineering is tested across qualitative charting standards, mathematical machine-operator coupling models, Therblig classifications, and the classical principles of motion economy.

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1. Systematic Methods Engineering Procedure

Methods engineering follows a rigorous, closed-loop problem-solving procedure. Rather than applying intuitive or localized fixes, an industrial engineer moves through seven structured steps:

                      The Methods Engineering Cycle
                      
  1. Select Project ──► High labor cost, bottleneck, high scrap, fatigue
          │
          ▼
  2. Get & Record Facts ──► Process charts, flow diagrams, video analysis
          │
          ▼
  3. Analyze Facts ──► Critical Examination (Why? What? Where? When? Who? How?)
          │             Apply ECRS: Eliminate, Combine, Rearrange, Simplify
          ▼
  4. Develop Ideal Method ──► Motion economy, ergonomic layout, low-cost automation
          │
          ▼
  5. Present & Install ──► Economic justification, SOPs, operator training
          │
          ▼
  6. Job Standardization ──► Standard operating sheet, tooling, feeds & speeds
          │
          ▼
  7. Follow-Up & Maintain ──► Periodic shop-floor audit to prevent regression

The ECRS Analysis Framework

During the fact analysis stage, every recorded work element is interrogated through the ECRS hierarchy in strict sequential priority:

1. E — Eliminate: Can the operation, transit, or inspection be eliminated entirely? If an operation produces no customer-perceived value or if an upstream process can be redesigned to make the step redundant, elimination yields a 100% savings in labor, tooling, and space.
2. C — Combine: If an element cannot be eliminated, can it be combined with another operation or inspection? Combining steps (e.g., gauging a part while a machine cut proceeds, or using combination tools) reduces handling and setup steps.
3. R — Rearrange: Can the sequence of operations be altered to smooth workflow, balance cycle times, eliminate backtracking, or group related operations?
4. S — Simplify: After eliminating, combining, and rearranging, can the remaining necessary steps be made simpler? Simplification includes reducing reach distances, using gravity feed chutes, and employing clamping fixtures instead of manual holds.

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2. Process Charting Symbology and ASME Standards

Process charts record operational sequences visually and quantitatively. Standardized by the American Society of Mechanical Engineers (ASME Standard for Process Charts), five graphical symbols represent every state an entity (material, human, or paperwork) can experience:

Exam Distinction: Do not confuse Delay (D) with Storage ($\nabla$). Delay is an unplanned queue or staging pause where material simply sits waiting for capacity. Storage is controlled, secure inventory retention where material cannot be moved without formal inventory transactions.

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3. Macro-Level Process Charts: Flow Process Chart & Flow Diagram

Flow Process Chart

A Flow Process Chart records the chronological sequence of all operations, inspections, transportations, delays, and storages across an entire manufacturing value stream. Charts are constructed for three distinct subjects:

• Material Flow Process Chart: Tracks the physical transformations and movements of a part or raw stock.
• Worker Flow Process Chart: Tracks the physical actions, tasks, and travel of an operator.
• Equipment Flow Process Chart: Tracks the utilization, cutting cycles, and idle periods of a machine.

The header of every Flow Process Chart contains a Summary Table that totals the count of each symbol, cumulative transit distances (in feet or meters), and total elapsed durations (in minutes or hours). The methods engineer compares the Present Method summary against the Proposed Method summary to quantify improvements:

                     Flow Process Chart Summary Table
┌─────────────────┬───────────┬────────────┬─────────────┬──────────────┐
│ Activity Class  │ Present   │ Proposed   │ Difference  │ Savings (%)  │
├─────────────────┼───────────┼────────────┼─────────────┼──────────────┤
│ Operations      │    14     │     9      │     -5      │    35.7%     │
│ Inspections     │     4     │     2      │     -2      │    50.0%     │
│ Transportations │    11     │     4      │     -7      │    63.6%     │
│ Delays          │     7     │     1      │     -6      │    85.7%     │
│ Storages        │     3     │     2      │     -1      │    33.3%     │
├─────────────────┼───────────┼────────────┼─────────────┼──────────────┤
│ Total Distance  │  840 ft   │   220 ft   │   -620 ft   │    73.8%     │
│ Total Time      │ 186.0 min │  72.5 min  │  -113.5 min │    61.0%     │
└─────────────────┴───────────┴────────────┴─────────────┴──────────────┘

Flow Diagram

A Flow Diagram is a scale drawing of the physical shop-floor layout (including walls, machinery, workstations, storage racks, and aisles) upon which the path of the material or operator is traced using lines and ASME symbols. While a Flow Process Chart shows the sequence of activities, the Flow Diagram exposes:

• Long travel distances and excessive transit paths.
• Backtracking (loops where parts double back over previously traversed routes).
• Floor congestion and cross-traffic intersections where collisions or material handling bottlenecks occur.
• Opportunities for cellular machine rearrangement (converting disconnected process layouts into compact U-shaped cells).

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4. Micro-Level Analysis: Worker and Machine Chart & Two-Handed Process Chart

Worker and Machine Chart (Man-Machine Chart)

A Worker and Machine Chart visualizes the synchronous relationship between an operator and one or more machines along a shared chronological time axis. It identifies idle periods and evaluates the economic feasibility of multi-machine coupling (assigning multiple machines to a single operator).

                Worker and Machine Time Synchronization

  Time    Operator Activity                      Machine Activity
 (min)   ┌──────────────────────────┐           ┌──────────────────────────┐
  0.0 ───┤ Load/Unload Machine (l)  │◄─────────►│ Concurrent Loading (l)  │
  1.2 ───┼──────────────────────────┤           ├──────────────────────────┤
         │ Walk to Machine 2 (w)    │           │                          │
  1.6 ───┼──────────────────────────┤           │                          │
         │                          │           │ Machine Automatic        │
         │ Operator Idle Time       │           │ Run Time (m)             │
         │                          │           │                          │
  5.6 ───┼──────────────────────────┤           │                          │
         │ Walk to Machine 1 (w)    │           │                          │
  6.0 ───┴──────────────────────────┴───────────┴──────────────────────────┘

Time Component Breakdown

• Independent Operator Service Time: Tasks performed by the operator while the machine is running (e.g., retrieving raw forgings, inspecting finished parts, walking between equipment).
• Concurrent Service Time / Coupling Time ($l$): Tasks that require the operator and the machine to interact while the machine is stopped (e.g., loading raw blanks into a chuck, clamping fixtures, unloading finished parts).
• Machine Automatic Run Time ($m$): Time during which the machine operates under automated power without human intervention (e.g., automatic spindle feed, CNC milling cycle).
• Operator Walk / Transit Time ($w$): Time spent traversing between adjacent machines.
• Operator Idle Time: Time the operator waits for a machine to complete its run.
• Machine Idle Time (Machine Interference): Time a machine sits stopped waiting for the operator to finish servicing another machine.

Mathematical Machine Coupling Model

To determine the theoretical maximum number of identical machines ($n$) an operator can tend without creating machine interference:

$n = \frac{l + m}{l + w}$

Where:

• $l$ = loading and unloading time (concurrent service)
• $m$ = machine automatic run time
• $w$ = worker transit, setup, or inspection time between machines

Because $n$ is rarely an exact integer, the methods engineer must evaluate two integer options: $n_1 = \lfloor n \rfloor$ (rounded down) versus $n_2 = \lceil n \rceil$ (rounded up):

1. Under-Coupling ($n_1 = \lfloor n \rfloor$):
   • Operator has sufficient time to service all machines.
   • Cell cycle time is machine-paced: $T_c = l + m$.
   • Machines experience zero idle time ($0%$ interference).
   • Operator experiences idle time: $T_{\text{idle, op}} = (l + m) - n_1(l + w)$.
2. Over-Coupling ($n_2 = \lceil n \rceil$):
   • Machines must wait for the operator to service them.
   • Cell cycle time is operator-paced: $T_c = n_2(l + w)$.
   • Operator experiences zero idle time.
   • Machines experience machine interference idle time: $T_{\text{idle, mach}} = n_2(l + w) - (l + m)$.

Economic Selection Rule

To select between $n_1$ and $n_2$, compute the total cost per finished unit ($C_u$):

$C_u = \frac{(C_o + n \cdot C_m) \cdot T_c}{n}$

Where:

• $C_o$ = operator hourly wage ($/hr)
• $C_m$ = machine hourly operating cost ($/hr per machine)
• $T_c$ = cell cycle time (hours)
• $n$ = number of machines assigned

Select the integer $n$ that minimizes total unit cost $C_u$.

Two-Handed Process Chart (Operator Process Chart)

A Two-Handed Process Chart records the synchronized micro-motions of an operator's left hand (LH) and right hand (RH) against a shared vertical sequence. It is applied to highly repetitive, short-cycle manual assembly operations.

• Adapted Symbols: Operation (grasping/modifying), Transportation (reaching/moving), Hold (triangle $\nabla$, representing a hand acting as a static clamp), and Delay (hand idle).
• Primary Engineering Objective: Identify and eliminate Hold (holding a part is non-value-added and induces muscle fatigue) by introducing mechanical fixtures, clamps, or vacuum jigs; balance the workload evenly between both hands.

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5. Therbligs: Fundamental Micro-Motions

Formulated by Frank and Lillian Gilbreth, Therbligs (an anagram of Gilbreth spelled backwards with 'th' transposed) are the fundamental elemental subdivisions of human physical work. The Gilbreths originally listed 18; modern methods-engineering texts standardize on the 17 below, having dropped the redundant Find (the instant of recognition at the end of Search). Every manual job consists of combinations of these 17 micro-motions. Industrial engineers categorize Therbligs into Effective and Ineffective groups:

                      The 17 Gilbreth Therbligs

        Effective Therbligs                  Ineffective Therbligs
      (Value-Adding / Direct)              (Non-Value-Adding / Waste)
 ┌────────────────────────────────┐   ┌────────────────────────────────┐
 │ 1. Reach (RE)                  │   │ 9. Search (Sh)                 │
 │ 2. Move (M)                    │   │ 10. Select (St)                │
 │ 3. Grasp (G)                   │   │ 11. Inspect (I)                │
 │ 4. Release Load (RL)           │   │ 12. Hold (H)                   │
 │ 5. Pre-position (PP)           │   │ 13. Unavoidable Delay (UD)     │
 │ 6. Use (U)                     │   │ 14. Avoidable Delay (AD)       │
 │ 7. Assemble (A)                │   │ 15. Plan (Pn)                  │
 │ 8. Disassemble (DA)            │   │ 16. Rest for Fatigue (R)       │
 └────────────────────────────────┘   │ 17. Position (P)               │
                                      └────────────────────────────────┘

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6. Principles of Motion Economy

Originally formulated by Frank and Lillian Gilbreth and expanded by Ralph M. Barnes, the Principles of Motion Economy provide actionable engineering guidelines for designing productive, low-fatigue work environments. They are categorized into three core domains:

1. Use of the Human Body

• Simultaneous and Symmetrical Motions: Both hands should begin and complete their motions at the exact same instant. Both hands should not be idle at the same time (except during authorized rest periods). Arm motions should be simultaneous and in opposite, symmetrical directions; symmetrical arm paths naturally balance biological reaction forces across the torso, minimizing postural muscle fatigue.
• Five Classes of Human Motion: Hand and arm motions are classified according to the biological pivots involved. Methods must be designed to utilize the lowest feasible class (lowest energy expenditure and fastest cycle time):
  • Class 1: Fingers only (e.g., keyboarding, picking miniature screws). Fastest, lowest energy.
  • Class 2: Fingers and wrist (e.g., writing, turning a dial).
  • Class 3: Fingers, wrist, and forearm (e.g., assembly bench work, screwdriver rotation).
  • Class 4: Fingers, wrist, forearm, and upper arm (e.g., reaching across an assembly table). High energy, causes shoulder strain.
  • Class 5: Entire body: trunk bending, torso twisting, shoulder flexion, walking. Highest fatigue, slowest execution. Avoid Class 5 motions through ergonomic layout.
• Continuous Curved Motions: Smooth, continuous curved hand sweeps are faster and require far less physical effort than straight-line motions that incorporate sudden, abrupt changes in direction. Reversing or making sharp angle changes requires muscular deceleration to zero velocity followed by acceleration in a new direction, quadrupling energy consumption.
• Momentum Utilization: Kinetic momentum should be harnessed to assist the worker whenever physical forces are needed (e.g., utilizing the momentum of a hammer swing). Conversely, muscular effort required to overcome or arrest moving loads must be minimized by providing mechanical stops or bumpers.

2. Arrangement of the Workplace

• Definite and Fixed Locations: All tools, fixtures, containers, and materials must possess definite, unchanging, and visually marked locations. This develops sub-conscious muscular automaticity (motor habits), eliminating the ineffective therbligs Search (Sh), Select (St), and Plan (Pn).
• Normal and Maximum Working Areas:
  • Normal Working Area: The comfortable horizontal boundary circumscribed by sweeping the forearm across the bench while the upper arm hangs naturally at the side (elbow remains stationary). All high-frequency components, hand tools, and assembly fixtures must reside within this zone.
  • Maximum Working Area: The outer horizontal boundary reached by fully extending the arm from the shoulder without bending the torso or leaning forward. Low-frequency parts, secondary tools, and finished goods drop chutes must be located within this zone.

                  Ergonomic Horizontal Working Envelopes

            ┌───────────────────────────────────────────────┐
            │            Maximum Working Area               │
            │   ┌───────────────────────────────────────┐   │
            │   │          Normal Working Area          │   │
            │   │      ┌─────────────────────────┐      │   │
            │   │      │   Assembly Fixture      │      │   │
            │   │      └─────────────────────────┘      │   │
            │   │   Left Hand Sweep     Right Hand Sweep│   │
            │   └───────────────────────────────────────┘   │
            │          Extended Arm Reach Boundary          │
            └───────────────────────────────────────────────┘
                                 ▲
                              Operator

• Gravity Feed and Drop Delivery:
  • Gravity Feed Bins: Bins tilted toward the operator allow parts to slide to the front pick point via gravity, presenting components at the exact same location at fingertips without requiring the operator to reach deep into a tote.
  • Drop Delivery: Providing a hole, chute, or conveyor directly beneath or adjacent to the assembly fixture allows the finished part to drop into a container the instant the hands release it, completely eliminating the Move (M) motion required to transport finished goods to a staging tote.
• Workstation Lighting and Height: Provide glare-free illumination (minimum 50 to 100 foot-candles for medium assembly; 200+ foot-candles for fine precision work). The working surface height should sit 2 to 4 inches below the operator's resting elbow height for seated or standing assembly, and lower for heavy lifting tasks.

3. Design of Tools and Equipment

• Relieve Hands with Fixtures: Hands are poor clamping devices. Always relieve the hands of static holding tasks by employing foot-operated vises, mechanical toggles, magnetic chucks, or pneumatic clamps.
• Combined Tools: Combine two or more tools into a single functional unit whenever possible (e.g., combination socket and torque wrench, reversible screwdriver, hammer with nail-puller claw).
• Ergonomic Tool Handles: Handles must be designed to maximize contact surface area with the palm to prevent localized pressure hotspots on the median nerve (carpal tunnel syndrome). Handles should be contoured or angled so that the wrist remains in a neutral, straight alignment, completely avoiding extreme ulnar deviation, radial deviation, flexion, or extension.

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7. Step-by-Step Worked Engineering Calculations

Worked Example 18.1.1: Man-Machine Allocation and Economic Analysis

Problem: An industrial engineer in an automotive machining department must configure a semi-automated manufacturing cell. An operator tends identical CNC turning machines. The operational time parameters and operating cost rates are:

• Loading and unloading time (concurrent service): $l = 1.2\text{ minutes/machine}$
• Machine automatic cutting time: $m = 4.8\text{ minutes/machine}$
• Operator walking and inspection time between machines: $w = 0.4\text{ minutes/machine}$
• Operator labor wage rate: $C_o = $24.00/\text{hour} = $0.40/\text{minute}$
• Machine operating rate (per machine): $C_m = $36.00/\text{hour} = $0.60/\text{minute}$

1. Calculate the theoretical number of machines ($n$) an operator can tend without idle machine interference.
2. Evaluate cell cycle time, operator idle time, machine idle time, and hourly production rate for both under-coupling ($n_1 = \lfloor n \rfloor$) and over-coupling ($n_2 = \lceil n \rceil$).
3. Calculate the total unit production cost ($C_u$) for both configurations and select the economically optimal machine allocation.

Solution:

Step 1: Compute Theoretical Machine Allocation ($n$) $n = \frac{l + m}{l + w} = \frac{1.2 + 4.8}{1.2 + 0.4} = \frac{6.0\text{ minutes}}{1.6\text{ minutes}} = 3.75\text{ machines}$

Because $n = 3.75$, the engineer must evaluate assigning either $n_1 = 3$ machines or $n_2 = 4$ machines.

Step 2: Operational Evaluation of $n_1 = 3$ Machines (Under-Coupling)

• Cell Cycle Time: Because $n_1 (l + w) = 3 \times 1.6 = 4.8\text{ min} < 6.0\text{ min}$, the cell is machine-paced: $T_c = l + m = 1.2 + 4.8 = 6.0\text{ minutes}$
• Operator Work Time in Cycle: $3 \times (l + w) = 3 \times 1.6 = 4.8\text{ minutes}$
• Operator Idle Time per Cycle: $T_{\text{idle, op}} = 6.0 - 4.8 = 1.2\text{ minutes}$
• Machine Idle Time per Cycle (Machine Interference): $T_{\text{idle, mach}} = 0.0\text{ minutes}$ ($0%$ interference; machines run continuously)
• Production Rate: 3 parts are completed every 6.0 minutes: $\text{Rate}_3 = \frac{3\text{ parts}}{6.0\text{ min}} \times 60\text{ min/hr} = 30.0\text{ parts/hour}$

Step 3: Operational Evaluation of $n_2 = 4$ Machines (Over-Coupling)

• Cell Cycle Time: Because $n_2 (l + w) = 4 \times 1.6 = 6.4\text{ min} > 6.0\text{ min}$, the cell is operator-paced: $T_c = n_2(l + w) = 4 \times 1.6 = 6.4\text{ minutes}$
• Operator Work Time in Cycle: $4 \times 1.6 = 6.4\text{ minutes}$
• Operator Idle Time per Cycle: $T_{\text{idle, op}} = 0.0\text{ minutes}$ (operator is fully utilized)
• Machine Idle Time per Cycle (Machine Interference): $T_{\text{idle, mach}} = T_c - (l + m) = 6.4 - 6.0 = 0.4\text{ minutes per machine}$
• Machine Interference Percentage: $\frac{0.4\text{ min}}{6.4\text{ min}} \times 100% = 6.25%$
• Production Rate: 4 parts are completed every 6.4 minutes: $\text{Rate}_4 = \frac{4\text{ parts}}{6.4\text{ min}} \times 60\text{ min/hr} = 37.5\text{ parts/hour}$

Step 4: Economic Unit Cost Comparison

• For $n_1 = 3$ machines: $\text{Cost per cycle} = (C_o + 3 \cdot C_m) \cdot T_c = (\$0.40 + 3 \times \$0.60) \times 6.0 = (\$0.40 + \$1.80) \times 6.0 = \$2.20 \times 6.0 = \$13.20$ $C_{u, 3} = \frac{\$13.20}{3\text{ parts}} = \$4.40\text{ per part}$
• For $n_2 = 4$ machines: $\text{Cost per cycle} = (C_o + 4 \cdot C_m) \cdot T_c = (\$0.40 + 4 \times \$0.60) \times 6.4 = (\$0.40 + \$2.40) \times 6.4 = \$2.80 \times 6.4 = \$17.92$ $C_{u, 4} = \frac{\$17.92}{4\text{ parts}} = \$4.48\text{ per part}$

Step 5: Engineering Conclusion Assigning 3 machines yields a unit manufacturing cost of $4.40/part, compared to $4.48/part when assigning 4 machines. Even though assigning 4 machines yields higher gross hourly volume (37.5 parts/hr vs. 30.0 parts/hr), the machine interference idle time (0.4 min/cycle) on expensive machine capital outweighs the labor utilization gain. Unless the plant is capacity-constrained and willing to pay an 8-cent per part penalty for extra throughput, $n = 3$ is the economically optimal allocation.

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8. NCEES Reference Handbook Tips & Realistic Exam Traps

• ASME Symbol Confusion: On conceptual exam questions, examinees frequently confuse the Delay (D-shape) and Storage (inverted triangle $\nabla$) symbols. Remember: if material sits in an aisle or bin waiting for the next machine, it is a Delay. Material is in Storage only if it is housed under formal inventory custody where a requisition, receipt, or ERP transaction is required to withdraw it.
• Hold is Ineffective: On Therblig classification questions, students frequently assume Hold (H) is an effective assembly motion. Hold is strictly ineffective. Holding a workpiece statically with one hand generates static muscle ischemia and robs that hand of productive work. Eliminate Hold using mechanical clamps.
• Motion Class Inversion: Motion classes rank from 1 to 5 based on physical pivots. Class 1 is fingers only; Class 5 is entire body/bending. Do not invert these! Lowest class (Class 1) is fastest, most accurate, and consumes the least energy.
• Cycle Time in Man-Machine Charts: Never assume that cell cycle time is always $l + m$. If the operator is overloaded ($n(l + w) > l + m$), the cycle time stretches to $n(l + w)$, and machines experience idle interference!