9.4 Predetermined Motion Time Systems (PMTS, MTM, MOST) & Work Sampling

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9.4 Predetermined Motion Time Systems (PMTS, MTM, MOST) & Work Sampling

Key Takeaways Explain This Topic AI

Predetermined Motion Time Systems (PMTS) synthesize standard times by aggregating pre-calibrated synthetic elemental motion values, eliminating subjective operator performance rating and enabling pre-production cycle time modeling.

Methods-Time Measurement (MTM-1) is standardized in Time Measurement Units (TMU), where 1 TMU = 0.00001 hour = 0.0006 minute = 0.036 seconds 1 \text{ TMU} = 0.00001 \text{ hour} = 0.0006 \text{ minute} = 0.036 \text{ seconds} 1 TMU = 0.00001 hour = 0.0006 minute = 0.036 seconds ( 100 , 000 TMU = 1 hour 100,000 \text{ TMU} = 1 \text{ hour} 100 , 000 TMU = 1 hour ).

Maynard Operation Sequence Technique (MOST) accelerates work measurement by modeling human activities into structured activity sequences—General Move, Controlled Move, and Tool Use—applying standardized index values multiplied by 10 to establish TMUs.

Work sampling applies the binomial probability distribution to estimate the proportion of time ( p p p ) workers or machines spend in designated activity states through instantaneous, randomized observations.

The number of random observations ( N N N ) required in a work sampling study is governed by N = z 2 ⋅ p ( 1 − p ) e 2 N = \frac{z^2 \cdot p(1-p)}{e^2} N = e 2 z 2 ⋅ p ( 1 − p ) ​ , where e e e represents the allowable absolute error margin at a specified confidence level z z z .

Last updated: October 2026

9.4 Predetermined Motion Time Systems (PMTS, MTM, MOST) & Work Sampling

While direct stopwatch time study requires an existing, physical operation with an operator present, modern industrial engineering demands methodologies that can establish labor standards before equipment is purchased, eliminate subjective pace rating disputes, and economically evaluate non-cyclical work across complex facilities. These needs are fulfilled by Predetermined Motion Time Systems (PMTS) and Work Sampling .

1. Rationale and Foundations of PMTS

A Predetermined Motion Time System (PMTS) is a work measurement procedure that establishes standard times for basic manual human motions (e.g., reaching, moving, grasping, positioning) based on extensive empirical laboratory and high-speed motion picture analysis. The normal time required to perform a complete task is synthesized by decomposing the task into its constituent micro-motions and summing their predetermined time values.

Strategic Advantages of PMTS

Pre-Production Standard Setting: Allows engineers to calculate labor standards, assembly line workstation assignments, and tooling requirements directly from engineering drawings and CAD models before tooling is ordered or the factory floor is configured.

Elimination of Subjective Performance Rating: Pre-calibrated PMTS values represent 100% standard normal pace. The observer does not need to rate the operator's speed, eliminating a primary source of labor friction and grievance.

Forces Method Optimization: To apply PMTS, the engineer must document the exact path, distance, fixture orientation, and hand movements required, ensuring method inefficiencies (such as unnecessary reaches or awkward grasps) are designed out upfront.

Global Cross-Facility Consistency: Standards established via PMTS are consistent across disparate manufacturing facilities worldwide, eliminating regional rating variance.

2. Methods-Time Measurement (MTM-1)

Developed in 1948 by Harold B. Maynard, Gustave J. Stegemerten, and John L. Schwab, Methods-Time Measurement (MTM-1) is the most widely recognized and rigorous predetermined motion time system.

The Time Measurement Unit (TMU)

Because traditional units of time (seconds, minutes, hours) are too coarse for micro-motion analysis, MTM utilizes the Time Measurement Unit (TMU) , defined as exactly one hundred-thousandth of an hour (0.00001 hour) .

Conversion Relationship Mathematical Ratio Engineering Application

1 TMU 1 \text{ TMU} 1 TMU to Hours 1 TMU = 0.00001 hr = 10 − 5 hr 1 \text{ TMU} = 0.00001 \text{ hr} = 10^{-5} \text{ hr} 1 TMU = 0.00001 hr = 1 0 − 5 hr Used in plant-wide aggregate labor accounting.

1 TMU 1 \text{ TMU} 1 TMU to Minutes 1 TMU = 0.0006 min = 6 × 10 − 4 min 1 \text{ TMU} = 0.0006 \text{ min} = 6 \times 10^{-4} \text{ min} 1 TMU = 0.0006 min = 6 × 1 0 − 4 min Used in assembly line balancing calculations.

1 TMU 1 \text{ TMU} 1 TMU to Seconds 1 TMU = 0.036 seconds 1 \text{ TMU} = 0.036 \text{ seconds} 1 TMU = 0.036 seconds Used in high-speed micro-motion analysis.

Hours to TMU 1 hour = 100 , 000 TMU 1 \text{ hour} = 100,000 \text{ TMU} 1 hour = 100 , 000 TMU Direct definition benchmark.

Minutes to TMU 1 minute = 1 , 666.67 TMU 1 \text{ minute} = 1,666.67 \text{ TMU} 1 minute = 1 , 666.67 TMU Rapid conversion factor ( 50 / 3 50/3 50/3 ).

Seconds to TMU 1 second = 27.78 TMU 1 \text{ second} = 27.78 \text{ TMU} 1 second = 27.78 TMU Rapid conversion factor ( 1 / 0.036 1/0.036 1/0.036 ).

MTM-1 Core Motion Categories

MTM-1 isolates eight fundamental manual motions, each indexed in standard lookup tables according to governing physical variables:

Reach ( R R R ): Moving the empty hand or fingers to a destination. Governed by: transit distance (inches), and Case :

Case A: Reach to object in fixed location or object in other hand.

Case B: Reach to single object in approximate location (most common).

Case C: Reach to object jumbled with other objects in a group.

Case D: Reach to very small object where accurate grasp is required.

Case E: Reach to indefinite location for balance or out of the way.

Move ( M M M ): Transporting an object with the hand or fingers. Governed by: transit distance, Case (A: to other hand or stop; B: to approximate location; C: to exact location), and Net Weight / Resistance ( F W F_W F W ​ dynamic and static weight factor allowances).

Turn ( T T T ) and Apply Pressure ( A P AP A P ): Rotating the hand/wrist along the forearm axis, or applying short, sustained muscular force to overcome mechanical resistance.

Grasp ( G G G ): Closing digits to gain physical control of an object. Categorized into Pick-up ( G 1 A , G 1 B , G 1 C G1A, G1B, G1C G 1 A , G 1 B , G 1 C ), Regrasp ( G 2 G2 G 2 ), Transfer ( G 3 G3 G 3 ), Jumbled Grasp ( G 4 G4 G 4 ), and Contact Grasp ( G 5 G5 G 5 ).

Position ( P P P ): Aligning, orienting, and engaging an object with a mating receptacle. Governed by: Class of fit (Loose 1, Close 2, Exact 3), Symmetry (Symmetrical S S S , Semi-symmetrical S S SS SS , Non-symmetrical N S NS NS ), and Ease of handling.

Release ( R L RL R L ): Opening fingers to relinquish control ( R L 1 RL1 R L 1 normal release, R L 2 RL2 R L 2 contact release).

Disengage ( D D D ): Breaking contact between mating parts (Class 1 Loose, Class 2 Tight, Class 3 Binding).

Body, Eye, and Leg Motions: Foot pedals ( F F F ), Leg motions ( L M LM L M ), Eye travel ( E T ET ET ), Eye focus ( E F EF EF ), Bend ( B B B ), Stoop ( S S S ), Kneel ( K K K ), and Walk ( W W W ).

3. Maynard Operation Sequence Technique (MOST)

MTM-1 is precise but slow to apply, because every reach, grasp, and move must be coded. MOST (Maynard Operation Sequence Technique) was developed by Kjell Zandin at H.B. Maynard and Company in the early 1970s (his MOST textbook followed in 1980). It is a higher-level PMTS built from MTM data that analyzes work in standard activity sequences, so it is much faster to apply with acceptable accuracy for most industrial work.

MOST structures human manual work into three standardized, overarching activity sequence models :

1. General Move Sequence Model

Applies to the spatial displacement of an object through an unrestricted path via hands and fingers:

A B G A B P A \mathbf{A} \quad \mathbf{B} \quad \mathbf{G} \quad \mathbf{A} \quad \mathbf{B} \quad \mathbf{P} \quad \mathbf{A} A B G A B P A

Where the parameter letters represent:

A A A (Action Distance): Horizontal movement of the body or limbs (steps walked or reach distance).

B B B (Body Motion): Vertical movement (bending at waist, crouching, sitting, standing up).

G G G (Gain Control): Manual grasp of the object.

P P P (Place): Placement, alignment, or positioning of the object at the destination.

2. Controlled Move Sequence Model

Applies to the movement of an object over a restricted or guided path (sliding along a table, cranking a handwheel, rotating a lever, opening an access door):

A B G M X I A \mathbf{A} \quad \mathbf{B} \quad \mathbf{G} \quad \mathbf{M} \quad \mathbf{X} \quad \mathbf{I} \quad \mathbf{A} A B G M X I A

Where:

M M M (Move Controlled): Manual movement along a constrained track.

X X X (Process Time): Machine feed or automated cycle time.

I I I (Alignment): Multi-axis alignment to reference scales or indicators.

3. Tool Use Sequence Model

Applies to the retrieval, operation, and return of hand tools (screwdrivers, wrenches, calipers, rags, markers):

A B G A B P [ Tool Action ] A B P A \mathbf{A} \quad \mathbf{B} \quad \mathbf{G} \quad \mathbf{A} \quad \mathbf{B} \quad \mathbf{P} \quad [ \text{Tool Action} ] \quad \mathbf{A} \quad \mathbf{B} \quad \mathbf{P} \quad \mathbf{A} A B G A B P [ Tool Action ] A B P A

Where [Tool Action] corresponds to a specific tool function:

Fasten / Loosen ( F / L F / L F / L ): Torquing screws or bolts.

Cut ( C C C ): Scissors, snips, or utility knife.

Surface Adjust ( S S S ): Sanding, filing, scraping, or cleaning.

Measure ( M M M ): Applying steel rule, micrometer, or calipers.

Record ( R R R ): Writing serial numbers or checkmarks.

Think ( T T T ): Reading gauges, verifying instructions, or inspecting.

MOST Index Numbers and Calculation Rule

Each parameter in a MOST sequence is assigned an integer index value based on standard lookup definitions:

Index Scale: 0 , 1 , 3 , 6 , 10 , 16 , 24 , 32 , 42 , 54 \text{Index Scale: } 0, \; 1, \; 3, \; 6, \; 10, \; 16, \; 24, \; 32, \; 42, \; 54 Index Scale: 0 , 1 , 3 , 6 , 10 , 16 , 24 , 32 , 42 , 54

Important

The Multiplier Rule of MOST: The total Time Measurement Units (TMU) for any MOST sequence is obtained by summing all index values in the completed model and multiplying the sum by 10 :

Total TMUs = 10 × ∑ ( Index Values ) \text{Total TMUs} = 10 \times \sum (\text{Index Values}) Total TMUs = 10 × ∑ ( Index Values )

4. Work Sampling Methodology

Work Sampling (originally termed the ratio-delay study by L.H.C. Tippett in 1934) is a statistical technique that determines the proportion of time workers or machines spend across defined activity categories (e.g., active assembly, setup, material waiting, machine breakdown, idle personal time).

Instead of continuous stopwatch observation, an observer records instantaneous, randomized observations over days or weeks.

Statistical Basis: The Binomial Distribution

Work sampling is governed by the binomial distribution. If an operator spends a true fraction p p p of total working time in a given state (such as productive assembly), and N N N instantaneous observations are taken at completely random intervals, the number of times X X X the operator is observed in that state is a binomial random variable:

p ^ = X N \hat{p} = \frac{X}{N} p ^ ​ = N X ​

The expected value of the sample proportion is E [ p ^ ] = p E[\hat{p}] = p E [ p ^ ​ ] = p , and its standard error σ p \sigma_p σ p ​ is:

• σ p = p ( 1 − p ) N \sigma_p = \sqrt{\frac{p(1 - p)}{N}} σ p ​ = N p ( 1 − p ) ​ ​
• Sample Size Determination for Absolute Precision ( e e e )

When management specifies that the estimated proportion p ^ \hat{p} p ^ ​ must lie within ± e \pm e ± e absolute percentage points of the true proportion p p p with a ( 1 − α ) (1 - \alpha) ( 1 − α ) confidence level:

e = z α / 2 ⋅ σ p = z α / 2 p ( 1 − p ) N e = z_{\alpha/2} \cdot \sigma_p = z_{\alpha/2} \sqrt{\frac{p(1 - p)}{N}} e = z α /2 ​ ⋅ σ p ​ = z α /2 ​ N p ( 1 − p ) ​ ​

Solving for the total number of observations N N N :

N = z α / 2 2 ⋅ p ( 1 − p ) e 2 N = \frac{z_{\alpha/2}^2 \cdot p(1 - p)}{e^2} N = e 2 z α /2 2 ​ ⋅ p ( 1 − p ) ​

Sample Size Determination for Relative Precision ( k k k )

When management specifies that the margin of error must be within a relative percentage k k k of the parameter itself (i.e., e = k ⋅ p e = k \cdot p e = k ⋅ p , such as within ± 5 % \pm 5\% ± 5% of the true proportion):

k ⋅ p = z α / 2 p ( 1 − p ) N ⟹ N = z α / 2 2 ⋅ ( 1 − p ) k 2 ⋅ p k \cdot p = z_{\alpha/2} \sqrt{\frac{p(1 - p)}{N}} \implies N = \frac{z_{\alpha/2}^2 \cdot (1 - p)}{k^2 \cdot p} k ⋅ p = z α /2 ​ N p ( 1 − p ) ​ ​ ⟹ N = k 2 ⋅ p z α /2 2 ​ ⋅ ( 1 − p ) ​

Tip

If the true proportion p p p is completely unknown prior to the study, conservative planning assumes p = 0.50 p = 0.50 p = 0.50 , which maximizes the product p ( 1 − p ) = 0.25 p(1 - p) = 0.25 p ( 1 − p ) = 0.25 , guaranteeing that the resulting sample size N N N is sufficient regardless of the actual outcome.

Randomization and Prevention of Bias

Observations must be scheduled using pseudo-random number tables or computer algorithms to specify exact observation minutes (e.g., Day 1 at 08:14, 08:37, 09:02, 10:41). Randomization:

Eliminates Worker Reactivity (Hawthorne Effect): Prevents operators from anticipating visits and temporarily altering their pace or behavior.

Avoids Periodic Cyclic Aliasing: If a machine completes an automated cycle every 10 minutes, observing the station at fixed 10-minute intervals would falsely show it as 100% active or 100% idle.

Deriving Standard Time from Work Sampling

Work sampling can synthesize accurate Standard Times when paired with total production counts and average performance ratings recorded across the study duration:

Total Working Time = T total × p ^ \text{Total Working Time} = T_{\text{total}} \times \hat{p} Total Working Time = T total ​ × p ^ ​ Average Observed Time per Unit ( O T ) = Total Working Time Total Finished Units Produced ( Q ) \text{Average Observed Time per Unit } (OT) = \frac{\text{Total Working Time}}{\text{Total Finished Units Produced } (Q)} Average Observed Time per Unit ( OT ) = Total Finished Units Produced ( Q ) Total Working Time ​ N T = O T × P R NT = OT \times PR NT = OT × PR S T = N T × ( 1 + A total ) ST = NT \times (1 + A_{\text{total}}) ST = NT × ( 1 + A total ​ )

• 5. Comprehensive Worked Numerical Problem
• Part A: Basic MOST Synthesis

An operator standing at a workbench executes the following manual sequence:

Walks 3 paces to a shelf ( A 6 A_6 A 6 ​ ).

Bends over to the floor to pick up a container weighing 12 lbs ( B 6 , G 3 B_6, G_3 B 6 ​ , G 3 ​ ).

Stands up and walks 3 paces back to the workbench ( A 6 , B 0 A_6, B_0 A 6 ​ , B 0 ​ ).

Places the container on the bench with light alignment ( P 1 P_1 P 1 ​ ).

Returns to a neutral resting position at the bench without moving feet ( A 0 A_0 A 0 ​ ).

Calculation:

Structural General Move Model: A 6 B 6 G 3 A 6 B 0 P 1 A 0 A_6 \; B_6 \; G_3 \; A_6 \; B_0 \; P_1 \; A_0 A 6 ​ B 6 ​ G 3 ​ A 6 ​ B 0 ​ P 1 ​ A 0 ​

Sum of index values: 6 + 6 + 3 + 6 + 0 + 1 + 0 = 22 6 + 6 + 3 + 6 + 0 + 1 + 0 = 22 6 + 6 + 3 + 6 + 0 + 1 + 0 = 22

Total TMU: 22 × 10 = 220 TMU 22 \times 10 = 220 \text{ TMU} 22 × 10 = 220 TMU

Equivalent seconds: 220 × 0.036 s/TMU = 7.92 seconds 220 \times 0.036 \text{ s/TMU} = 7.92 \text{ seconds} 220 × 0.036 s/TMU = 7.92 seconds

Equivalent minutes: 220 × 0.0006 min/TMU = 0.132 minutes 220 \times 0.0006 \text{ min/TMU} = 0.132 \text{ minutes} 220 × 0.0006 min/TMU = 0.132 minutes

Part B: Work Sampling Study and Standard Time Derivation

An industrial engineering team investigates a packaging station to establish labor standards via work sampling over a 2-week period (80 total operating hours = 4,800 minutes):

Preliminary historical estimates indicate the packaging operator is actively packing approximately 75% of the time ( p = 0.75 p = 0.75 p = 0.75 ).

Management demands a 95% confidence level ( z = 1.96 z = 1.96 z = 1.96 ) with an absolute precision of ± 2.5 % \pm 2.5\% ± 2.5% ( e = 0.025 e = 0.025 e = 0.025 ).

Step 1: Compute Required Work Sampling Observations ( N N N )

N = z 2 ⋅ p ( 1 − p ) e 2 = ( 1.96 ) 2 × 0.75 × ( 1 − 0.75 ) ( 0.025 ) 2 = 3.8416 × 0.1875 0.000625 = 0.7203 0.000625 = 1 , 152.48 ⟹ 1 , 153 observations N = \frac{z^2 \cdot p(1 - p)}{e^2} = \frac{(1.96)^2 \times 0.75 \times (1 - 0.75)}{(0.025)^2} = \frac{3.8416 \times 0.1875}{0.000625} = \frac{0.7203}{0.000625} = 1,152.48 \implies 1,153 \text{ observations} N = e 2 z 2 ⋅ p ( 1 − p ) ​ = ( 0.025 ) 2 ( 1.96 ) 2 × 0.75 × ( 1 − 0.75 ) ​ = 0.000625 3.8416 × 0.1875 ​ = 0.000625 0.7203 ​ = 1 , 152.48 ⟹ 1 , 153 observations

Step 2: Calculate Standard Time from Field Observations

During the 80 hours (4,800 minutes), exactly 1,200 random observations were conducted:

The operator was observed in active packaging work in 900 observations ( p ^ = 900 / 1200 = 0.750 \hat{p} = 900 / 1200 = 0.750 p ^ ​ = 900/1200 = 0.750 ).

Total finished packages produced during the study: Q = 600 units Q = 600 \text{ units} Q = 600 units .

Average performance rating during active observations: P R = 110 % = 1.10 PR = 110\% = 1.10 PR = 110% = 1.10 .

Total PFD allowances applied to normal time: A total = 15 % = 0.15 A_{\text{total}} = 15\% = 0.15 A total ​ = 15% = 0.15 .

Calculate Observed Time per unit: Total Active Packaging Time = 4 , 800 minutes × 0.750 = 3 , 600 minutes \text{Total Active Packaging Time} = 4,800 \text{ minutes} \times 0.750 = 3,600 \text{ minutes} Total Active Packaging Time = 4 , 800 minutes × 0.750 = 3 , 600 minutes O T = 3 , 600 minutes 600 units = 6.00 minutes per unit OT = \frac{3,600 \text{ minutes}}{600 \text{ units}} = 6.00 \text{ minutes per unit} OT = 600 units 3 , 600 minutes ​ = 6.00 minutes per unit

Calculate Normal Time per unit: N T = O T × P R = 6.00 × 1.10 = 6.60 minutes per unit NT = OT \times PR = 6.00 \times 1.10 = 6.60 \text{ minutes per unit} NT = OT × PR = 6.00 × 1.10 = 6.60 minutes per unit

Calculate Standard Time per unit: S T = N T × ( 1 + A total ) = 6.60 × ( 1 + 0.15 ) = 6.60 × 1.15 = 7.59 minutes per unit ST = NT \times (1 + A_{\text{total}}) = 6.60 \times (1 + 0.15) = 6.60 \times 1.15 = 7.59 \text{ minutes per unit} ST = NT × ( 1 + A total ​ ) = 6.60 × ( 1 + 0.15 ) = 6.60 × 1.15 = 7.59 minutes per unit

Standard Production Rate: R hour = 60 min/hr 7.59 min/unit = 7.91 units per hour R_{\text{hour}} = \frac{60 \text{ min/hr}}{7.59 \text{ min/unit}} = 7.91 \text{ units per hour} R hour ​ = 7.59 min/unit 60 min/hr ​ = 7.91 units per hour