9.2 Worker–Machine (Man–Machine) Charts, Multiple Activity Analysis & Synchronous Servicing

9.2 Worker–Machine Charts & Synchronous Servicing

The specification lists man–machine charts with therbligs and motion study as methods for analysis and improvement. Process charts follow one subject, such as a part or a worker. A multiple activity chart puts several subjects side by side on one time scale, so you can see who waits for whom.

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1. Building a Worker–Machine Chart

Draw one vertical column per subject (the worker and each machine), with time running down the page. Each block is shaded by type:

• Combined (concurrent) work: the worker and machine are both engaged, such as loading or unloading.
• Independent work: the worker inspects, packs, or walks while the machine runs automatically, or the machine runs while the worker is elsewhere.
• Idle: waiting for the other party.

At the bottom, summarize the cycle time, the working and idle time of each subject, and the utilization (working time ÷ cycle time).

Example: one operator, one CNC lathe. Loading takes 1.0 min (worker and machine together), the automatic cut takes 4.0 min, and the operator spends 0.5 min deburring the previous part.

Time (min)   OPERATOR                 LATHE
0.0 - 1.0    Load / unload (with M)   Being loaded
1.0 - 1.5    Deburr previous part     Cutting (automatic)
1.5 - 5.0    IDLE                     Cutting (automatic)
Cycle = 5.0 min | Operator busy 1.5 min (30%) | Lathe busy 5.0 min (100%)

The operator is idle 70% of the cycle. That idle time is the opportunity to have one person tend several machines.

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2. Synchronous Servicing

Synchronous servicing applies when machines run identical, regular cycles and the worker visits them in a fixed order. Define:

• $l$ = loading and unloading time per machine (worker and machine both occupied)
• $m$ = automatic machine run time
• $w$ = worker's independent time per machine (walking to the next machine, inspecting, packing)

The ideal number of machines per operator, where neither worker nor machines wait, is:

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

Usually $n'$ is not an integer, so compare the integers on either side:

Each cycle produces $n$ units. With operator cost rate $K_1$ and machine cost rate $K_2$ (per minute), the cost per unit is:

$TEC_n = \frac{(K_1 + n K_2)\, T_c}{n}$

Worked Example

Using the lathe data, $l = 1.0$, $m = 4.0$, and $w = 0.5$ min:

$n' = \frac{1.0 + 4.0}{1.0 + 0.5} = 3.33$

Labor costs $30/hr ($0.50/min) and each machine costs $60/hr ($1.00/min).

Assign 3 machines. The worker is idle $5.0 - 3(1.5) = 0.5$ min per cycle, but that costs less than leaving four expensive machines idle 1 min each cycle. When machine time is cheap relative to labor, the answer often shifts to the higher integer, so always compute both.

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3. Random Servicing and Machine Interference

When machines stop at random (jams, tool breaks, random material runouts), several may need the operator at the same moment. A machine that waits while the operator serves another is suffering machine interference.

• A simple binomial model treats each machine as independently down with probability $p$ at a random instant. The chance that $k$ of $n$ machines are down is $\binom{n}{k} p^k (1-p)^{n-k}$, and the expected number waiting beyond the one being served estimates interference.
• Finite-source queueing models (the calling population equals the number of machines) and simulation give more exact answers.

Example: Four machines are each down 10% of the time at random. $P(\text{2 or more down}) = 1 - 0.9^4 - 4(0.1)(0.9)^3 = 1 - 0.6561 - 0.2916 = 0.052$. About 5% of the time a stopped machine waits for the operator, which is usually acceptable.

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4. Related Multiple Activity Charts

• Left-hand/right-hand (operator) charts compare the two hands of one worker; see therblig analysis in the methods section.
• Gang (crew) charts show several workers and machines, such as a crew loading a press or a pit crew, to balance their work.
• Service versions apply the same logic to people and equipment in services: one technician running several analyzers in a laboratory, or one agent handling several chat sessions.