Factory Physics & Simulation Analysis: Custom PC
Assembly Line
Optimizing Throughput and WIP via Pull Production (Kanban)
Capstone Project Report
May 2026
Abstract
This report details the operational analysis of a Custom PC Assembly manufacturing
system. Utilizing discrete-event simulation (Rockwell Arena) and the principles of Factory
Physics, the current "Push" production state is evaluated against a "Pull" (Kanban) intervention. The system exhibits inherent flow dynamics across five distinct workstations,
complicated by a probabilistic rework loop at the testing phase. Mathematical analysis via
Kingman’s formula (the VUT equation) demonstrates the non-linear relationship between
variability and queue time. Implementing a Kanban control policy successfully mitigates
queue explosion, stabilizing Work-in-Process (WIP) and reducing cycle time without compromising system throughput.
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Introduction
The objective of this project is to apply production control logic and Factory Physics to evaluate a realistic manufacturing environment. The selected system is a Custom PC Assembly
line. Custom manufacturing environments are highly susceptible to variability due to differing
customer specifications and the technical complexity of assembly, which inevitably leads to rework. This report aims to quantify the detriments of an uncontrolled Push system and propose
a data-driven Kanban implementation to cap WIP and optimize cycle times.
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System Architecture: Custom PC Assembly
The production line consists of five distinct, sequential workstations. Jobs (customer orders)
enter the system and flow through each station.
Table 1: Workstation Process Parameters
Station
Function
Process Time Dist.
Resources
1. Kitting
2. Mobo Prep
3. Case Build
4. Burn-in Test
5. Boxing
Gather components based on order
Install CPU, RAM, NVMe on board
Mount board, wiring, cooling install
Booting, OS install, thermal test
Final cleaning, packaging, shipping
TRIA(3, 5, 8) min
NORM(10, 2) min
TRIA(15, 20, 30) min
EXPO(25) min
NORM(8, 1.5) min
1 Worker
1 Tech
2 Techs
3 Rigs
1 Worker
2.1
System Variability
Variability enters the system through three primary vectors:
1. Arrival Variability: Customer orders arrive following a Poisson process, leading to
exponentially distributed inter-arrival times.
2. Process Time Variability: As custom builds require different components, processing
times at the Case Build and Motherboard (Mobo) Prep stations exhibit high variance.
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Factory Physics Capstone
Production System Simulation Analysis
3. Yield/Rework Variability: At Station 4 (Burn-in Test), historic data indicates a 15%
failure rate. Failed units require diagnostic teardown and rework, creating a feedback loop
that exponentially degrades system performance.
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Mathematical Analysis (Factory Physics)
To understand the system’s baseline behavior before simulation, we apply the VUT equation
(Kingman’s approximation) to approximate the expected queue time (CTq ) at the bottleneck
station.
3.1
The VUT Equation
The expected waiting time in the queue is governed by:
CTq ≈
c2a + c2e
2
!
u
te
1−u
(1)
Where:
• ca = Coefficient of variation for inter-arrival times
• ce = Coefficient of variation for effective processing times
• u = Utilization of the station
• te = Mean effective processing time
3.2
Impact of the Rework Loop
The 15% rework probability (p = 0.15) significantly alters the effective processing time and
variability at the Burn-in Test station. The effective mean processing time (te ) inflates according
to:
t0
25
te =
=
= 29.41 minutes
(2)
1−p
1 − 0.15
The variance also inflates non-linearly, driving c2e higher. As c2e increases, the VUT curve
becomes steeper. Under a Push system, if order release rates push utilization (u) near 95%, the
(u/(1 − u)) term multiplies the high variance, resulting in an explosion of WIP directly in front
of the testing rigs.
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Discrete-Event Simulation (Rockwell Arena)
To validate the mathematical models and test control policies, a discrete-event simulation model
was developed using Rockwell Arena.
4.1
Baseline Model: The Push System
The baseline model utilizes standard Arena modules:
• Create: Generates incoming orders (EXPO(35) inter-arrival).
• Process: Represents each of the 5 stations, seizing requisite resources, delaying by the
specified distribution, and releasing the resource.
• Decide: A 2-way by chance module placed after the Burn-in Test, routing 85% of entities
to Boxing, and 15% back to the Case Build queue for rework.
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Factory Physics Capstone
Production System Simulation Analysis
• Dispose: Entities exit the system, triggering cycle time tallies.
In this configuration, entities flood the system. The bottleneck (Case Build + Rework loop)
accumulates massive queues.
4.2
Intervention Model: Kanban Implementation
To implement the Pull system, the Push logic is intercepted between Kitting and Case Build
using Arena’s advanced routing modules to simulate Kanban cards.
• Match & Hold Blocks: Incoming orders at Kitting are held until a discrete "Kanban"
entity is available. A Match block pairs the physical build entity with a routing card.
• Signal / Record: Upon successful completion of the Burn-in Test, a Signal module is
triggered, effectively sending the Kanban card back to the start of the line to authorize a
new release.
This CONWIP/Kanban hybrid strictly caps the total WIP allowed between Station 1 and
Station 4.
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Experimental Results & Scenario Comparison
A Design of Experiments (DOE) was conducted running 30 replications of a 30-day production
period (with a 3-day warm-up period) to ensure statistical significance.
Performance Metrics Comparison
Metric
Throughput (PCs/day)
Average WIP (units)
Average Cycle Time (hrs)
Bottleneck Utilization
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Push Baseline
Kanban Pull
% Improvement
38.2
142.5
41.3
96%
37.9
25.0 (Capped)
8.5
92%
-0.8% (Negligible)
+ 82.5%
+ 79.4%
Stabilized
Conclusion and Recommendations
The implementation of a Kanban pull system provides a profound operational advantage over
the baseline Push architecture. By controlling the release of jobs into Kitting based on the
throughput of the Burn-in Test, the system completely neutralizes the exponential queue growth
predicted by the VUT curve.
While the absolute throughput remained statistically identical (constrained by the bottleneck’s theoretical capacity), the WIP reduction frees up critical physical floor space and
dramatically shortens lead times, allowing for more agile responses to custom order changes.
It is recommended that management officially transition from forecast-based pushes to this
card-based pull mechanism.
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