Advanced Cost of Quality Model Generator

Advanced Total Cost of Quality (TCoQ) Model Generator

Created By : Ir. MD Nursyazwi

Generate a custom TCoQ model using granular cost data to find the optimal quality level for your business.

How to Use This Quality Cost Optimization Tool

This tool lets you build a personalized Total Cost of Quality (TCoQ) model by breaking down your costs into four key categories. Use the sliders to input your data for each field below, and the generator will create a custom model for you.

Understanding the Data Inputs:

Cost of Conformance is the investment you make to prevent or find defects. These costs go up as your quality level increases.

1. Prevention Costs: Money spent to prevent defects from happening (e.g., training, process design, quality planning).
   • Fixed: A one-time or base cost (e.g., a software license for a quality management system).
   • Variable: The cost that increases with the level of quality you're targeting (e.g., ongoing training or process-improvement effort per percentage of quality increase).
2. Appraisal Costs: Money spent on inspecting, testing, and auditing to ensure quality (e.g., quality control checks, lab testing, materials inspection).
   • Fixed: A base cost for equipment or an initial audit setup.
   • Variable: The cost that increases as you perform more frequent or thorough inspections.

Cost of Non-Conformance is the financial loss you incur because of defects. These costs decrease significantly as your quality level improves.

1. Internal Failure Costs: Costs from defects found before the product reaches the customer (e.g., rework, scrap, re-testing, downtime).
   • Base Cost: The total cost of internal failures if your quality was at 0%. This is the maximum potential cost.
   • Reduction Rate (k_i): This determines how quickly these costs decrease as you improve quality. A higher number means costs drop off more steeply (exponential decay).
2. External Failure Costs: Costs from defects found after the product is delivered to the customer (e.g., warranty claims, recalls, liability, lost reputation).
   • Base Cost: The total cost of external failures if your quality was at 0%. This is often much higher than internal failure costs due to reputation damage.
   • Reduction Rate (k_e): Determines how quickly these costs decrease with quality improvements.

As you enter your data, the chart will update automatically, showing your specific cost curves and identifying the optimal quality level where your total costs are at their minimum, maximizing profitability.

Input Your Company's Cost Data

Adjust the sliders below to accurately reflect your organization's cost structure. The currency selected will be used for all chart labels.

Select Currency: US Dollar ($) Euro (€) Japanese Yen (¥) British Pound (£) Australian Dollar (A$) Malaysian Ringgit (RM)

Cost of Conformance (Investment)

Fixed Prevention Costs

2000

Variable Prevention Costs (per % quality)

20

Fixed Appraisal Costs

1000

Variable Appraisal Costs (per % quality)

15

Cost of Non-Conformance (Loss)

Internal Failure Base Cost (at 0% quality)

8000

Internal Failure Reduction Rate (k_i)

0.04

External Failure Base Cost (at 0% quality)

12000

External Failure Reduction Rate (k_e)

0.06

Enter your data to calculate the optimal quality level.

Total Cost of Quality Model Visualization

This chart displays the classic TCoQ curve (blue line), showing the equilibrium point where total costs are minimized.

Individual Cost Component Breakdown

View the distinct behavior of the four main cost types (Prevention, Appraisal, Internal Failure, External Failure) as Quality Level increases.

Prevention Costs

Appraisal Costs

Internal Failure Costs

External Failure Costs

Theoretical Framework of the Advanced TCoQ Model

This advanced model is built upon identifying the optimal equilibrium between the investment made to ensure quality and the costs resulting from poor quality. The Total Cost of Quality (TCoQ) is the sum of these opposing financial forces, and the objective is to find the ideal Quality Level (Q) where this total cost is minimized.

Modeling the Cost of Conformance (Prevention & Appraisal)

The Cost of Conformance clearly represents the proactive investment made to prevent and detect product defects. As quality improves, spending on activities like employee training (Prevention) and thorough testing (Appraisal) increases. This relationship is modeled as a simple linear function, rising predictably in direct proportion to the Quality Level (Q).

Cost_Conformance(Q) = (Fixed_P + Fixed_A) + (Var_P + Var_A) * Q

In this equation, the sum of fixed costs establishes a mandatory baseline cost. The variable costs define the linear slope of the increase as the Quality Level (Q, expressed as a percentage) improves.

Modeling the Cost of Non-Conformance (Internal & External Failure)

Conversely, the Cost of Non-Conformance represents the significant financial losses incurred due to defects and quality failures. These losses follow an asymptotic relationship with quality. As the Quality Level approaches 100%, these failure costs decay rapidly, modeled using an exponential curve that approaches zero.

Cost_Internal(Q) = Base_I * e^(-k_i * Q)

Cost_External(Q) = Base_E * e^(-k_e * Q)

In these exponential equations, the Baseline Cost represents the maximum potential failure cost if quality were zero. The Reduction Rate (k_i for internal, k_e for external) determines the steepness of the exponential decay curve, which is key to understanding how fast failure costs are reduced as quality improves.

The Total Cost of Quality (TCoQ) Optimization

The Total Cost of Quality (TCoQ) is simply the summation of all the Conformance and Non-Conformance components.

Cost_Total(Q) = Cost_Conformance(Q) + Cost_Internal(Q) + Cost_External(Q)

The resulting TCoQ curve is typically parabolic: it initially decreases sharply as dramatic failure costs are eliminated by modest conformance spending, but it eventually rises again when the organization invests excessively in conformance to achieve the final, marginal gains in quality. The lowest point on this combined curve represents the theoretical Optimal Quality Level, where total costs are minimized and the investment in quality is most effective for maximum profitability.

References and Further Reading

1. Blog post: The Cost of Quality Model
2. Book: Juran's Quality Handbook
3. Book: Total Quality Control, Revised (Fortieth Anniversary Edition)
4. Book: Agile Practice Guide
5. Book: A Guide to the Project Management Body of Knowledge
6. Book: A Guide to The Project Management Body of Knowledge by Project Management Institute 7th Edition
7. Future reference will be added here.

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