What is Robust Quality Engineering(RQE)?

　The quality loss function is a mathematical expression that quantifies the social loss caused by variability in product and process functions, based on deviations from their target values. Robust Quality Engineering (RQE), also known as Robust Engineering or the Taguchi Method, aims to minimize such societal losses. The definition of quality proposed by Dr. Genichi Taguchi is presented below.

　The quality of goods and services is determined by the loss to society that occurs after they are introduced to the market. This quality is assessed based on monetary loss: the smaller the loss, the higher the quality.
　It's important to note that this assessment does not include losses resulting from the intended function of the product itself (such as alcohol). Instead, it takes into account factors like loss due to variability, pricing, usage costs, maintenance expenses, and environmental pollution, among others.             　　　　　　　　 – Genichi Taguchi

What can poor engineering quality lead to?
　Poor engineering quality leads to failure modes and quality problems. When such issues occur during the warranty period, repair costs are borne by the producer; after the warranty period, the costs are borne by the customer. Regardless of who pays, a loss is incurred.
These losses are not limited to direct costs such as repair expenses. From a long-term, societal perspective, losses may be short-term or long-term, direct or indirect, and tangible or intangible.

The content of Quality Loss can include the following.
　・Costs and time incurred by customers and users for repair, maintenance, and replacement
　・Customer and user dissatisfaction, discomfort, anxiety, injury, and loss of life
　・Reduced resale value
　・Waste of global resources
　・Losses due to environmental pollution
　・Warranty and recall costs (short-term losses for producers)
　・Decreases in repeat customers (long-term losses for producers)
　・Damage to corporate image and reputation (long-term losses for producers)
　・Declines in competitiveness and market share (long-term losses for producers)
And others

　Traditional quality assessment, typically represented by inspection, evaluates whether specified requirements are met. This approach is essentially a go/no-go judgment and reflects an accounting-oriented mindset.
　In contrast, Taguchi’s loss function evaluates quality loss as a continuous function. For example, the difference in evaluating a quality characteristic relative to its target value m can be illustrated as follows

The Quality Loss Function (QLF) provides a monetary evaluation of quality and performance.
　Dr. Genichi Taguchi developed this concept as the basis of the QLF, which is an equation for estimating the loss associated with deviations from ideal performance. The illustrations above show the case of a Nominal-the-Best characteristic with a target value. Loss functions are also derived for Smaller-the-Better, Larger-the-Better, and dynamic characteristics. In this framework, the key question is not whether a requirement is met, but how far the actual performance deviates from the ideal. The fundamental principle is that loss is proportional to the square of the deviation from the ideal value. By expressing quality loss in monetary terms, the QLF enables rational decision-making in situations where trade-offs between cost and quality must be considered.

Applications of the Quality Loss Function:
Tolerance design for investment decision-making
　　Example: Should we invest in a $20,000 measuring instrument that reduces 　　
　　measurement error by half?
Multi-factor tolerance design using orthogonal arrays
　　Example: Which of the 14 components should be upgraded to meet the required 　　
　　performance?
Setting tolerances and specifications (tolerancing)
　　Example: How should the specification for braking stopping distance be determined?
Optimization of process control schemes
　　Example: How should the frequency of process inspections, adjustment limits, and 　　
　　preventive actions be determined in process control? What actions should be taken, to
　　what extent, and where should costs be allocated?