Quality concepts and cost of quality

Why it matters

Poor quality is expensive long before a customer complains: scrap, rework, re-inspection, warranty claims and lost orders often add up to several per cent of sales. Measuring the cost of quality turns "quality" from a slogan into a number that managers can budget for, and it shows where money spent on prevention pays back most. Quality definitions and cost categories are also standard short questions in exams and interviews.

Key ideas

What quality means. Different authorities stress different aspects:

• Juran: fitness for use, as judged by the user.
• Crosby: conformance to requirements; the standard is zero defects.
• Deming: a predictable degree of uniformity and dependability at low cost, suited to the market; quality is improved by reducing variation in the system.
• Taguchi: the loss a product causes to society after it is shipped; any deviation from the target value causes a loss, even inside the tolerance.
• ISO 9000: the degree to which a set of inherent characteristics of an object fulfils requirements.

Dimensions of quality (Garvin). Performance, features, reliability, conformance, durability, serviceability, aesthetics and perceived quality. A product can score well on some and poorly on others.

Quality of design, conformance and performance.

• Quality of design: how good the specification is (grade, features, tolerances chosen). Raising it usually raises cost.
• Quality of conformance: how well production matches the design. Raising it usually lowers total cost, because failures fall.
• Quality of performance: how the product actually behaves in service; it depends on both of the above.

Inspection, quality control, quality assurance, TQM. Inspection sorts good from bad after the fact. Quality control uses measurement and feedback (for example control charts) to keep a process on target. Quality assurance is the planned system that gives confidence requirements will be met (procedures, audits, ISO 9001). TQM extends quality to every function and every person, with customer focus and continuous improvement.

Cost of quality (PAF model). Quality costs are grouped into four categories:

• Prevention costs (stop defects being made): quality planning, process capability studies, design reviews, training, supplier development, preventive maintenance of quality-critical equipment, poka-yoke devices.
• Appraisal costs (find defects by measuring): incoming, in-process and final inspection and testing, gauges and their calibration, inspection staff, quality audits of product.
• Internal failure costs (defects found before the product reaches the customer): scrap, rework, re-inspection of reworked parts, downgrading, machine downtime caused by quality problems, failure analysis.
• External failure costs (defects found by the customer): warranty repairs and replacements, returns, complaint handling, recalls, penalties, product liability and lost goodwill and future sales.

Prevention plus appraisal is the cost of good quality (cost of conformance); internal plus external failure is the cost of poor quality (cost of non-conformance).

The economics. The classical model shows failure costs falling and prevention-plus-appraisal costs rising as conformance improves, giving an optimum below 100 % conformance. Modern practice (Crosby, Deming, Six Sigma) argues that prevention costs do not rise steeply when improvement comes from better processes rather than more inspection, so total cost keeps falling towards zero defects. The "1-10-100" rule of thumb expresses the escalation: a defect that costs 1 unit to prevent costs about 10 to find and fix inside the plant and about 100 once it reaches the customer. Many failure costs (lost goodwill, the "hidden factory" of unrecorded rework) never appear in accounts, so the measured cost of quality understates the true one.

Formulas

CoQ = C_P + C_A + C_IF + C_EF

• CoQ = total cost of quality; C_P = prevention cost; C_A = appraisal cost; C_IF = internal failure cost; C_EF = external failure cost (all in ₹ per period, e.g. per year).

CoQ % = (CoQ / Sales) × 100

• Cost of quality as a percentage of sales revenue in the same period; also used per unit of production or per hour of direct labour for comparison between plants.

L(y) = k (y − m)²

• Taguchi quadratic loss for one part (₹). y = measured value of the characteristic; m = target (nominal) value; k = loss coefficient (₹ per unit²), found from k = A₀ / Δ₀², where A₀ = loss (₹) when the deviation equals the customer tolerance Δ₀.

L̄ = k [σ² + (ȳ − m)²]

• Expected loss per part for a process with mean ȳ and standard deviation σ (same unit as y). It shows that both off-centring and spread cost money.

Worked examples

Example 1 (standard): classifying costs and finding CoQ Given: a plant's annual sales are ₹5 crore (₹500 lakh). Its quality-related costs for the year, in ₹ lakh: operator training 3; supplier quality audits 2; incoming inspection 4; final testing 6; gauge calibration 1; scrap 9; rework 5; warranty replacements 10; customer complaint handling 2. Find each category, the total CoQ, CoQ as a percentage of sales and the share of failure costs.

1. Prevention: training + supplier audits = 3 + 2 = ₹5 lakh.
2. Appraisal: incoming inspection + final testing + calibration = 4 + 6 + 1 = ₹11 lakh.
3. Internal failure: scrap + rework = 9 + 5 = ₹14 lakh.
4. External failure: warranty + complaints = 10 + 2 = ₹12 lakh.
5. CoQ = 5 + 11 + 14 + 12 = ₹42 lakh.
6. CoQ % = 42 / 500 × 100 = 8.4 %.
7. Failure share = (14 + 12) / 42 = 61.9 %.

CoQ = ₹42 lakh, 8.4 % of sales; 61.9 % of it is failure cost. The low prevention share (about 12 %) suggests money moved into prevention would pay back.

Example 2 (GATE level): Taguchi loss Given: a shaft has target diameter 50.00 mm and customer tolerance ±0.05 mm. A shaft at the tolerance limit causes a loss of ₹200. The process produces shafts with mean 50.01 mm and standard deviation 0.02 mm. Find the expected loss per shaft and the annual loss for 10 000 shafts.

1. k = A₀ / Δ₀² = 200 / 0.05² = 200 / 0.0025 = 80 000 ₹/mm².
2. L̄ = k [σ² + (ȳ − m)²] = 80 000 × [0.02² + 0.01²].
3. = 80 000 × (0.0004 + 0.0001) = 80 000 × 0.0005 = ₹40 per shaft.
4. Annual loss = 40 × 10 000 = ₹4 00 000.

Expected loss ₹40 per shaft, ₹4 lakh per year. Re-centring the process on 50.00 mm would remove the (ȳ − m)² term and cut the loss to 80 000 × 0.0004 = ₹32 per shaft (₹3.2 lakh a year), even though nearly every shaft is already within tolerance.

Common mistakes

• Putting inspection under prevention; inspection finds defects, it does not prevent them, so it is appraisal.
• Classifying scrap found at final inspection as external failure; it is internal, because the customer has not received it.
• Treating cost of quality as "the cost of the quality department"; most of it sits in production, service and sales.
• Assuming higher quality always costs more; that is true of quality of design, not of quality of conformance.
• In the Taguchi loss, forgetting to square the tolerance when finding k, or dropping the off-centre term (ȳ − m)².

For GATE PI

Expect classification questions (which cost belongs to which category), statements about the cost-of-quality trade-off, matching quality pioneers to their definitions, and short numericals: total CoQ or a missing component, CoQ as a percentage of sales, and Taguchi loss with a given loss coefficient or tolerance-limit loss. Practise reading which costs occur before and after delivery.

Quick check

1. Is the cost of calibrating gauges a prevention or an appraisal cost?
2. Name the cost category for a product recall.
3. Prevention ₹4 lakh, appraisal ₹6 lakh, total CoQ ₹25 lakh. What is the total failure cost?
4. In the Taguchi loss function, what happens to the loss when a part is exactly on target?

Answers: 1. Appraisal. 2. External failure. 3. ₹15 lakh. 4. It is zero.