Advancing QE Skills (34) | Decision-making for 100% Inspection and No Inspection: A Quantitative Balance of Cost and Risk
A certain electronics assembly company has been continuously complained to by customers for "missed inspections" over the past three months, and the customers have requested an 8D report. The general manager decided at a quality-focused meeting: starting next month, all batches will undergo 100% inspection. Three months later, customer complaints indeed decreased, but the on-time delivery rate dropped from 96% to 78%, the inspection workforce increased by 9 people, and monthly overtime exceeded 1200 hours. However, the customer's production line still found 2 batches of defective products. The general manager began to doubt: Is 100% inspection really effective?
This contradiction is not an issue of execution but of decision-making. 100% inspection, sampling inspection, and no inspection are not three levels of "strict" and "lenient," but three different cost structures for managing risk. The choice should be made based on numerical calculations, not slogans. The value of a quality engineer (QE) in this matter is not to declare "I support 100% inspection," but to provide a table that can calculate the critical point.
1. Principle: 100% Inspection Buys Probability, Not Zero Defects
Three statistical facts that must be accepted:
First, 100% inspection also has an escape rate. The detection rate for visual inspection by humans is typically between 70% and 95%, and it is even lower for fine defects, fast-paced operations, and long periods of continuous work. In other words, 100% inspection reduces the batch defect rate from p to p·e (where e is the escape rate), not to 0. In industry measurements, e ranging from 5% to 30% is common. Any judgment that "100% inspection is reassuring" essentially assumes e=0.
Second, no inspection does not mean no risk, but rather shifting the risk. No inspection moves the exposure point of defects from within the factory to the customer's hands, using external failure costs (sorting, returns, transportation, line stoppages, claims) to cover the risk. It may be cheaper, or it may be much more expensive, depending on the single-piece escape cost and the process defect rate.
Third, there is a clear critical point for decision-making. Let the unit cost of 100% inspection be c, the single-piece escape cost be C, the escape rate be e, and the process defect rate be p:
- Total cost per piece for 100% inspection = c + p·e·C
- Total cost per piece for no inspection = p·C
- Critical defect rate p = c / [C·(1-e)]*
When p is higher than p*, 100% inspection is cheaper. When p is lower than p*, no inspection or sampling inspection is cheaper. This formula, with only four parameters, can transform the debate over "whether to perform 100% inspection" into a calculation.
2. Five Practical Steps: Calculate the Decision
Step One: Calculate the unit cost of 100% inspection c, not just labor costs.
For a workstation with a cycle time of 45 seconds per piece, the inspector's monthly comprehensive cost is 9000 yuan, and the monthly effective working hours are 160 hours:
- Labor cost per piece = 9000 ÷ (160×3600÷45) = 9000 ÷ 12800 ≈ 0.70 yuan
- Amortization of fixtures, magnifying glasses, and consumables ≈ 0.30 yuan
- Cycle time occupation, handling, and work-in-progress occupation ≈ 0.80 yuan
- Total c = 1.80 yuan per piece
Calculating only the labor cost would yield 0.70 yuan, which is 60% lower than the actual value. This is the source of many incorrect conclusions that "100% inspection is very cheap."
Step Two: Calculate the single-piece escape cost C, categorized by exposure location.
| Exposure Location | Typical Loss Composition | Cost per Piece |
|---|---|---|
| Discovered in the next in-house process | Rework time, scrapped materials | 20～60 yuan |
| Discovered in customer incoming quality control (IQC) | Sorting time, return transportation, line stoppage claims, expedited replenishment | 200～400 yuan |
| Discovered by end-user or OEM | Claims, recall costs, reputation and order loss | 800 yuan or more |
Calculate the expected value based on the probability of each scenario. In the example, C = 260 yuan.
Step Three: Calculate p, compare it with the actual p, and make a three-tier decision.*
p* = 1.80 ÷ [260×(1-0.15)] ≈ 0.81%
| Actual Process Defect Rate p | Total Cost per Piece for 100% Inspection | Total Cost per Piece for No Inspection | Decision |
|---|---|---|---|
| 0.3% (＜p*/2) | 1.92 yuan | 0.78 yuan | No inspection or skip batch, retain periodic verification |
| 0.8% (≈p*) | 2.11 yuan | 2.08 yuan | Critical zone, dual-track sampling inspection + process improvement |
| 1.5% (＞p*) | 2.39 yuan | 3.90 yuan | 100% inspection, saves 1.51 yuan per piece |
Note the third row: when the defect rate is 1.5%, 100% inspection saves 1.51 yuan per piece, which amounts to 3 million yuan for an annual production of 2 million pieces. This is the only valid reason for 100% inspection—not because it is "stricter," but because the numbers add up. Conversely, insisting on 100% inspection at a defect rate of 0.3% means spending 1.14 yuan per piece on a non-existent benefit.
Step Four: Use blind samples to measure the actual escape rate e.
e is the parameter most easily determined by guesswork in the entire formula. The method is: take 50 known defective pieces (10 of which are borderline samples with minor defects), randomly mix them with 450 normal pieces, and have the inspector inspect them under normal cycle time and lighting conditions, repeating the process 3 times. e = cumulative number of missed inspections ÷ cumulative number of defective pieces input. If e > 20%, it indicates that the current inspection method itself is nonconforming. Adding more people to perform 100% inspection is an ineffective investment—first, improve the tooling, magnification, lighting, poka-yoke, or implement automatic inspection to reduce e to below 10%, then discuss the inspection intensity.
Step Five: Establish written rules for the entry and rollback of sampling inspection and no inspection.
Low sample size sampling inspection is often mistakenly considered "cheaper 100% inspection." In the same example, when N=2000, n=32, Ac=0, and p=1.5%, the acceptance probability Pₐ = 0.985³² ≈ 0.62, the outgoing defect rate still reaches 1.01%, and the cost per piece is 2.66 yuan, which is more expensive than the 2.39 yuan for 100% inspection. The true value of sampling inspection lies in batch judgment—it is the signal source for triggering rollback and improvement, not a means to reduce escape.
No inspection (skip batch) must meet four entry conditions simultaneously, without exception:
| Entry Condition | Quantitative Threshold |
|---|---|
| Continuous batch quality | Zero defects in 5 consecutive batches (10 batches for high-risk characteristics) |
| Process control | Cpk ≥ 1.33, or no abnormal rules triggered in the control chart for 25 consecutive points |
| System and history | Process/supplier score ≥ 90 points, no customer complaints related to the characteristic in the past 6 months |
| Monitoring retention | One batch out of every 10 batches is inspected using a stricter scheme, and process parameters are monitored as usual |
Rollback rules must also be clearly defined: if one batch is nonconforming, one related customer complaint occurs, or the process capability falls below 1.33, skip batch inspection must be immediately interrupted and revert to normal inspection. Recovery requires 5 consecutive batches to be conforming and a root cause analysis to be completed. Safety characteristics, regulatory characteristics, and customer-designated special characteristics are never eligible for no inspection.
3. Common Misconceptions
Misconception One: Treating 100% inspection as a corrective action. 100% inspection is a containment measure and is reasonable in the D3 temporary measures of the 8D process. However, using it to close D5/D6 means turning a one-time cost into a permanent one and masking the root cause of the process. The judgment standard is simple: does 100% inspection have an associated expiration date and exit conditions?
Misconception Two: Using AQL as the basis for no inspection. AQL is the acceptance quality level for sampling inspection, not the "allowed defect rate," and it cannot prove batch conformity. The criteria for no inspection are process capability and historical batch quality, which are independent of AQL values. Conversely, do not assume that 100% inspection is necessary just because "the customer specifies AQL 0.65"—AQL only constrains the sampling scheme, not your process improvement path.
Misconception Three: Removing all monitoring after no inspection. The cost advantage of no inspection is based on the premise of "process stability." Once the verification batches and parameter monitoring are removed, the premise disappears, and the risk returns in the form of customer complaints. No inspection must retain three points: periodic verification batches, process parameter monitoring, and a feedback channel from the customer.
Misconception Four: Calculating only inspection labor costs, not cycle time and delivery losses. Placing 100% inspection on a bottleneck process often incurs hidden costs that are 2 to 3 times the labor cost. In the example, the 0.70 yuan labor cost is actually 1.80 yuan when considering the true cost. If this is further compounded by expedited shipping costs and order losses due to delivery delays, many "cost-effective" 100% inspections are actually not cost-effective.
Misconception Five: Using e=0 for decision-making. Substituting e=0 will lower p* (from 0.81% to 0.69% in the example), systematically pushing the decision towards 100% inspection. Any model that ignores the escape rate will overestimate the value of inspection.
4. Self-Check List
- Does the unit cost of 100% inspection c include cycle time occupation, fixture and consumable costs, re-evaluation handling, and handling losses, and not just labor costs?
- Is the single-piece escape cost C estimated and weighted for the three exposure locations: in-house, customer, and end-user?
- Have the actual p values for the past 3 months, categorized by characteristics, been used to calculate p*, and have they been clearly defined for no inspection, sampling inspection, and 100% inspection?
- Has the actual escape rate e for this workstation been measured using blind samples? When e > 20%, has the inspection method been improved before adding more people?
- Are there written entry conditions, rollback rules, approvers, and records for no inspection, and have safety, regulatory, and customer-designated special characteristics been excluded?
100% inspection, sampling inspection, and no inspection are not inherently right or wrong. The mistake is making a decision without calculation. By putting c, C, e, and p on the table, the decision is no longer a matter of differing positions but a calculable arithmetic problem.
100% inspection buys the probability of interception, not zero defects
Knowledge code: 11.1.2
Version: v20261021
Author: QTank QTank is dedicated to providing systematic professional knowledge, methodologies, and practical tools for quality management practitioners, helping companies continuously improve their quality capabilities.