Pareto Chart, Scatter Diagram, and Control Chart: What Problems Do They Solve in Quality Costs —— COQ Analysis Tool Division Table
The most common way to write a quality cost report is: one line for the total amount, four categories for the proportions, and year-over-year changes. Such a report can report but cannot improve. The reason is usually not a lack of data, but rather the misuse of tools—viewing "ranking issues" as "trend issues" and "relationship issues" as "distribution issues," leading to conclusions that merely emphasize the importance of quality costs.
The seven tools cannot substitute for each other because they answer different questions. The following division table ensures that each type of cost data is analyzed using the appropriate tool.
1. First, Distinguish the Three Forms of Cost Data
Before deciding which tool to use, first determine what the quality cost data looks like.
| Data Form | Typical Cost Data | Questions It Can Answer | Appropriate Tool |
|---|---|---|---|
| Categorized Summary (amounts grouped by subject, product, process) | Rework costs, scrap costs, reinspection costs, claim costs | Where is the money spent, which category, which area | Check sheet, stratification, Pareto chart |
| Continuous Measurement (one value per piece, per batch) | Rework time per piece, loss amount per piece, loss amount per batch | How much fluctuation, whether there is drift, correlation with what | Histogram, scatter diagram, control chart |
| Causal Candidates (multiple parties with different opinions) | "It's the mold temperature," "It's the incoming material," "It's the manpower" | Which causes are worth verifying | Fishbone diagram (with 5Why closure) |
Misidentifying the data form is the most common waste: using a bunch of data with only monthly totals to draw a control chart, or using a Pareto chart to view fluctuations in time per piece.
2. Division and Interpretation Criteria of the Seven Tools in COQ
| Tool | Input | Output | Interpretation Criteria | Typical Misuse |
|---|---|---|---|---|
| Check sheet | Loss records per batch/day | Analyzable raw table | Fields must be uniform: date, process, machine, failure mode, quantity, loss per piece, amount | Grouping by "discovery process," attributing costs to final inspection |
| Stratification | Check sheet | Stratified grouped data | Conclusions can only be drawn if each stratum has at least 5 events (or at least 30 samples) | Over-stratification, slicing into individual units, making it impossible to see patterns |
| Pareto chart | Amount or quantity after stratification | Ranking and cumulative percentage | Focus on the top 3 items that cumulatively reach 70%; if "other" exceeds 25%, the classification is too coarse | Using quantity ranking to discuss costs and using amount ranking to assign on-site improvements |
| Fishbone diagram | List of candidate causes | Causes to be verified | Divide into "occurrence" and "outflow" branches; end causes must be verifiable | Drawing a full wall without verification, ultimately deciding based on impressions |
| Scatter diagram | Paired data in two columns (n ≥ 15) | Correlation direction and strength, outliers | Stratify before drawing; a consistent direction must appear in at least 3 batches to be considered stable | Mixing data from two teams, diluting the correlation |
| Histogram | Continuous amount or time per piece/batch | Distribution shape | Bimodal = two types of processes or two teams mixed; do not interpret shape if n < 30 | Using average loss per piece to replace distribution, masking large individual losses |
| Control chart | Time series by week or day | Whether influenced by special causes | Cost data is single value, use I-MR; control limits are calculated using at least 20 points from the baseline period | Using budget lines or target lines as control limits, causing daily alerts |
One detail worth mentioning separately: the conclusions from ranking by amount and by quantity in a Pareto chart are often opposite. A small number of high-cost nonconformities (scraping an entire mold, customer returns) rank high in the amount list, while a large number of low-cost nonconformities (flash, scratches) rank high in the quantity list. Cost improvement focuses on the amount list, while on-site improvement focuses on the quantity list. Both lists should be produced, but it must be clear what decisions each is used for.
3. An Example: How to Break Down 860,000 RMB of Monthly Internal Failure Costs
A plastic injection molding factory has monthly internal failure costs of 860,000 RMB, broken down by subject as follows: rework 420,000 RMB, scrap 280,000 RMB, downtime due to material shortage 90,000 RMB, reinspection 40,000 RMB, and concession acceptance 30,000 RMB.
- Pareto chart to define the scope. Rework 49%, scrap 33%, cumulative 82% for these two items; the other three items are temporarily left untouched.
- Stratification to pinpoint the location. In the 420,000 RMB rework costs, Machine 3 accounts for 180,000 RMB, with 120,000 RMB from flash trimming, indicating that one machine is responsible for 30% of the entire factory's rework.
- Histogram to see the shape. The rework time per piece shows a clear bimodal distribution, peaking at around 0.8 minutes and 2.4 minutes, corresponding to the differences in trimming techniques between Team A and Team B.
- Scatter diagram to find relationships. Using 20 batches of data from Machine 3, the mold temperature (185-215°C) is negatively correlated with rework time per piece (r ≈ -0.72), and the rework time sharply increases when the mold temperature is below 195°C, indicating a typical interval effect rather than a linear relationship.
- Control chart to see drift. Weekly rework costs are plotted on an I-MR chart, showing a continuous upward trend from Week 9 with out-of-control points, corresponding to the week when the first article inspection was canceled after a mold change.
At this point, the fishbone diagram comes into play: "No lower limit set for mold temperature," "First article inspection missing after mold change," and "Trimming blade wear cycle determined by feel" are identified as causes to be verified, and each is confirmed with data and on-site verification. After three months of implementing the measures, rework costs dropped from 420,000 RMB to 310,000 RMB, reducing the monthly internal failure costs by 110,000 RMB.
4. Three Red Lines for Interpretation
- Pareto chart: look at "other." If the "other" category exceeds 25%, it indicates that the classification dimensions are not fine enough. Go back and revise the check sheet before continuing the discussion.
- Scatter diagram: stratify first. Correlation does not equal causation; the r value from mixed stratification data is meaningless. A consistent direction must appear in at least 3 batches before taking action.
- Control chart: do not recognize budgets. Control limits for cost data come from the baseline fluctuations of the process itself, not financial targets. Using target lines as control limits means treating every data point as an anomaly.
5. Three Steps for Implementation
- Subject alignment (about one month). Confirm the aggregation criteria for each loss subject with the finance department, produce a "financial subject—quality subject" mapping table to avoid double accounting.
- Granularity of data collection (about two weeks). Reduce the recording unit from "month" to "batch," with fixed fields for process, machine, failure mode, quantity, loss per piece, and amount. Pilot this in one workshop first.
- Fixed analysis sequence (once a month). Follow the sequence of ranking, stratification, relationship, trend, and causation, producing a one-page conclusion: focus items, amount, responsible process, measures, and verification methods. Fixing the sequence ensures that the analysis meeting does not turn into a departmental explanation session.
Choose the right tool, and the money will be broken down: use the Pareto chart for ranking, the scatter diagram for relationships, and the control chart for drift.
Knowledge code: 5.2.4
Version: v20261020
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.