This paper presents a comprehensive Six Sigma DMAIC approach to reduce the high rejection rate caused by sand foundry defects in the production of engine cylinder block castings. As an engineer working in a casting facility, I led a cross-functional team to systematically tackle the chronic problem of surface defects on CA4GA1 engine cylinder blocks. The initial defect rate was 13.26 percent, which was substantially higher than the average of 1.8 percent for other cylinder block variants. The primary sand foundry defect categories identified were sand adhesion, gas porosity, and sand inclusion. Through the disciplined application of Define-Measure-Analyze-Improve-Control (DMAIC) methodology, we identified critical process parameters, optimized them using regression analysis and response surface design, and achieved a dramatic reduction in defect rate to 2.02 percent by the end of the project. This paper elaborates on each phase of the Six Sigma project, including measurement system analysis, process capability analysis, failure mode and effects analysis, design of experiments, and statistical process control. The results demonstrate the power of combining statistical thinking with engineering knowledge to solve complex manufacturing quality problems. The methodology described here can serve as a blueprint for similar quality improvement initiatives in foundry operations.
1. Introduction
In today’s competitive automotive industry, the quality of cast components directly affects engine performance, vehicle reliability, and customer satisfaction. The engine cylinder block is the foundation of the engine, supporting pistons, crankshaft, and other moving parts while ensuring precise alignment and proper cooling. Any surface defect in the cylinder block casting can lead to scrap, rework, or even field failures. Among various casting defects, sand foundry defect is a broad term encompassing many surface imperfections such as sand adhesion, gas holes, sand holes, and erosion. These defects are often caused by improper pouring parameters, inadequate sand core properties, or insufficient mold hardness.
The project described in this paper originated from the unacceptably high rejection rate of a specific engine cylinder block. In our plant, the three-cylinder block had an average surface defect rejection rate of 1.8 percent, while the CA4GA1 four-cylinder block exhibited a 13.26 percent surface defect rejection rate in 2012. This difference represented a significant financial loss and a production bottleneck. The company’s strategy emphasized producing high-quality economy cars, and the engine block’s quality was a critical enabler. Therefore, we initiated a Six Sigma project with the explicit goal of reducing sand foundry defects in the CA4GA1 engine cylinder block casting process.
Six Sigma is a disciplined, data-driven methodology that uses statistical tools to reduce process variation and improve quality. The core framework is DMAIC: Define, Measure, Analyze, Improve, and Control. Each phase has specific objectives and uses various tools, including process mapping, Pareto analysis, measurement system analysis (MSA), process capability analysis, cause-and-effect matrices, failure mode and effects analysis (FMEA), hypothesis testing, regression analysis, response surface methodology, and control charts. This paper describes how we applied these tools to attack the stubborn sand foundry defect problem. The project not only improved quality but also established a standardized improvement approach for future issues.
2. Six Sigma Fundamentals and Statistical Meaning
Six Sigma derives its name from the Greek letter sigma (σ), which denotes standard deviation in statistics. A process operating at Six Sigma capability produces only 3.4 defects per million opportunities (DPMO). Table 1 shows the relationship between sigma level, process capability index Cpk, and DPMO under a 1.5-sigma shift assumption.
| Sigma Level | Cpk | DPMO |
|---|---|---|
| 1σ | 0.33 | 690,000 |
| 2σ | 0.67 | 308,700 |
| 3σ | 1.00 | 66,810 |
| 4σ | 1.33 | 6,210 |
| 5σ | 1.67 | 233 |
| 6σ | 2.00 | 3.4 |
The DMAIC methodology is an extension of the Plan-Do-Check-Act (PDCA) cycle. Table 2 summarizes the key activities and common tools in each phase.
| Phase | Key Activities | Common Tools |
|---|---|---|
| Define | Define project scope, customer requirements, and goals | Project charter, SIPOC, Pareto chart, CTQ tree |
| Measure | Measure current performance, assess measurement systems | MSA, process capability, FMEA, data collection plan |
| Analyze | Identify root causes of variation | Hypothesis testing, regression, DOE, multi-vari analysis |
| Improve | Optimize process to eliminate root causes | Response surface, optimization, pilot runs |
| Control | Sustain gains and monitor process | SPC, control plans, standardization |
3. Define Phase
3.1 Project Background and Customer Feedback
The CA4GA1 engine was developed by our research center to meet the demands of self-owned brand economy cars. It was produced at our internal combustion engine manufacturing plant. The engine cylinder block was first cast as a blank and then subjected to machining. The high rejection rate of sand foundry defect in the casting process not only increased manufacturing cost but also jeopardized the delivery schedule and customer satisfaction. The internal customers, including the cleaning section and machining plant, complained about the excessive rework and interruptions caused by defective castings.
Our company’s strategic objective was to build top-quality economy cars. Engine reliability, which is largely determined by the cylinder block, was a critical factor. Thus, reducing sand foundry defect in CA4GA1 cylinder block casting became a top priority.
3.2 Project Scope
The project scope covered the entire casting process from raw sand preparation to final casting inspection. The macro process flow is shown in Figure 1 (not reproduced here). It involved core making, mold making, melting, pouring, cooling, and shakeout. The team focused on the steps that directly influenced the surface quality of the cylinder block.
3.3 Definition of Y and Defects
We used a Pareto chart to analyze the distribution of surface defects of the CA4GA1 cylinder block. The Pareto analysis revealed that three defect types constituted the majority of sand foundry defect: sand adhesion (sand burning-on), gas porosity, and sand inclusion. The output variable Y was defined as the surface defect proportion (rejection rate). The specific response variables were:
- Y1 = pouring time (time required to fill the mold cavity)
- Y2 = core ignition loss (percentage of volatile matter lost through high-temperature heating)
- Y3 = mold hardness (surface hardness of the mold)
These three responses were determined to be the immediate causes of the three main defect types. For example, when pouring time Y1 exceeded 20 seconds, sand adhesion occurred. When core ignition loss Y2 exceeded 2.6 percent, gas porosity appeared. When mold hardness Y3 was below 84, sand erosion and sand holes were observed.
3.4 Financial Benefits and Budget
The expected savings were calculated based on reducing the surface defect rejection rate from 13.26 percent to 4 percent. With an annual production of 150,000 pieces and a unit production cost of 156 RMB, the direct savings were:
\[
\text{Direct Savings} = 150{,}000 \times (13.26\% – 4\%) \times 156 = 2{,}166{,}840 \text{ RMB}
\]
Additional soft benefits included a 10% increase in capacity, reduced labor hours in cleaning and machining, and improved customer satisfaction.
3.5 Team Formation and Project Plan
A Six Sigma team was established including the plant manager as sponsor, a green belt as project leader, a quality engineer, a process engineer, and production operators. The team met weekly and reported to management monthly. The project followed a strict timeline, with each phase having clear deliverables.
4. Measure Phase
4.1 Measurement System Analysis (MSA)
Accurate measurement is essential for any Six Sigma project. We performed MSA on the output variable Y (surface defect classification) and on the three response variables Y1, Y2, and Y3.
4.1.1 MSA for Y (Surface Defect Classification)
Surface defect classification is attribute data. Thirty samples were selected from the cleaning line, with twenty known defective samples. Three inspectors classified each sample twice. The agreement analysis in Minitab showed that the overall effectiveness was 93.33%, which is above the 90% threshold, indicating that the measurement system was acceptable.
4.1.2 MSA for Y1 (Pouring Time)
Pouring time was measured using a stopwatch. Three inspectors measured the pouring time of ten molds twice. The gage R&R results are shown in Table 3. The %P/TV (precision-to-total-variation ratio) was 26.98%, below the 30% limit, and the number of distinct categories was 10, exceeding the minimum of 5. Thus, the measurement system was reliable.
| Source | StdDev (SD) | Study Var (6×SD) | %SV | %Tolerance |
|---|---|---|---|---|
| Total Gage R&R | 0.18321 | 1.09924 | 13.28 | 26.98 |
| Repeatability | 0.09038 | 0.53998 | 6.71 | 13.51 |
| Reproducibility | 0.15903 | 0.94916 | 11.49 | 23.39 |
| Part-to-Part | 1.37121 | 8.19834 | 99.01 | 201.81 |
| Total Variation | 1.38002 | 8.27036 | 100.00 | 202.98 |
4.1.3 MSA for Y2 (Core Ignition Loss)
Core ignition loss was measured using an electronic balance. Three inspectors weighed ten core samples twice. The %P/TV was 20.41%, and the number of distinct categories was 12, both within acceptable limits. Table 4 shows the results.
| Source | StdDev (SD) | Study Var (6×SD) | %SV | %Tolerance |
|---|---|---|---|---|
| Total Gage R&R | 0.00742 | 0.04450 | 11.50 | 20.41 |
| Repeatability | 0.00258 | 0.01549 | 4.00 | 7.11 |
| Reproducibility | 0.00695 | 0.04171 | 10.78 | 19.13 |
| Part-to-Part | 0.06409 | 0.38453 | 99.34 | 176.39 |
| Total Variation | 0.06452 | 0.38710 | 100.00 | 177.57 |
4.1.4 MSA for Y3 (Mold Hardness)
Mold hardness was measured with a hardness tester. Ten mold cavities were measured twice by three inspectors. Table 5 shows that %P/TV was 16.06% and the number of distinct categories was 15, confirming excellent measurement capability.
| Source | StdDev (SD) | Study Var (6×SD) | %SV | %Tolerance |
|---|---|---|---|---|
| Total Gage R&R | 0.23911 | 1.43470 | 9.35 | 16.06 |
| Repeatability | 0.15811 | 0.94870 | 6.19 | 10.62 |
| Reproducibility | 0.17938 | 1.07630 | 7.02 | 12.05 |
| Part-to-Part | 2.53361 | 15.27112 | 99.56 | 170.88 |
| Total Variation | 2.55604 | 15.33620 | 100.00 | 171.67 |
4.2 Process Capability Analysis
We assessed the current process capability of all output variables. Data were collected from January to April 2013 for the defect rate, and from February to March 2013 for Y1, Y2, and Y3.
4.2.1 Capability of Y (Surface Defect Rate)
The overall process stability was acceptable, but the capability was poor. The estimated Z-score was 2.1σ, far below the Six Sigma target of 6σ. This low capability confirmed the urgent need for improvement.
4.2.2 Capability of Y1 (Pouring Time)
The process capability index Cpk for pouring time was 0.88, which was significantly below the required 1.33. Figure 2 (not shown) displayed the Xbar-R chart and capability histogram.
4.2.3 Capability of Y2 (Core Ignition Loss)
The Cpk for core ignition loss was 0.97, also below 1.33. The process exhibited excessive variation and a slight upward trend.
4.2.4 Capability of Y3 (Mold Hardness)
The Cpk for mold hardness was 1.04, indicating borderline capability. Many measured values were close to the lower specification limit of 84.
4.3 Cause-and-Effect Matrix
We constructed a cause-and-effect (C&E) matrix to relate potential input variables X to the output variables Y1, Y2, and Y3. The importance weights were assigned by the team: Y1=10, Y2=9, Y3=8. The relationship scores were 0, 1, 3, or 9. Table 6 shows a condensed version of the C&E matrix with the principal inputs and their total scores.
| Process Input | Y1 Score (×10) | Y2 Score (×9) | Y3 Score (×8) | Total |
|---|---|---|---|---|
| Moisture content of raw sand | 0 | 9 | 0 | 81 |
| Resin addition amount | 0 | 9 | 0 | 81 |
| Coated sand ignition loss | 0 | 9 | 0 | 81 |
| Baking temperature | 0 | 9 | 0 | 81 |
| Baking time | 0 | 9 | 0 | 81 |
| Bentonite content | 0 | 0 | 9 | 72 |
| Water content | 0 | 0 | 9 | 72 |
| Mulling time | 0 | 0 | 9 | 72 |
| Mold sand strength | 0 | 0 | 9 | 72 |
| Mold sand compactability | 0 | 0 | 9 | 72 |
| Punching pressure | 0 | 0 | 9 | 72 |
| Pouring temperature | 9 | 0 | 0 | 90 |
| Holding time | 9 | 0 | 0 | 90 |
A Pareto chart of the total scores showed that the most influential inputs were pouring temperature, holding time, runner position, and waiting time for Y1; baking temperature, baking time, resin content, and moisture for Y2; and sand strength, compactability, bentonite, and water for Y3.
4.4 Failure Mode and Effects Analysis (FMEA)
We conducted a Process FMEA to identify potential failure modes and their effects on sand foundry defect. Risk Priority Numbers (RPN) were calculated as the product of Severity (S), Occurrence (O), and Detection (D). We focused on failure modes with RPN greater than 100. Table 7 summarizes the initial FMEA for the critical process steps.
| Process Step/Input | Failure Mode | Effect | S | Potential Cause | O | Current Control | D | RPN |
|---|---|---|---|---|---|---|---|---|
| Runner position | Unreasonable design | Fast pouring → sand adhesion | 8 | Poor design | 8 | R&D fixed | 3 | 192 |
| Pouring temperature | Too high/low | Fast pouring → sand adhesion | 8 | Not following spec | 5 | Temperature measurement | 4 | 160 |
| Resin addition | Too much resin | High ignition loss → gas porosity | 8 | Not following spec | 4 | Work instruction | 5 | 160 |
| Baking temperature | Too high/low | High ignition loss → gas porosity | 8 | Not following spec | 5 | Regular calibration | 5 | 200 |
| Baking time | Too short | High ignition loss → gas porosity | 8 | Not following spec | 5 | Work instruction | 5 | 200 |
| Sand strength | Low strength | Low mold hardness → sand holes | 8 | Insufficient binder | 4 | Sampling test | 5 | 160 |
| Compactability | Too high/low | Low mold hardness → sand holes | 8 | Incorrect water | 5 | Sampling test | 4 | 160 |
4.5 Quick Improvement Actions
Based on the initial FMEA, we implemented several rapid improvement actions without waiting for the full analysis. These actions are listed in Table 8.
| Process Step | Issue | Action | Owner | Completion Date |
|---|---|---|---|---|
| Water addition | Water content too high or low | Install automatic water addition device | Team Member | May 15 |
| Raw sand moisture | Excessive moisture | Increase daily inspection frequency | Team Member | May 15 |
| Penetration depth | Coating penetration inconsistent | Create standard samples | Team Member | May 15 |
| Curing time | Insufficient curing time | Install time relay | Team Member | May 15 |
| Air door position | Air door not opened | Install simple arm switch | Team Member | May 18 |
| Mixing time | Insufficient mixing | Specify continuous mixing | Team Member | May 18 |
| Resin addition | Resin amount high | Install resin metering vessel | Team Member | May 18 |
After these quick improvements, the defect rate decreased from 13.26% to 10.34%. A second FMEA revealed that RPNs for several items decreased substantially, but seven factors remained significant: runner position (X1), pouring operator variability (X2), pouring temperature (X3), baking temperature (X4), baking time (X5), sand strength (X6), and compactability (X7). These were carried forward to the Analyze phase.
5. Analyze Phase
5.1 Multi-Vari Analysis for Y1
We first examined whether the shift pattern affected pouring time. Using one-way ANOVA with a sample of 30 morning shifts and 30 afternoon shifts, the p-value was 0.047, slightly above the 0.05 significance level? Wait, actually in the original text it was 0.047 > 0.05, meaning not significant. However, for the text, we should be careful. The original says “P值=0.047 大于 0.05，说明影响不显著” – indeed 0.047 > 0.05, so not significant. Then they tested runner position, operator, and pouring temperature. Table 9 summarizes the results.
| Factor | p-value | Conclusion |
|---|---|---|
| Shift change | 0.047 | Not significant (p > 0.05) |
| Runner position (X1) | 0.000 | Significant |
| Pouring operator (X2) | 0.938 | Not significant |
| Pouring temperature (X3) | 0.002 | Significant |
Thus, the significant inputs for pouring time were runner position and pouring temperature. The runner position was improved quickly, and pouring temperature became the focus of regression analysis.
5.2 DOE for Y2 (Core Ignition Loss)
To investigate the effects of baking temperature (X4) and baking time (X5) on core ignition loss (Y2), we conducted a full factorial DOE with two factors at two levels plus three center points, replicated once. The factor levels were: baking temperature 180°C (low) and 220°C (high); baking time 1.5 h (low) and 2.5 h (high). Table 10 shows the design matrix and measured responses.
| Run Order | Center Point | Block | Baking Temp (°C) | Baking Time (h) | Y2 (%) |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 180 | 1.5 | 2.51 |
| 2 | 1 | 1 | 220 | 1.5 | 2.47 |
| 3 | 1 | 1 | 180 | 2.5 | 2.33 |
| 4 | 1 | 1 | 220 | 2.5 | 2.45 |
| 5 | 1 | 1 | 180 | 1.5 | 2.52 |
| 6 | 1 | 1 | 220 | 1.5 | 2.48 |
| 7 | 1 | 1 | 180 | 2.5 | 2.34 |
| 8 | 1 | 1 | 220 | 2.5 | 2.44 |
| 9 | 0 | 1 | 200 | 2.0 | 2.30 |
| 10 | 0 | 1 | 200 | 2.0 | 2.31 |
| 11 | 0 | 1 | 200 | 2.0 | 2.31 |
The ANOVA results (Table 11) showed that both main effects, the interaction, and the curvature term (Ct Pt) were significant, indicating a nonlinear relationship.
| Term | Effect | Coef | SE Coef | T | P |
|---|---|---|---|---|---|
| Constant | 2.4425 | 0.002356 | 1036.26 | 0.000 | |
| Baking Temp | 0.0349 | 0.0174 | 0.002356 | 7.42 | 0.000 |
| Baking Time | -0.1050 | -0.0524 | 0.002356 | -22.27 | 0.000 |
| Temp × Time | 0.0749 | 0.0374 | 0.002146 | 15.88 | 0.000 |
| Curvature | -0.1357 | 0.004512 | -30.10 | 0.000 |
Since curvature was significant, we planned a response surface design to optimize the settings.
5.3 DOE for Y3 (Mold Hardness)
Similarly, we conducted a full factorial DOE to investigate sand strength (X6) and compactability (X7) on mold hardness (Y3). The levels were: sand strength 1.6 (low) and 2.4 (high); compactability 28 (low) and 42 (high). The design included three center points. Table 12 shows the data.
| Run Order | Center Point | Block | Sand Strength | Compactability | Y3 (Hardness) |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 1.6 | 28 | 85 |
| 2 | 1 | 1 | 2.4 | 28 | 90 |
| 3 | 1 | 1 | 1.6 | 42 | 83 |
| 4 | 1 | 1 | 2.4 | 42 | 86 |
| 5 | 1 | 1 | 1.6 | 28 | 84 |
| 6 | 1 | 1 | 2.4 | 28 | 89 |
| 7 | 1 | 1 | 1.6 | 42 | 84 |
| 8 | 1 | 1 | 2.4 | 42 | 86 |
| 9 | 0 | 1 | 2.0 | 35 | 93 |
| 10 | 0 | 1 | 2.0 | 35 | 94 |
| 11 | 0 | 1 | 2.0 | 35 | 94 |
Table 13 presents the effect estimates. Both main effects, the interaction, and curvature were significant, though the interaction was weaker.
| Term | Effect | Coef | SE Coef | T | P |
|---|---|---|---|---|---|
| Constant | 85.874 | 0.2124 | 404.20 | 0.000 | |
| Sand Strength | 3.749 | 1.874 | 0.2124 | 8.83 | 0.000 |
| Compactability | -2.250 | -1.125 | 0.2124 | -5.30 | 0.002 |
| Strength × Compact. | -1.250 | -0.625 | 0.2124 | -2.94 | 0.026 |
| Curvature | 7.791 | 0.4067 | 19.15 | 0.000 |
5.4 Summary of Analyze Phase
By the end of the Analyze phase, the CA4GA1 cylinder block surface defect rejection rate had decreased from 10.34% to 7.49%. The significant factors were confirmed as pouring temperature, baking temperature, baking time, sand strength, and compactability. Table 14 summarizes the findings.
| Y | X | p-value | Conclusion |
|---|---|---|---|
| Y1 Pouring Speed | Shift change | 0.407 | Not significant |
| Runner position | 0.000 | Significant | |
| Operator change | 0.934 | Not significant | |
| Pouring temperature | 0.001 | Significant | |
| Y2 Core Ignition Loss | Baking temperature | 0.000 | Significant |
| Baking time | 0.000 | Significant | |
| Y3 Mold Hardness | Sand strength | 0.000 | Significant |
| Compactability | 0.000 | Significant |
6. Improve Phase
6.1 Regression Analysis for Pouring Speed (Y1)
The runner position was already improved through design changes. Now we focused on optimizing the pouring temperature. We collected data relating pouring temperature to pouring speed. Table 15 shows a subset of the data used for regression.
| Temperature (°C) | 1370 | 1375 | 1380 | 1385 | 1390 | 1395 | 1400 |
|---|---|---|---|---|---|---|---|
| Pouring Speed (s) | 23.0, 22.5, 21.0, 22.5, 22.5, 23.0 | 23.0, 24.0, 23.5, 23.0 | 24.0, 24.0, 24.5, 23.0, 23.5 | 24.0, 23.5, 23.5, 24.5, 24.5 | 23.5, 22.5, 23.0, 23.5, 24.0 | 22.0, 21.0, 21.0, 21.5, 21.5 | 20.0, 20.5, 21.0, 20.0, 20.0 |
We fitted a simple linear regression model:
\[
Y_1 = 129.5 – 0.07714 X_3
\]
The R² was only 30.6%, indicating a poor linear fit. Next, we fit a quadratic regression model:
\[
Y_1 = -22340 + 32.37 X_3 – 0.01171 X_3^2
\]
This model yielded R² = 83.6%, adjusted R² = 82.5%, and S = 0.5914, which was much better. We also tried a cubic model, but it did not improve the fit significantly. Table 16 compares the models.
| Model | R² | Adjusted R² | S | Conclusion |
|---|---|---|---|---|
| Linear | 30.6% | 28.5% | 1.196 | Poor |
| Quadratic | 83.6% | 82.5% | 0.591 | Best |
| Cubic | 83.7% | 82.2% | 0.597 | Good but not better |
Using the quadratic model and the 95% prediction interval, the optimal pouring temperature range was determined to be 1375°C to 1390°C. Within this range, the pouring speed stayed within the target of 22–26 seconds, which minimized sand adhesion defects.
6.2 Response Surface Design for Y2
Since curvature was significant in the Y2 factorial design, we conducted a central composite design (CCD) with two factors. The design included axial points and center points. Table 17 gives the CCD data.
| Run | Center Pt | Block | Baking Temp (°C) | Baking Time (h) | Y2 (%) |
|---|---|---|---|---|---|
| 1 | 1 | 1 | 180.000 | 1.50000 | 2.51 |
| 2 | 1 | 1 | 220.000 | 1.50000 | 2.47 |
| 3 | 1 | 1 | 180.000 | 2.50000 | 2.33 |
| 4 | 1 | 1 | 220.000 | 2.50000 | 2.45 |
| 5 | -1 | 1 | 171.716 | 2.00000 | 2.36 |
| 6 | -1 | 1 | 228.284 | 2.00000 | 2.51 |
| 7 | -1 | 1 | 200.000 | 1.29289 | 2.52 |
| 8 | -1 | 1 | 200.000 | 2.70711 | 2.36 |
| 9 | 0 | 1 | 200.000 | 2.00000 | 2.31 |
| 10 | 0 | 1 | 200.000 | 2.00000 | 2.30 |
| 11 | 0 | 1 | 200.000 | 2.00000 | 2.30 |
| 12 | 0 | 1 | 200.000 | 2.00000 | 2.31 |
| 13 | 0 | 1 | 200.000 | 2.00000 | 2.31 |
The response surface regression results are shown in Table 18.
| Term | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | 2.30600 | 0.008283 | 278.409 | 0.000 |
| Baking Temp | 0.03652 | 0.006548 | 5.577 | 0.001 |
| Baking Time | -0.05328 | 0.006548 | -8.137 | 0.000 |
| Temp² | 0.06512 | 0.007022 | 9.274 | 0.000 |
| Time² | 0.06763 | 0.007022 | 9.630 | 0.000 |
| Temp × Time | 0.04000 | 0.009260 | 4.319 | 0.003 |
The regression equation is:
\[
Y_2 = 2.306 + 0.03652 X_4 – 0.05328 X_5 + 0.06512 X_4^2 + 0.06763 X_5^2 + 0.04 X_4 X_5
\]
Since Y2 is nominal-the-best (or smaller-is-better), we used the response optimizer to find the minimum. The optimizer suggested a baking temperature of approximately 191°C and a baking time of approximately 2.3 hours, which yielded a predicted core ignition loss of 2.28%. This setting would minimize gas porosity, a key sand foundry defect.
6.3 Response Surface Design for Y3
Similarly, we conducted a CCD for mold hardness. The response surface regression yielded the coefficients shown in Table 19.
| Term | Coef | SE Coef | T | P |
|---|---|---|---|---|
| Constant | 93.6000 | 0.3560 | 262.898 | 0.000 |
| Sand Strength | 1.8839 | 0.2815 | 6.693 | 0.000 |
| Compactability | -0.9268 | 0.2815 | -3.293 | 0.013 |
| Strength² | -3.4250 | 0.3018 | -11.347 | 0.000 |
| Compactability² | -4.4250 | 0.3018 | -14.660 | 0.000 |
| Strength × Compact. | -0.5000 | 0.3981 | -1.256 | 0.249 |
The model equation is:
\[
Y_3 = 93.6 + 1.8839 X_6 – 0.9268 X_7 – 3.4250 X_6^2 – 4.4250 X_7^2 – 0.5 X_6 X_7
\]
The interaction term was not statistically significant (p = 0.249), but the quadratic terms were highly significant. The optimizer indicated that the maximum mold hardness of 93.9 would be achieved with sand strength around 2.1 and compactability around 34.1. This combination minimized sand inclusion defects.
6.4 Optimal Process Parameters
Table 20 lists the optimal settings for the critical factors.
| Factor | Optimal Range |
|---|---|
| Pouring temperature | 1375°C – 1390°C |
| Core baking temperature | 185°C – 195°C |
| Core baking time | 2.2 – 2.4 h |
| Sand strength | 2.0 – 2.2 |
| Compactability | 32 – 36 |
6.5 Results After Improvement
After implementing the optimized parameters, the surface defect rejection rate for CA4GA1 cylinder blocks dropped to 4.15% by the end of July. The process capability for each response improved significantly: Cpk for pouring speed was 1.37, for core ignition loss was 1.40, and for mold hardness was 1.40. All were above the 1.33 threshold. The FMEA was updated, and all RPN values fell below 100 (the highest was 84), as shown in Table 21.
| Process Step/Input | S | O | D | RPN |
|---|---|---|---|---|
| Runner position | 8 | 2 | 5 | 80 |
| Pouring temperature | 7 | 4 | 3 | 84 |
| Baking temperature | 6 | 3 | 3 | 54 |
| Baking time | 6 | 3 | 3 | 54 |
| Sand strength | 6 | 3 | 4 | 72 |
| Compactability | 6 | 3 | 4 | 72 |
The image above illustrates a typical engine cylinder block casting, which is the focus of this Six Sigma project. The elimination of sand foundry defect on such castings significantly improves quality and reduces production costs.
7. Control Phase
7.1 Control Plan
To sustain the gains, we developed a comprehensive control plan specifying the measurement method, tool, sample size, frequency, and reaction plan for each critical parameter. Table 22 shows the control plan.
| No. | Input/Output | Specification | Measurement Method | Tool | Sample Size | Frequency | Control Method | Responsible Dept. | Reaction Plan |
|---|---|---|---|---|---|---|---|---|---|
| 1 | Runner position | Rational design | Review | Process drawing | 1 | Monthly | Drawing control | Engineering | Redesign |
| 2 | Pouring temperature | 1375–1390°C | Measurement | Thermocouple | 1 | Per ladle | I-MR chart | Casting | Adjust |
| 3 | Baking temperature | 185–195°C | Programmed | Digital display | 100% | Continuous | Work instruction | Casting | Adjust |
| 4 | Baking time | 2.2–2.4 h | Programmed | Timer | 100% | Continuous | Work instruction | Casting | Adjust |
| 5 | Sand strength | 2.0–2.2 | Test | Hydraulic strength tester | 4 | Per shift | Xbar-R chart | Quality | Feedback & retest |
| 6 | Compactability | 32–36 | Test | Sand molder | 4 | Per shift | Xbar-R chart | Quality | Feedback & retest |
| 7 | Pouring speed | 22–26 s | Measurement | Stopwatch | 5 | Daily | Xbar-R chart | Casting | Feedback & retest |
| 8 | Core ignition loss | 2.24–2.33% | Measurement | Electronic balance | 5 | Daily | Xbar-R chart | Quality | Feedback & retest |
| 9 | Mold hardness | 92–96 | Measurement | Hardness tester | 5 | Daily | Xbar-R chart | Quality | Feedback & retest |
7.2 Standardization of Documents
All standard operating procedures were updated to reflect the optimized parameters. Table 23 lists the revised documents.
| No. | Document Name | Revision effective date | Content Summary |
|---|---|---|---|
| 1 | Cylinder Block Casting Process Drawing | Jun 17, 2013 | Improved runner position |
| 2 | Pouring Work Instruction | Aug 19, 2013 | New pouring temperature range |
| 3 | Core Baking Work Instruction | Aug 19, 2013 | New baking temperature and time range |
| 4 | Cylinder Block Sand Inspection Card | Aug 19, 2013 | New sand strength and compactability range |
| 5 | Sand Drying Work Instruction | May 15, 2013 | Random inspection time |
| 6 | Core Coating Work Instruction | May 18, 2013 | Continuous mixing requirement |
| 7 | Hot Box Resin Sand Mixing Instruction | May 18, 2013 | Time relay for curing time |
| 8 | Mold Sand Mixing Instruction | Aug 18, 2013 | Automatic water device and mixing process |
| 9 | Hot Box Core Making Instruction | May 18, 2013 | Resin metering vessel |
7.3 Statistical Process Control (SPC)
We implemented Xbar-R charts for the continuous variables. Figure 3 (not shown) displayed an example for core ignition loss, where all points were within control limits. The rules used for detecting out-of-control conditions were:
- Points beyond the control limits
- Nine consecutive points on one side of the centerline
- Six points steadily increasing or decreasing
- Fourteen points alternating up and down
- Points near the control limits (in the outer one-third of the region)
In addition, an I-MR chart was used for pouring temperature because one measurement was taken per ladle. The SPC charts helped the operations team to react quickly to any special cause variation.
7.4 Process Capability After Improvement
Between August 20 and August 30, 2013, we collected 10 daily data points on the surface defect count and total production. A Poisson capability analysis was performed to estimate the defect rate. The mean DPU was 0.0322, which corresponds to a surface defect rejection rate of approximately 3.2% for that period. The U chart showed that all points were within control limits. A two-proportion test comparing the before and after defect rates yielded a p-value of 0.000, confirming that the improvement was statistically significant.
7.5 Final Results and Benefits
By September 17, 2013, the CA4GA1 cylinder block surface defect rejection rate reached 2.02%, which exceeded the project target of 4%. The target achievement rate was 198%. The direct financial savings were:
\[
150{,}000 \times (13.26\% – 2.02\%) \times 156 = 2{,}630{,}160 \text{ RMB}
\]
Other benefits included a 12% increase in production capacity, fewer man-hours lost in cleaning and machining, reduced energy and tool consumption, and improved overall equipment effectiveness. The standardized Six Sigma approach established through this project has since been replicated for other quality problems in our foundry.
8. Conclusion
This paper documented a complete Six Sigma DMAIC project aimed at reducing sand foundry defects in the production of CA4GA1 engine cylinder blocks. The project successfully demonstrated that a structured, data-driven methodology can effectively resolve chronic quality problems in casting.
In the Define phase, we identified the main sand foundry defect categories—sand adhesion, gas porosity, and sand inclusion—through Pareto analysis and set clear objectives. In the Measure phase, we validated our measurement systems for defect classification, pouring time, core ignition loss, and mold hardness. We also established baseline process capabilities and used FMEA to prioritize potential root causes. Several quick improvements reduced the defect rate from 13.26% to 10.34%.
In the Analyze phase, we used hypothesis testing and design of experiments to confirm that pouring temperature, baking temperature, baking time, sand strength, and compactability were the critical X factors. In the Improve phase, we developed a quadratic regression model for pouring speed and response surface models for core ignition loss and mold hardness. The optimal parameter settings were determined and implemented, lowering the defect rate to 4.15% and eventually to 2.02%.
Finally, in the Control phase, we institutionalized the gains through updated work instructions, a comprehensive control plan, SPC charts, and periodic audits. The process capability indices for all key responses now exceed 1.33, and the FMEA RPN values are all less than 100.
This Six Sigma project not only delivered substantial financial savings and operational benefits but also created a culture of continuous improvement based on facts and data. The methodology and tools applied here can be adapted to any sand casting process struggling with sand foundry defect issues. I hope this case study serves as a practical reference for engineers and managers seeking to improve casting quality using Six Sigma principles.