# Decision-Making Model of Production Data Management for Multi-Quality Characteristic Products in Consideration of Industry 4.0

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## Abstract

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## 1. Introduction

## 2. Process Capability Analysis Chart with Asymmetric Tolerances

## 3. Construct the Measurement Coordinate Point

## 4. An Empirical Example

- quality characteristic 1: (${T}_{1}$ = 1.2, ${d}_{L1}$ = 0.01, ${d}_{U1}$ = 0.03, ${d}_{1}^{\ast}$ = 0.01, ${d}_{11}$ = 1/3, ${d}_{12}$ = 1), ${\overline{X}}_{1}=$ 1.201 and ${S}_{1}$ = 0.002;
- quality characteristic 2: (${T}_{2}$ = 1.8, ${d}_{L2}$ = 0.03, ${d}_{U2}$ = 0.02, ${d}_{2}^{\ast}$ = 0.02, ${d}_{21}$ = 1, ${d}_{22}$ = 2/3), ${\overline{X}}_{2}=$ 1.796 and ${S}_{2}=$ 0.005;
- quality characteristic 3: (${T}_{3}$ = 30, ${d}_{L3}$ = 0.05, ${d}_{U3}$ = 0.05, ${d}_{3}^{\ast}$ = 0.05, ${d}_{31}$ = 1, ${d}_{32}$ = 1), ${\overline{X}}_{3}=$ 30.02 and ${S}_{3}=$ 0.005;
- quality characteristic 4: (${T}_{4}$ = 12, ${d}_{L4}$ = 0.1, ${d}_{U4}$ = 0.1, ${d}_{4}^{\ast}$ = 0.1, ${d}_{41}$ = 1, ${d}_{42}$ = 1), ${\overline{X}}_{4}=$ 12.01 and ${S}_{4}=$ 0.01.

- quality characteristic 1: ${\widehat{\delta}}_{1}^{\prime}$ $=$ 0.2 and ${\widehat{\gamma}}_{1}^{\prime}$ $=$ 0.2;
- quality characteristic 2: ${\widehat{\delta}}_{2}^{\prime}$ $=$ −0.2 and ${\widehat{\gamma}}_{2}^{\prime}$ $=$ 0.25;
- quality characteristic 3: ${\widehat{\delta}}_{3}^{\prime}$ $=$ 0.4 and ${\widehat{\gamma}}_{3}^{\prime}$ $=$ 0.167;
- quality characteristic 4: ${\widehat{\delta}}_{4}^{\prime}$ $=$ 0.2 and ${\widehat{\gamma}}_{4}^{\prime}$ $=$ 0.2.

- quality characteristic 1: The value of $\left[{\delta}_{L1}^{\prime},{\delta}_{U1}^{\prime}\right]$ is [−0.325, −0.075]. Thus, the value of ${\delta}_{L1}^{\prime}$ is bigger than zero (${\delta}_{L1}^{\prime}$ $=$ 0.1 $\ge $ 0), and the measurement coordinate point is$$({x}_{1},{y}_{1})=\left({\delta}_{L1},{\gamma}_{L1}\right)=(0.033,0.050).$$
- quality characteristic 2: The value of $\left[{\delta}_{L2}^{\prime},{\delta}_{U2}^{\prime}\right]$ is [0.1, 0.3]. Thus, the value of ${\delta}_{U2}^{\prime}$ is smaller than zero (${\delta}_{U2}^{\prime}$ $=$ −0.75 < 0), and the measurement coordinate point is$$({x}_{2},{y}_{2})=\left({\delta}_{U2},{\gamma}_{L2}\right)=(-0.05,0.126).$$
- quality characteristic 3: The value of is $\left[{\delta}_{L3}^{\prime},{\delta}_{U3}^{\prime}\right]$ is [0.315, 0.485]. Thus, the value of ${\delta}_{L3}^{\prime}$ is bigger than zero (${\delta}_{L3}^{\prime}$ $=$ 0.315 $\ge $ 0), and the measurement coordinate point is$$({x}_{3},{y}_{3})=\left({\delta}_{L3},{\gamma}_{L3}\right)=(0.315,0.126).$$
- quality characteristic 4: The value of $\left[{\delta}_{L4}^{\prime},{\delta}_{U4}^{\prime}\right]$ is [0.100, 0.300]. Thus, the value of ${\delta}_{L4}^{\prime}$ is bigger than zero (${\delta}_{L4}^{\prime}$ $=$ 0.300 $\ge $ 0), and the measurement coordinate point is$$({x}_{4},{y}_{4})=\left({\delta}_{L4},{\gamma}_{L4}\right)=(0.100,0.151).$$

## 5. Conclusions

## 6. Research Limitations and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Proof:**

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Quality Characteristic | Tolerance | Unit |
---|---|---|

1. Inner Diameter | ${1.2}_{-0.01}^{+0.03}$ | mm |

2. Outer Diameter | ${1.8}_{-0.03}^{+0.02}$ | mm |

3. Length | 30 ± 0.03 | mm |

4. Weight | 12 ± 0.05 | mg |

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**MDPI and ACS Style**

Chen, K.-S.; Lin, S.-C.; Lai, K.-K.; Wang, W.-P.
Decision-Making Model of Production Data Management for Multi-Quality Characteristic Products in Consideration of Industry 4.0. *Appl. Sci.* **2023**, *13*, 7883.
https://doi.org/10.3390/app13137883

**AMA Style**

Chen K-S, Lin S-C, Lai K-K, Wang W-P.
Decision-Making Model of Production Data Management for Multi-Quality Characteristic Products in Consideration of Industry 4.0. *Applied Sciences*. 2023; 13(13):7883.
https://doi.org/10.3390/app13137883

**Chicago/Turabian Style**

Chen, Kuen-Suan, Song-Chang Lin, Kuei-Kuei Lai, and Wen-Pai Wang.
2023. "Decision-Making Model of Production Data Management for Multi-Quality Characteristic Products in Consideration of Industry 4.0" *Applied Sciences* 13, no. 13: 7883.
https://doi.org/10.3390/app13137883