### Abstract

Statistical Process Control (SPC) is a technical tool that is used to control and to improve almost any kind of process. However, because of cost consideration, management need to decide which part should apply SPC. In this paper, we propose the use of probability and fuzzy membership function to determine SPC position. Conditional probability is used to analyze process failure and process repair. Then, using Markov Matrix, we calculate the probability of out-of-control process (PO). Nevertheless, in a production line that consists of many parts, the probability values are not adequate to be used as a reference to determine SPC position since these values would cause ambiguity. To illustrate this ambiguity, consider the following crisp definition of the out-of-control condition: If the probability of out-of-control process (PO) is 0.25 (or 25%), with a tolerance of 0.05, then the process is considered "high", otherwise it is considered "low". Now, suppose the value of PO is 0.23 (or 23%), with the same value of tolerance, could we definitely say it as "low"? Therefore, to overcome this problem we apply fuzzy membership function (MF) that uses linguistic terms and degree of memberships to analyze PO instead of the probability values.

Original language | English |
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Title of host publication | IEEE International Engineering Management Conference |

Editors | M. Xie, T.S. Durrani, H.K. Tnag |

Pages | 1066-1070 |

Number of pages | 5 |

Volume | 3 |

Publication status | Published - 2004 |

Event | Proceedings - 2004 IEEE International Engineering Management Conference: Innovation and Entrepreneurship for Sustainable Development, IEMC 2004 - Duration: 18 Oct 2004 → 21 Oct 2004 |

### Other

Other | Proceedings - 2004 IEEE International Engineering Management Conference: Innovation and Entrepreneurship for Sustainable Development, IEMC 2004 |
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Period | 18/10/04 → 21/10/04 |

### Fingerprint

### Keywords

- Conditional probability
- Fuzzy membership function
- Markov matrix
- Statistical process control (SPC)

### ASJC Scopus subject areas

- Hardware and Architecture
- Industrial and Manufacturing Engineering

### Cite this

*IEEE International Engineering Management Conference*(Vol. 3, pp. 1066-1070)

**Fuzzy membership function in determining Statistical Process Control position.** / Nababan, E. B.; Hamdan, Abdul Razak; Hasan, Mohammad Khatim; Mohamed, Hazura.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Engineering Management Conference.*vol. 3, pp. 1066-1070, Proceedings - 2004 IEEE International Engineering Management Conference: Innovation and Entrepreneurship for Sustainable Development, IEMC 2004, 18/10/04.

}

TY - GEN

T1 - Fuzzy membership function in determining Statistical Process Control position

AU - Nababan, E. B.

AU - Hamdan, Abdul Razak

AU - Hasan, Mohammad Khatim

AU - Mohamed, Hazura

PY - 2004

Y1 - 2004

N2 - Statistical Process Control (SPC) is a technical tool that is used to control and to improve almost any kind of process. However, because of cost consideration, management need to decide which part should apply SPC. In this paper, we propose the use of probability and fuzzy membership function to determine SPC position. Conditional probability is used to analyze process failure and process repair. Then, using Markov Matrix, we calculate the probability of out-of-control process (PO). Nevertheless, in a production line that consists of many parts, the probability values are not adequate to be used as a reference to determine SPC position since these values would cause ambiguity. To illustrate this ambiguity, consider the following crisp definition of the out-of-control condition: If the probability of out-of-control process (PO) is 0.25 (or 25%), with a tolerance of 0.05, then the process is considered "high", otherwise it is considered "low". Now, suppose the value of PO is 0.23 (or 23%), with the same value of tolerance, could we definitely say it as "low"? Therefore, to overcome this problem we apply fuzzy membership function (MF) that uses linguistic terms and degree of memberships to analyze PO instead of the probability values.

AB - Statistical Process Control (SPC) is a technical tool that is used to control and to improve almost any kind of process. However, because of cost consideration, management need to decide which part should apply SPC. In this paper, we propose the use of probability and fuzzy membership function to determine SPC position. Conditional probability is used to analyze process failure and process repair. Then, using Markov Matrix, we calculate the probability of out-of-control process (PO). Nevertheless, in a production line that consists of many parts, the probability values are not adequate to be used as a reference to determine SPC position since these values would cause ambiguity. To illustrate this ambiguity, consider the following crisp definition of the out-of-control condition: If the probability of out-of-control process (PO) is 0.25 (or 25%), with a tolerance of 0.05, then the process is considered "high", otherwise it is considered "low". Now, suppose the value of PO is 0.23 (or 23%), with the same value of tolerance, could we definitely say it as "low"? Therefore, to overcome this problem we apply fuzzy membership function (MF) that uses linguistic terms and degree of memberships to analyze PO instead of the probability values.

KW - Conditional probability

KW - Fuzzy membership function

KW - Markov matrix

KW - Statistical process control (SPC)

UR - http://www.scopus.com/inward/record.url?scp=17644425344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17644425344&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:17644425344

VL - 3

SP - 1066

EP - 1070

BT - IEEE International Engineering Management Conference

A2 - Xie, M.

A2 - Durrani, T.S.

A2 - Tnag, H.K.

ER -