### Abstract

Knowing the time of changes, called change-point (CP), in a process is crucial for engineers to recognize the root cause fast and accurately. Since special causes may induce simultaneous changes in mean and variance, detecting changes in both at once is required. Many methodologies in quality control were developed for detecting changes in either mean or variance only, and process parameters were assumed known often. However, they are rarely known exactly and a small estimation error may lead to unfavorable CP estimates. Fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality. A new mechanism, called fuzzy classification maximum likelihood change-point (FCML-CP) algorithm, is proposed to detect shifts in mean and variance simultaneously. A CP framework is transferred into a mixture model and then a FCML-CP algorithm is created through fuzzy classification maximum likelihood procedures. The proposed FCML-CP can be applied to phase I and II processes without knowledge of in-control process parameters; it can estimate multiple CPs of process mean or/and variance simultaneously. The effectiveness and superiority of FCML-CP are shown by extensive experiments with numerical and real data sets. Specifically, the proposed FCML-CP is superior to the commonly used statistical mixture likelihood approach using expectation–maximization (EM) algorithm; it is much more time-saving especially. The remarkable performance of FCML-CP in detecting CPs for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out-of-control signal resulted from small changes is usually delayed long.

Original language | English |
---|---|

Pages (from-to) | 447-463 |

Number of pages | 17 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 308 |

DOIs | |

Publication status | Published - 2016 Dec 15 |

### Fingerprint

### Keywords

- Change-point
- Control chart
- Fuzzy classification maximum likelihood change-point algorithm
- Fuzzy clustering
- Mixture model

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

**Detecting change-points for shifts in mean and variance using fuzzy classification maximum likelihood change-point algorithms.** / Lu, Kang Ping; Chang, Shao-Tung.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Detecting change-points for shifts in mean and variance using fuzzy classification maximum likelihood change-point algorithms

AU - Lu, Kang Ping

AU - Chang, Shao-Tung

PY - 2016/12/15

Y1 - 2016/12/15

N2 - Knowing the time of changes, called change-point (CP), in a process is crucial for engineers to recognize the root cause fast and accurately. Since special causes may induce simultaneous changes in mean and variance, detecting changes in both at once is required. Many methodologies in quality control were developed for detecting changes in either mean or variance only, and process parameters were assumed known often. However, they are rarely known exactly and a small estimation error may lead to unfavorable CP estimates. Fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality. A new mechanism, called fuzzy classification maximum likelihood change-point (FCML-CP) algorithm, is proposed to detect shifts in mean and variance simultaneously. A CP framework is transferred into a mixture model and then a FCML-CP algorithm is created through fuzzy classification maximum likelihood procedures. The proposed FCML-CP can be applied to phase I and II processes without knowledge of in-control process parameters; it can estimate multiple CPs of process mean or/and variance simultaneously. The effectiveness and superiority of FCML-CP are shown by extensive experiments with numerical and real data sets. Specifically, the proposed FCML-CP is superior to the commonly used statistical mixture likelihood approach using expectation–maximization (EM) algorithm; it is much more time-saving especially. The remarkable performance of FCML-CP in detecting CPs for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out-of-control signal resulted from small changes is usually delayed long.

AB - Knowing the time of changes, called change-point (CP), in a process is crucial for engineers to recognize the root cause fast and accurately. Since special causes may induce simultaneous changes in mean and variance, detecting changes in both at once is required. Many methodologies in quality control were developed for detecting changes in either mean or variance only, and process parameters were assumed known often. However, they are rarely known exactly and a small estimation error may lead to unfavorable CP estimates. Fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality. A new mechanism, called fuzzy classification maximum likelihood change-point (FCML-CP) algorithm, is proposed to detect shifts in mean and variance simultaneously. A CP framework is transferred into a mixture model and then a FCML-CP algorithm is created through fuzzy classification maximum likelihood procedures. The proposed FCML-CP can be applied to phase I and II processes without knowledge of in-control process parameters; it can estimate multiple CPs of process mean or/and variance simultaneously. The effectiveness and superiority of FCML-CP are shown by extensive experiments with numerical and real data sets. Specifically, the proposed FCML-CP is superior to the commonly used statistical mixture likelihood approach using expectation–maximization (EM) algorithm; it is much more time-saving especially. The remarkable performance of FCML-CP in detecting CPs for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out-of-control signal resulted from small changes is usually delayed long.

KW - Change-point

KW - Control chart

KW - Fuzzy classification maximum likelihood change-point algorithm

KW - Fuzzy clustering

KW - Mixture model

UR - http://www.scopus.com/inward/record.url?scp=84977527157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977527157&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2016.06.006

DO - 10.1016/j.cam.2016.06.006

M3 - Article

AN - SCOPUS:84977527157

VL - 308

SP - 447

EP - 463

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -