Efficient techniques for designing and evaluating multivariate Hotelling control chart with generalized sensitizing rules

Rashid Mehmood; Muhammad Naveed Khan; Iftikhar Ali; Tajammal Imran; Babar Zaman; Kassimu Mpungu; Fawwad Qureshi; Maysaa Elmahi Abdelwahab

Article Details

Efficient techniques for designing and evaluating multivariate Hotelling control chart with generalized sensitizing rules

Authors:

Rashid Mehmood | Muhammad Naveed Khan | Iftikhar Ali | Tajammal Imran | Babar Zaman | Kassimu Mpungu | Fawwad Qureshi | Maysaa Elmahi Abdelwahab

Publisher:

Hacettepe University

Main Topics:

Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1588-1621

Document Type:

Article

Publication Date:

8/2025

Document Language:

English

Document ID (Org No.):

2001356969

pISSN:

2651-477X

Keywords:

Abstract:

 In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations. The control limit of the proposed chart is derived relative to probability of a single point and number of process characteristics. To calculate probability of a single point for sustained in-control average run length, a generalized single polynomial equation is derived. For evaluation, performance measures are considered based on the average, the median, and the percentile run length. These measures are calculated using Monte Carlo simulation and numerical integration. The results indicate that the proposed control chart has consistent behavior when a process is in control. The in-control average run length is obtained equal to prefixed level which remains valid for all choices of sensitizing rules. This implies that the proposed control chart can resolve the issue of existing control chart in terms of sustained behavior. The effectiveness of sensitizing rules is dependent on process characteristics and variations of mean vector. A comparative analysis of different choices of sensitizing rules is conducted to locate optimal choices of process characteristics. Real-life example, dowel-pin manufacturing, shows that proposed control chart with sensitizing rules is efficient for diagnosing small variations.

 In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations. The control limit of the proposed chart is derived relative to probability of a single point and number of process characteristics. To calculate probability of a single point for sustained in-control average run length, a generalized single polynomial equation is derived. For evaluation, performance measures are considered based on the average, the median, and the percentile run length. These measures are calculated using Monte Carlo simulation and numerical integration. The results indicate that the proposed control chart has consistent behavior when a process is in control. The in-control average run length is obtained equal to prefixed level which remains valid for all choices of sensitizing rules. This implies that the proposed control chart can resolve the issue of existing control chart in terms of sustained behavior. The effectiveness of sensitizing rules is dependent on process characteristics and variations of mean vector. A comparative analysis of different choices of sensitizing rules is conducted to locate optimal choices of process characteristics. Real-life example, dowel-pin manufacturing, shows that proposed control chart with sensitizing rules is efficient for diagnosing small variations.

 In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations. The control limit of the proposed chart is derived relative to probability of a single point and number of process characteristics. To calculate probability of a single point for sustained in-control average run length, a generalized single polynomial equation is derived. For evaluation, performance measures are considered based on the average, the median, and the percentile run length. These measures are calculated using Monte Carlo simulation and numerical integration. The results indicate that the proposed control chart has consistent behavior when a process is in control. The in-control average run length is obtained equal to prefixed level which remains valid for all choices of sensitizing rules. This implies that the proposed control chart can resolve the issue of existing control chart in terms of sustained behavior. The effectiveness of sensitizing rules is dependent on process characteristics and variations of mean vector. A comparative analysis of different choices of sensitizing rules is conducted to locate optimal choices of process characteristics. Real-life example, dowel-pin manufacturing, shows that proposed control chart with sensitizing rules is efficient for diagnosing small variations.

 In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations. The control limit of the proposed chart is derived relative to probability of a single point and number of process characteristics. To calculate probability of a single point for sustained in-control average run length, a generalized single polynomial equation is derived. For evaluation, performance measures are considered based on the average, the median, and the percentile run length. These measures are calculated using Monte Carlo simulation and numerical integration. The results indicate that the proposed control chart has consistent behavior when a process is in control. The in-control average run length is obtained equal to prefixed level which remains valid for all choices of sensitizing rules. This implies that the proposed control chart can resolve the issue of existing control chart in terms of sustained behavior. The effectiveness of sensitizing rules is dependent on process characteristics and variations of mean vector. A comparative analysis of different choices of sensitizing rules is conducted to locate optimal choices of process characteristics. Real-life example, dowel-pin manufacturing, shows that proposed control chart with sensitizing rules is efficient for diagnosing small variations.

Article Details

Efficient techniques for designing and evaluating multivariate Hotelling control chart with generalized sensitizing rules

Authors:

Rashid Mehmood | Muhammad Naveed Khan | Iftikhar Ali | Tajammal Imran | Babar Zaman | Kassimu Mpungu | Fawwad Qureshi | Maysaa Elmahi Abdelwahab

Publisher:

Hacettepe University

Main Topics:

Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1588-1621

Document Type:

Article

Publication Date:

8/2025

Document Language:

English

Document ID (Org No.):

2001356969

pISSN:

2651-477X

Average run length

Hotelling

median run length

percentile run length

performance measures

sensitizing rules

single polynomial approach

Issues

Article Details

Authors: Rashid Mehmood | Muhammad Naveed Khan | Iftikhar Ali | Tajammal Imran | Babar Zaman | Kassimu Mpungu | Fawwad Qureshi | Maysaa Elmahi Abdelwahab

Publisher: Hacettepe University

Main Topics: Applied Statistics

Journal: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1588-1621

Document Type: Article

Publication Date: 8/2025

Document Language: English

Document ID (Org No.): 2001356969

pISSN: 2651-477X

Issues

Authors:

Rashid Mehmood | Muhammad Naveed Khan | Iftikhar Ali | Tajammal Imran | Babar Zaman | Kassimu Mpungu | Fawwad Qureshi | Maysaa Elmahi Abdelwahab

Publisher:

Hacettepe University

Main Topics:

Applied Statistics

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1588-1621

Document Type:

Article

Publication Date:

8/2025

Document Language:

English

Document ID (Org No.):

2001356969

pISSN:

2651-477X