Robust Surveillance Schemes Based on Proportional Hazard Model for Monitoring Reliability Data

Moezza Nabeel, Sajid Ali (), Ismail Shah, Mohammed M. A. Almazah and Fuad S. Al-Duais
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Moezza Nabeel: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Sajid Ali: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Ismail Shah: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Mohammed M. A. Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
Fuad S. Al-Duais: Mathematics Department, College of Humanities and Science, Prince Sattam Bin Abdulaziz University, Al Aflaj 16278, Saudi Arabia

Mathematics, 2023, vol. 11, issue 11, 1-21

Abstract: Product reliability is a crucial component of the industrial production process. Several statistical process control techniques have been successfully employed in industrial manufacturing processes to observe changes in reliability-related quality variables. These methods, however, are only applicable to single-stage processes. In reality, manufacturing processes consist of several stages, and the quality variable of the previous stages influences the quality of the present stage. This interdependence between the stages of a multistage process is an important characteristic that must be taken into account in process monitoring. In addition, sometimes datasets contain outliers and consequently, the analysis produces biased results. This study discusses the issue of monitoring reliability data with outliers. To this end, a proportional hazard model has been assumed to model the relationship between the significant quality variables of a two-stage dependent manufacturing process. Robust regression technique known as the M-estimation has been implemented to lessen the effect of outliers present in the dataset corresponding to reliability-related quality characteristics in the second stage of the process assuming Nadarajah and Haghighi distribution. The three monitoring approaches, namely, one lower-sided cumulative sum and two one-sided exponentially weighted moving average control charts have been designed to effectively monitor the two-stage dependent process. Using Monte Carlo simulations, the efficiency of the suggested monitoring schemes has been examined. Finally, two real-world examples of the proposed control approaches are provided in the study.

Keywords: average run length; exponentially weighted moving average; cumulative sum; proportional hazard model; reliability data; robust regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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