Use of median‐based estimator to construct Phase II exponential chart

Kumar, Nirpeksh; Jaiswal, Sonam

doi:10.1002/qre.2672

Cited by 6 publications

(4 citation statements)

References 37 publications

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“…For the robust regression parameter estimation, Susanti et al [28] proposed algorithms for MM-estimators, M-estimators, and S-estimators. In the presence of outliers in the phase-1 data, Kumar and Jaiswal [40] developed an estimator that is a function of the sample median and used it to generate the phase-II control limits. Maleki et al [41] developed and compared a multivariate robust T 2 control chart assuming an M-estimator and traditional estimators.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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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 manufacturingprocess. 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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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“…Susanti et al 27 provided algorithms for MM-estimators, M-estimators, and S-estimators for the robust regression parameter estimation. Kumar and Jaiswal 28 discussed an estimator that is a function of sample median and used it for the construction of Phase-II control limits in the presence of outliers in Phase-1 data. Maleki et al 29 developed a multivariate robust 𝑇 2 control chart and compared it with M-estimator and other classical estimators.…”

Section: Introductionmentioning

confidence: 99%

Proportional hazard‐based robust monitoring schemes using logistic distribution

Nabeel

Ali

Shah

2022

Quality & Reliability Eng

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In the manufacturing industry, process surveillance plays an important role in improving product reliability. Many monitoring procedures have been devised to improve the reliability of a product in the literature. Due to cascading nature of multistage processes, the quality variable of the final stage can be influenced by the quality variable in the previous stages. Furthermore, the ordinary least squares method produces biased estimates if there are outliers in the historical data. The existence of cascade property in the multistage process and the presence of influential observations (outliers) in the historical data make the analysis of control schemes more challenging. Therefore, it is essential to take into account the impact of effective covariates and outliers in the historical dataset. In this paper, a cumulative sum (CUSUM) and two exponentially weighted moving average (EWMA) charts have been developed to monitor a two-stage-dependent process. The proportional hazard (PH) model has been applied to model the relationship among the incoming and outgoing variables of the two stage process.To deal with the deleterious effects of outliers on the results, a robust regression technique known as the M-estimation has been implemented and the performance of the proposed monitoring procedures has been analyzed through Monte Carlo simulations. Lastly, two real-life applications of the proposed control schemes are presented.

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“…Similarly, Susanti et al 39 developed algorithms for M‐estimator, S‐estimator, and MM‐estimator in a robust regression modeling 22 . Kumar and Jaiswal 40 proposed a median‐based estimator to construct the phase ll control limits when the phase l data set contains outliers. Maleki et al 41 presented a new multivariate robust

T^{2}

control chart and compared the proposed robust estimators for the process mean vector and the variance covariance matrix with the classical estimators and the M‐estimators.…”

Section: Introductionmentioning

confidence: 99%

Robust proportional hazard‐based monitoring schemes for reliability data

Nabeel

Ali

Shah

2021

Quality & Reliability Eng

View full text Add to dashboard Cite

Reliability of products is a key factor for successful businesses. In general, the existing monitoring schemes have poor performance as reliability data are often censored. Also, the products are manufactured in multistage processes where the outgoing quality gets affected by the previous stage quality. Besides this cascade property, historical data with outliers make the analysis even more complicated. This paper discusses exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts for monitoring a two‐stage dependent process. In particular, the proportional hazard (PH) model is assumed for modeling the relationship of quality characteristics. Furthermore, to remove the detrimental effects of outliers on the results, robust regression method known as the M‐estimation is used. Besides a real case study, the performance of the proposed monitoring approach is assessed through a comprehensive simulation study. The results suggested that the EWMA chart outperforms the CUSUM chart.

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Use of median‐based estimator to construct Phase II exponential chart

Cited by 6 publications

References 37 publications

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

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

Proportional hazard‐based robust monitoring schemes using logistic distribution

Robust proportional hazard‐based monitoring schemes for reliability data

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