Robust proportional hazard‐based monitoring schemes for reliability data

Nabeel, Moezza; Ali, Sajid; Shah, Ismail

doi:10.1002/qre.2921

Cited by 4 publications

(15 citation statements)

References 36 publications

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“…\end{array} \right.} \end{equation}Similarly, the objective and weight functions of Tukey bisquare estimators 15 . are defined as

\begin{equation} \rho (r) ={\left\lbrace \def\eqcellsep{&}\begin{array}{cc}\dfrac{k^2}{6}\left(1-\left(1-{\left(\dfrac{r}{k} \right)}^2\right)^3\right)&for\, {\left|{r}\right|} \le k\\[12pt] \dfrac{k^2}{6}&for\, {\left|{r}\right|}&gt;k \end{array} \right.}

…”

Section: Process Model and Assumptionsmentioning

confidence: 99%

“…To this end, survival regression models are widely implemented to model reliability data by considering the effects of effective covariates. 15 In this paper, a PH model has been applied to construct the hazard and survival function of the reliability-related variable of the second stage. The parametric PH model assumes that the baseline hazard function follows a parametric distribution.…”

Section: Process Model and Assumptionsmentioning

confidence: 99%

“…For this purpose, the AFT model is implemented by assuming log‐logistic distribution for the survival time of patients. Nabeel et al 15 . proposed EWMA and CUSUM charts to monitor a two‐stage‐dependent process with reliability data.…”

Section: Introductionmentioning

confidence: 99%

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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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“…\end{array} \right.} \end{equation}Similarly, the objective and weight functions of Tukey bisquare estimators 15 . are defined as

\begin{equation} \rho (r) ={\left\lbrace \def\eqcellsep{&}\begin{array}{cc}\dfrac{k^2}{6}\left(1-\left(1-{\left(\dfrac{r}{k} \right)}^2\right)^3\right)&for\, {\left|{r}\right|} \le k\\[12pt] \dfrac{k^2}{6}&for\, {\left|{r}\right|}&gt;k \end{array} \right.}

…”

Section: Process Model and Assumptionsmentioning

confidence: 99%

Section: Process Model and Assumptionsmentioning

confidence: 99%

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Proportional hazard‐based robust monitoring schemes using logistic distribution

Nabeel

Ali

Shah

2022

Quality & Reliability Eng

Self Cite

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“…Under the GELF, the E-Bayesian estimation of α, S and h is computed from ( 14)-( 16), respectively, and (18) . The estimators are as follows:…”

Section: E-bayesian Estimations With Gelfmentioning

confidence: 99%

“…Demiray and K?z?laslan [10] studied classical and Bayesian approaches to estimate the stress¨Cstrength reliability in consecutive k-out of-n systems when the two variables are belonging to PHM. Nabeel et al [18] proposed robust PHM under monitoring schemes to evaluate the reliability.…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian Estimations and Its E-MSE For Compound Rayleigh Progressive Type-II Censored Data

Shojaee

Piriaei

Babanezhad

2022

Stat., optim. inf. comput.

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Over the past decades, various methods to estimate the unknown parameter, the survival function, and the hazard rate of a statistical distribution have been proposed from the availability of type-II censored data. They are all differing in terms of how the progressive type-II censored data of the underlying distribution are available. In this study, we estimate the parameter, the survival function, and the hazard rate of the compound Rayleigh distribution by using the E-Bayesian estimation when the progressive type-II censored data are available. The resulting estimators are evaluated based on the asymmetric general entropy and the symmetric squared error loss functions. In addition, the E-Bayesian estimators under the different loss functions have been compared through a real data analysis and Monte Carlo simulation studies by calculating the E-MSE of the resulting estimators.

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Memory‐type control charts for censored reliability data

Ali

Shamim

Shah

et al. 2023

Quality & Reliability Eng

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Control charts are commonly used to monitor a process to detect undesirable changes. The main goal of this work is to propose exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts to track a process by utilizing type‐I censored generalized exponential (GE) distributed data. In particular, the censored data are replaced with the conditional expected value (CEV). A comparison between CUSUM and CUSUM ignoring unobserved covariates (CUSUM‐IUC) charts is also a part of this study. The GE distribution is considered due to its application in reliability analysis. The performance of the charts is evaluated by using the average run length along with the standard deviation of the run length. Furthermore, the study also examines the effect of smoothing parameters, censoring rate, and shifts on the proposed methodologies. The results indicate that the EWMA chart performs better than other schemes (CUSUM and CUSUM‐IUC) for shifts in the shape parameter of the GE distribution. Finally, the proposed schemes are also applied to a real‐life data set.

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Robust proportional hazard‐based monitoring schemes for reliability data

Cited by 4 publications

References 36 publications

Proportional hazard‐based robust monitoring schemes using logistic distribution

Proportional hazard‐based robust monitoring schemes using logistic distribution

E-Bayesian Estimations and Its E-MSE For Compound Rayleigh Progressive Type-II Censored Data

Memory‐type control charts for censored reliability data

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