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This paper presents a comparative study of reliability analysis of a gas production plant, before and after applying optimal age replacement policy for a specific machine. The gas production plant has six machines connected in the series configuration a sulfur (S) shaft, coal pit, reaction furnace, sulfur separation machine, adiabatic reactor, and cooling machine. Here, the optimal age replacement policy has been applied to the cooling machine as this machine is working under a wear-out period, i.e., it has completed its prescribed age (say T) and is still operational. Two different situations have been discussed to analyze the performance variation of the system (i) when the model is working with high risk because the cooling machine is operational even after completion of its prescribed age (ii) when the old cooling machine is replaced by a new one after completing the age, T. The failure of any machine can cause the model failure. Additionally, a situation of employee walkout is also considered a responsible factor for model failure. Supplementary variable technique and copula methodology have been applied to solve the Markov model.

The primary motivation behind this study is to precisely predicting the behaviour of the distribution by employing neural networks and enhancing its performance through maximum likelihood estimation. The numerical findings were compared to the predictions derived from the multilayer artificial neural network model developed with seven neurons in the hidden layer. The R value was 0.999 and the deviation values were less than 0.045  for the artificial neural network models. Also, the results of a numerical investigation using maximum likelihood estimation agree exactly with those obtained from predictions made using artificial neural networks. The findings of this study reveal that neural networks might be a very promising tool for clinical data analysis.

In this article, we consider six process capability indices (PCIs) whose quality characteristics have a normal distribution, out of which first PCI 𝒞 p {\mathcal{C}_{p}} was developed in [J. M. Juran, Juran’s Quality Control Handbook, 3rd ed., McGraw-Hill, New York, 1974], next PCI 𝒞 p ⁢ m {\mathcal{C}_{pm}} was developed in [T. C. Hsiang and G. Taguchi, A tutorial on quality control and assurance, Annual Meeting on the American Statistical Association, Las Vegas 1985], third PCI 𝒞 p ⁢ m ⁢ c {\mathcal{C}_{pmc}} was developed in [M. Saha, S. Dey and L. Wang, Parametric inference of the loss based index C p ⁢ m C_{pm} for normal distribution, Qual. Reliab. Eng. Int. 38 2022, 10.1002/qre.2987], fourth PCI 𝒞 p ⁢ m ′ {\mathcal{C}^{\prime}_{pm}} was developed in [S. Dey, W. Wang and M. Saha, Modified estimation and confidence intervals of an asymmetric loss based process capability index 𝒞 p ⁢ m ′ \mathcal{C}^{\prime}_{pm} , Qual. Reliab. Eng. Int. 38 2022, 8, 4033–4048], fifth PCI 𝒞 p ⁢ c {\mathcal{C}_{pc}} and sixth one 𝒞 p ⁢ m ⁢ c ′ {\mathcal{C}^{\prime}_{pmc}} are newly proposed in the paper. Next, we estimate the cited process capability indices using the method of moment estimation (MOM) approach when the underlying process follows normal distribution. A simulation study is conducted to evaluate the performance of these indices with respect to their mean squared errors. Additionally, confidence intervals are constructed using the asymptotic confidence interval (ACI), the generalized confidence interval (GCI) and parametric bootstrap confidence interval (BCI). Using Monte Carlo simulation, the performance of the GCI and BCI is compared in terms of average width and associated coverage probabilities. Finally, four data sets, two related to electronic industries and two related to food industries are re-analyzed to show the applicability’s of the suggested indices, MOM estimation, GCI and BCI.

In this work, we provide five different classical estimation methods for the gamma distribution and unknown parameters, which are used to estimate the newly constructed process capability index (PCI) C c C_{c} . Next, we use the aforementioned estimation techniques to consider five bootstrap confidence intervals: standard bootstrap (SB), percentile bootstrap (PB), student’s 𝑡 bootstrap (STB), bias-corrected percentile bootstrap (BCPB), and bias-corrected accelerated bootstrap (BCAB). These allow us to construct confidence intervals of the PCI C c C_{c} . Using the suggested techniques of estimate for small, moderate, and large sample sizes, Monte Carlo simulations are run to compare the performances of the bootstrap confidence intervals’ average widths and coverage probabilities. Simulation results indicate that MLE gives the least AW for all BCIs (SB, PB, BCPB, TB, and BCAB) when compared to all other estimation approaches evaluated in this paper. Further, simulation results demonstrate that, for almost all sample sizes and all of the examined estimation approaches, BCAB CI generates smaller AW and larger CP than their counterparts. Finally, for illustrative purposes, three real data sets are analysed.

In this article, we developed group and double acceptance sampling inspection plans (GASIP) and (DASIP). In GASIP, multiple number of items, made as a group, can be tested simultaneously in an inspection procedure. We study both the GASIP and DASIP under the truncated life test assuming that the lifetime of an item is distributed as quasi-xgamma distribution (Sen and Chandra 2017). The plan parameters of both proposed plans are to be determined by satisfying the consumer’s risk at the specified ratio of true average life to the specified life and termination time. The results for different parameters are tabulated and explained in well manner for better understanding. Two suitable real data sets are considered for application purposes.

This paper investigates E-Bayesian estimation for the Weighted Power Function Distribution (WPFD), a modified version of the Power Function distribution which is widely applied in biosciences and engineering. Three distinct priors for hyper-parameters are considered, and E-posterior risks are derived using squared error, entropy (measuring uncertainty), and precautionary loss functions (penalizing extreme deviations). Properties of the E-Bayesian estimators are analyzed, supplemented by a simulation study and real data application. Results indicate that E-Bayesian estimators outperform Bayesian counterparts in terms of E-posterior risk, as demonstrated in simulation studies.

Ridge regression presents a method to tackle multicollinearity issues. Several estimators and predictors for the estimation of biasing parameter k have been extensively detailed in scholarly literature. We offer a thorough analysis of both conventional and emerging methods aimed at precisely determining the ridge parameter k . Our investigation provides valuable insights into the properties of these estimators and their practical efficacy in various applications. Proposed estimators for the parameter k are assessed using Monte Carlo simulations and a real-world example, with a focus on evaluating their performance based on Mean Squared Error (MSE). Our estimator, in conjunction with others, showcases commendable performance, as indicated by the results.