Volume 40, Issue 2

This article focuses on estimating the process capacity index (PCI), 𝒞 pc \mathcal{C}_{\rm pc} , where the underlying distribution is a power generalized Weibull distribution, using maximum likelihood and Bayesian techniques. The 𝒞 pc \mathcal{C}_{\rm pc} index may be used to both normal and non-normal quality attributes. This article aims to accomplish three things: Using the maximum likelihood approach, we first determine the estimator of the PCI 𝒞 pc \mathcal{C}_{\rm pc} . Secondly, the Metropolis-Hastings Algorithm is used to study Bayesian estimation under four loss functions (symmetric and asymmetric). Third, the index 𝒞 pc \mathcal{C}_{\rm pc} ’s 95  confidence intervals are built using Bayesian and four bootstrap techniques. The point estimates of 𝒞 pc \mathcal{C}_{\rm pc} have been evaluated using Monte Carlo simulation in terms of mean square errors (MSEs), four bootstrap methods, and highest posterior density (HPD) credible intervals in relation to their average width (AW) and coverage probabilities (CPs). Using two real data sets – one pertaining to the size of electrical connections and the other to the amount of protein (in g) for adult patients at the Hospital Carlos Van Buren in Valparaiso, Chile – a comparable analysis to that employed in the simulations is conducted in order to illustrate the effectiveness of the suggested methods.

The overall idea of this paper is to introduce a new family of inhomogeneous stochastic Rayleigh diffusion processes and use them to predict and forecast simulated data after establishing the main characteristics of these kinds of processes. They are interesting models for infectious diseases, health and renewable energies. First of all, we define the new processes by means of a τ-power of the stochastic Rayleigh diffusion model. Then the most important features of the process are examined, with particular attention to its analytic expression, transition probability density function and mean functions. Otherwise, the parameters that appear in the present model are estimated by maximum likelihood with discrete sampling. Lastly, in order to assess the quality of this process, we will use these statistical computations for simulated examples, specifying fitting and prediction possibilities.

An acceptance sampling plan (AS) for a truncated life test is proposed based on the Marshall–Olkin Birnbaum–Saunders (MOBS) distribution. The minimum sample size required to guarantee the specified mean life is determined. Additionally, the operating characteristic function values and producer’s risk associated with the proposed sampling plans are presented. Tables summarizing the results are provided, supported by numerical examples to illustrate the findings. Finally, the proposed method is demonstrated through numerical examples and a real-life application.

In this paper, we propose a nonparametric exponentially weighted moving average (EWMA) control chart with a variable sampling interval (VSI) for monitoring the median of a continuous symmetric process distribution. The proposed chart, referred to as the VSI EWMA WSR chart, is based on the Wilcoxon Signed-Rank (WSR) test. Its out-of-control statistical performance is numerically compared with that of the fixed sampling interval (FSI) EWMA WSR chart when the underlying process distributions are normal, uniform, Laplace, scaled Student’s t , and logistic. The metric used for the performance comparisons is the steady-state average time to signal, which is determined through Monte Carlo simulations. The simulation results reveal that the VSI EWMA WSR chart significantly outperforms the FSI EWMA WSR chart in detecting the median shifts of all sizes across all distributions. The practical utility of the proposed chart is demonstrated using both simulated and real datasets. Our findings underscore the efficacy of the VSI EWMA WSR chart, highlighting its value as a tool for quality control in manufacturing and other industries.

In this study, the synthetic triple sampling (STS) X ¯ {\overline{X}} chart is introduced to monitor the process mean more effectively. The developed STS X ¯ {\overline{X}} chart combines the triple sampling (TS) X ¯ {\overline{X}} chart and the conforming run length (CRL) chart to enhance shift detection capabilities. The performance of the STS X ¯ {\overline{X}} chart is compared with that of the TS X ¯ {\overline{X}} and synthetic double sampling (SDS) X ¯ {\overline{X}} charts on the basis of the average number of observations to signal (ANOS) and expected ANOS (EANOS) as key performance metrics. Results show that the process shift detection effectiveness of the STS X ¯ {\overline{X}} chart is generally superior to that of the TS X ¯ {\overline{X}} and SDS X ¯ {\overline{X}} charts. Real industrial data are adopted to demonstrate the implementation of the STS X ¯ {\overline{X}} chart.

In the present paper we consider the notion of subquantile functions of order n and discuss their applications in entropy and reliability analysis. Subquantiles appear as reversed mean life in reliability and conditional values at risk in risk analysis and are closely related to many other concepts in different disciplines. A systematic study of this concept is hoped to get better insight into the investigations made in related topics in other areas like reliability, risk, income analysis, etc. We propose some results that could be of applications in these areas.