Double acceptance sampling plan based on truncated life tests for two-parameter Xgamma distribution

In this paper, a double acceptance sampling plan (DASP) in terms oftruncated life tests is oered assuming that the lifetime of a product followsthe two-parameter Xgamma (TPXG) distribution. The mean of the TPXGdistribution is considered as the quality parameter. For a certain values ofthe consumer's condence level, the minimum sample sizes of the rst andsecond samples required to assert the identied mean life are achieved. Thecorresponding operating characteristic (OC) values for to the various qualitylevels are attained as well as the minimum ratios of the mean life to theindicated life are obtained. Numerical results and examples are presentedfor illustration

Fractional Survival Functional Entropy of Engineering Systems

An alternate measure of uncertainty, termed the fractional generalized cumulative residual entropy, has been introduced in the literature. In this paper, we first investigate some variability properties this measure has and then establish its connection to other dispersion measures. Moreover, we prove under sufficient conditions that this measure preserves the location-independent riskier order. We then elaborate on the fractional survival functional entropy of coherent and mixed systems’ lifetime in the case that the component lifetimes are dependent and they have identical distributions. Finally, we give some bounds and illustrate the usefulness of the given bounds

Stochastic Properties of Fractional Generalized Cumulative Residual Entropy and Its Extensions

The fractional generalized cumulative residual entropy (FGCRE) has been introduced recently as a novel uncertainty measure which can be compared with the fractional Shannon entropy. Various properties of the FGCRE have been studied in the literature. In this paper, further results for this measure are obtained. The results include new representations of the FGCRE and a derivation of some bounds for it. We conduct a number of stochastic comparisons using this measure and detect the connections it has with some well-known stochastic orders and other reliability measures. We also show that the FGCRE is the Bayesian risk of a mean residual lifetime (MRL) under a suitable prior distribution function. A normalized version of the FGCRE is considered and its properties and connections with the Lorenz curve ordering are studied. The dynamic version of the measure is considered in the context of the residual lifetime and appropriate aging paths

Further Properties of Tsallis Entropy and Its Application

The entropy of Tsallis is a different measure of uncertainty for the Shannon entropy. The present work aims to study some additional properties of this measure and then initiate its connection with the usual stochastic order. Some other properties of the dynamical version of this measure are also investigated. It is well known that systems having greater lifetimes and small uncertainty are preferred systems and that the reliability of a system usually decreases as its uncertainty increases. Since Tsallis entropy measures uncertainty, the above remark leads us to study the Tsallis entropy of the lifetime of coherent systems and also the lifetime of mixed systems where the components have lifetimes which are independent and further, identically distributed (the iid case). Finally, we give some bounds on the Tsallis entropy of the systems and clarify their applicability

Further Properties of Tsallis Entropy and Its Application

The entropy of Tsallis is a different measure of uncertainty for the Shannon entropy. The present work aims to study some additional properties of this measure and then initiate its connection with the usual stochastic order. Some other properties of the dynamical version of this measure are also investigated. It is well known that systems having greater lifetimes and small uncertainty are preferred systems and that the reliability of a system usually decreases as its uncertainty increases. Since Tsallis entropy measures uncertainty, the above remark leads us to study the Tsallis entropy of the lifetime of coherent systems and also the lifetime of mixed systems where the components have lifetimes which are independent and further, identically distributed (the iid case). Finally, we give some bounds on the Tsallis entropy of the systems and clarify their applicability

Scaled-Invariant Extended Quasi-Lindley Model: Properties, Estimation, and Application

In many research fields, statistical probability models are often used to analyze real-world data. However, data from many fields, such as the environment, economics, and health care, do not necessarily fit traditional models. New empirical models need to be developed to improve the fit. In this study, we investigated a further extension of the quasi-Lindley model. This extension was asymmetrically distributed on the positive real number line. Maximum likelihood, least square error, Anderson–Darling, and expectation maximization algorithms were used to estimate the parameters studied. All techniques provided accurate and reliable estimates of the parameters. However, the mean square error of the expectation-maximization approach was lower. The usefulness of the proposed model was demonstrated by analyzing a reliability data set, and the analysis showed that it outperformed all other alternative models

Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance. Usually, conventional PCIs perform well under normally distributed quality characteristics. However, when these PCIs are employed to evaluate nonnormally distributed process, they often provide inaccurate results. In this article, in order to estimate the PCI Spmk when the process follows power Lindley distribution, first, seven classical methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares methods of estimation, Cramèr–von Mises method of estimation, maximum product of spacings method of estimation, Anderson–Darling, and right-tail Anderson–Darling methods of estimation, are considered and the performance of these estimation methods based on their mean squared error is compared. Next, three bootstrap confidence intervals (BCIs) of the PCI Spmk, namely, standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap, are considered and compared in terms of their average width, coverage probability, and relative coverage. Besides, a new cost-effective PCI, namely, Spmkc is introduced by incorporating tolerance cost function in the index Spmk. To evaluate the performance of the methods of estimation and BCIs, a simulation study is carried out. Simulation results showed that the maximum likelihood method of estimation performs better than their counterparts in terms of mean squared error, while bias-corrected percentile bootstrap provides smaller confidence length (width) and higher relative coverage than standard bootstrap and percentile bootstrap across sample sizes. Finally, two real data examples are provided to investigate the performance of the proposed procedures

Asymmetric Right-Skewed Size-Biased Bilal Distribution with Mathematical Properties, Reliability Analysis, Inference and Applications

Asymmetric distributions, as opposed to symmetric distributions, may be more resilient to extreme values or outliers. Furthermore, when data show substantial skewness, asymmetric distributions can shed light on the underlying processes or phenomena being investigated. In this direction, the size-biased Bilal distribution (SBBD) is suggested in this study as a generalization to the Bilal distribution. The length-biased and area-biased Bilal distributions are discussed in detail as two special cases. The main statistical properties of the distribution including the rth moment, coefficients of variation, skewness, kurtosis, moment generating function, incomplete moments, moments of residual life, harmonic mean, Fisher’s information, and the Rényi entropy as a measure of uncertainty are presented. Graphical representations of the cumulative distribution, probability density, odds, survival, hazard, reversed hazard rate, and cumulative hazard functions are presented for further explanation of the distribution behavior. In addition, the methods of moments and maximum likelihood estimates are taken into account for estimating the model parameters. A simulation study is carried out to see the efficiency of the maximum likelihood in terms of standard errors and bias. Real data sets of precipitation and myeloid leukemia patients are considered to show the practical significance of the suggested distributions as an alternative to some well-known distributions such as the Rama, Rani, Bilal, and exponential distributions. It is found that the size-biased Bilal distribution is right-skewed and has a superior fitting performance compared to the other distributions in this study

A SkSP-R Plan under the Assumption of Gompertz Distribution

In this study, we designed a time-truncated SkSP-R sampling plan when the lifetime of units follows a Gompertz distribution (GmzD). The GmzD is briefly discussed. All of the plan parameters were obtained using a two-point approach, which is based on limiting quality level (LQL) and acceptable quality level (AQL). Moreover, operating characteristic (OC) values were calculated for the determined value of the plan parameters by using the OC function of the SkSP-R. Applications of two real life situations in engineering were presented to illustrate the applicability of the offered sampling inspection plan. It was found that the new SkSP-R sampling inspection plan can be used efficiently in the field

Goodness-of-Fit Tests for Weighted Generalized Quasi-Lindley Distribution Using SRS and RSS with Applications to Real Data

This paper deals with the problem of goodness-of-fit tests (GFTs) for the weighted generalized quasi-Lindley distribution (WGQLD) using ranked set sampling (RSS) and simple random sampling (SRS) techniques. The tests are based on the empirical distribution function and sample entropy. These tests include the Kullback–Leibler, Kolomogorov–Smirnov, Anderson–Darling, Cramér–von Mises, Zhang, Liao, and Shimokawa, and Watson tests. The critical values (CV) and power of each test are obtained based on a simulation study by using SRS and RSS methods considering various sample sizes and alternatives. A rain data set is used to investigate the effectiveness of the suggested GFTs. Based on the same number of measured units for the various alternatives taken into consideration in this study, it is discovered that the RSS tests are more effective than those of their rivals in SRS. Additionally, as the set size increases, the GFTs’ power increases