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This article aims to develop procedures for estimation and prediction in case of Type-I hybrid censored samples drawn from a two-parameter generalized half-logistic distribution (GHLD).

The GHLD is a versatile model which is useful in lifetime modelling. Also, hybrid censoring is a time and cost-effective censoring scheme which is widely used in the literature. The authors derive the maximum likelihood estimates, the maximum product of spacing estimates and Bayes estimates with squared error loss function for the unknown parameters, reliability function and stress-strength reliability. The Bayesian estimation is performed under an informative prior set-up using the “importance sampling technique”. Afterwards, we discuss the Bayesian prediction problem under one and two-sample frameworks and obtain the predictive estimates and intervals with corresponding average interval lengths. Applications of the developed theory are illustrated with the help of two real data sets.

The performances of these estimates and prediction methods are examined under Type-I hybrid censoring scheme with different combinations of sample sizes and time points using Monte Carlo simulation techniques. The simulation results show that the developed estimates are quite satisfactory. Bayes estimates and predictive intervals estimate the reliability characteristics efficiently.

The proposed methodology may be used to estimate future observations when the available data are Type-I hybrid censored. This study would help in estimating and predicting the mission time as well as stress-strength reliability when the data are censored.

Burr distribution has been proved to be a useful failure model. It can assume different shapes which allow it to be a good fit for various lifetimes data. Hybrid censoring is an important way of generating lifetimes data. The purpose of this paper is to estimate an unknown parameter of the Burr type XII distribution when data are hybrid censored.

The problem is dealt with through both the classical and Bayesian point of view. Specifically, the methods of estimation used to tackle the problem are maximum likelihood estimation method and Bayesian method. Empirical Bayesian approach is also considered. The performance of all estimates is compared through their mean square error values. The paper employs Monte Carlo simulation to evaluate the mean square error values of all estimates.

The key findings of the paper are that the Bayesian estimates are superior to the maximum likelihood estimates (MLE).

This work has practical importance. Indeed, the proposed methods are applied to real life data.

The paper is original and is quite applicable in lifetimes data analysis.

This article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis–Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints.

This article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints.

A real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes.

The proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.

In this paper, the author proposed an optimization design for a step-stress accelerated life test (SSALT) with two stress variables for the generalized exponential (GE) distribution under progressive type-I censoring.

In this paper, two stress variables were considered. Progressive censoring and accelerated life testing were used to reduce the time and cost of testing. It was assumed that the lifetimes of the test units followed a GE distribution. The effects of changing stress were considered as a cumulative exposure model. A log-linear relationship between the scale parameter of the GE distribution and the stress was proposed. The maximum likelihood estimators and approximate and bootstrap confidence intervals (CIs) for the model parameters were obtained. An optimum test plan was developed using minimization of the asymptotic variance (AV) of the percentile life under the usual operating condition.

According to the simulation results, the bootstrap CIs of the model parameters gave more accurate results than approximate CIs through the length of CIs. The sensitivity analysis was performed to illustrate the effect of initial estimates on optimal values that has been studied. Simulation results also indicated that the optimal times were not too sensitive to the initial values of parameters; thus, the proposed design was robust.

In most studies, only one accelerating stress variable is used. Sometimes accelerating one stress variable does not yield enough failure data. Thus, two stress variables may be needed for additional acceleration. In this paper, two stress variables are considered. The inclusion of two stress variables in a test design will lead to a better understanding of the effect of two simultaneously operating stress variables. Also, the author assumes that the failure time of the test units follows a GE distribution. It is observed that the GE distribution can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. Also, most studies in this field have focused on the derivation of optimum test plans. In this paper, the author examined the estimation of model parameters and the optimization of the test design. In this paper, the asymptotic and bootstrap CIs for the model parameters are calculated. In addition, a sensitivity analysis is performed to examine the effect of the changes in the pre-estimated parameters on the optimal hold times. For determining the optimal test plan, due to nonlinearity and complexity of the objective function, the particle swarm optimization (PSO) algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and optimization ability is more.

In this paper, the authors design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this paper we design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this study, the authors design accelerated life test under Type-I censoring when the lifetime of test items follows PID and also provides its application in the field of warranty policy. The following conclusion is made on the basis of this study. (1) An inverse relationship is shown between the shape parameter with the expected total cost and expected cycle time, while the shape parameter directly relates to the expected cost rate (see Table 5). (2) A direct relationship is shown between the scale parameter with the expected total cost and expected time cycle, while the inverse relationship is shown with the expected cost rate (see Table 5). (3) An inverse relationship is shown between the replacement age and the expected cost rate, while there are direct relationships between expected total cost and expected time cycle (see Table 5).

This paper is neither published or neither accepted anywhere.

In this chapter, we are among the first to investigate the actual course of affairs in AGMs with respect to shareholder forum rights. In the first part of the chapter, we provide descriptive statistics on the use of the right to ask questions and speak in AGMs in the Netherlands. We find that in an average meeting there are around 42 questions and remarks made by around 8 shareholders. Most of these questions and remarks seem to be relevant; with a categorization framework of 14 topics, we could already identify over 50% of these questions and remarks. However, we also find that the average number of shareholders that physically ask questions is only 8. Next, we consider the determinants of the use of these forum rights. In several panel data analyses with a Poisson distribution and a negative binomial distribution, we, inter alia, found that the ‘importance of the meeting’ generally contributes to the amount of questions and remarks and the number of shareholders that actively engage in discussions. We have also found that the number of speakers – and the number of private investors – that actively attend the AGM depends on previous attendance numbers. This may imply that there is a small base of very active (private) investors in the Netherlands. We conclude that the forum function of AGMs is definitely relevant, but given the low number of shareholders that make use of these rights, amendments may be considered.

We estimate a double-hurdle (DH) model of the Hungarian wage distribution assuming censoring at the minimum wage and wage under-reporting (i.e. compensation consisting of the minimum wage, subject to taxation and an unreported cash supplement). We estimate the probability of under-reporting for minimum wage earners, simulate their genuine earnings and classify them and their employers as ‘cheaters’ and ‘non-cheaters’. In the possession of the classification, we check how cheaters and non-cheaters reacted to the introduction of a minimum social security contribution base, equal to 200 per cent of the minimum wage, in 2007. The findings suggest that cheaters were more likely to raise the wages of their minimum wage earners to 200 per cent of the minimum wage, thereby reducing the risk of tax audit. Cheating firms also experienced faster average wage growth and slower output growth. The results suggest that the DH model is able to identify the loci of wage under-reporting with some precision.