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Modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Exponentiated Pareto distribution, is introduced. Some structural properties of the proposed distribution are studied including explicit expressions for the moments and generating function. An explicit expression for Rényi entropy is obtained. The method of maximum likelihood is used for estimating the model parameters.

The expression for the Operating Characteristics (OC) and Average Sample Number (ASN) functions are derived under inspection error. Two types of error are defined i.e. (i) failing to find one or more of the nonconformities in the sample and (ii) declaring one or more nonconformities when none exist. It is seen by OC and ASN curves that inspector errors have considerable effects on the results of a sequential test for Poisson distribution.

It is widely recognized that measurement errors often exist in practice and may considerably affect the performance of control charts in some cases. Measurement error variability has uncertainty which may be originated from several sources. Recently, Chakraborty and Khurshid [3] studied the effects of measurement error on control charts for zero-truncated Poisson distribution. In this paper, we study the effect of the two sources of variability on the power characteristics of control charts and obtain the values of average run length (ARL) for the binomial distribution based on the ratio of two Poisson distributions as studied by Sahai and Khurshid [20]. Expression of the power of the control chart under the standardized normal variable for the binomial distribution is also derived when the underlying distribution is the ratio of two Poisson distributions.

In this paper we develop a bivariate version of the confluent hypergeometric series distribution through its probability generating function and study some of its properties by deriving its probability mass function, factorial moments, probability generating functions of its marginal and conditional distributions and recursion formulae for probabilities, raw moments and factorial moments. Further certain mixtures and limiting cases of this distribution are also obtained.

This paper investigates the behaviour of a system composed of N independent unit subject to failure. A single repair facility is available to attend to the failed unit. At a random time interval the system is overhauled and put back in operation as a new. The method of the supplementary variable is used to set the equations describing the reliability. Induction is further used to obtain a closed solution.

The success of the implementation of control chart depends upon the assumptions made on the distribution of the quality characteristics. If the distributional assumption deviates too much from the true one or if it is misspecified, the performance of the control chart is seriously affected and one may make wrong conclusions about the process. To avoid such situations, we propose a new class of control chart based on the empirical likelihood (EL). We propose to monitor the EL ratio statistic for mean and use resampling method to arrive at its empirical distribution which is inverted to obtain the control limits. Our simulation results clearly indicated that EL control charts have a comparable performance with Shewhart control chart, when the distribution of the quality characteristic follows a normal distribution. When the distribution of quality characteristics are misspecified, the EL control chart shows a better performance with all competing control charts. Finally, our proposed method is illustrated by a real example.

In the course of many crises (e.g. the finance and bank crises), wars, terror and the climate change, risk analysis has become one of the most discussed topics, not only in scientific circles. Especially, after the Fukushima disaster, the quality of traditional risk analysis has become doubtful. As known today, when the nuclear power plant at Fukushima was planned in the 1960s, the design was based on an unreliable risk analysis and also the regular controls under the supervision of the IAEA did not lead to any changes. Motivated by the Fukushima disaster, the risk of tsunamis is taken in this paper as an example to illustrate a risk analysis of high quality. Although it is performed only as an example, it shows how one has to proceed to get reliable and accurate prediction and measurement procedures as a basis for making appropriate decisions whenever risks are involved.

In any manufacturing process, identification of changes in the process conditions is of great interest. Recently, a Bayesian approach for the identification of the change in process mean was proposed assuming that the response of interest follow an exponential family distribution. In this approach, the expectation – maximization (EM) algorithm was used for estimating the process parameters. In general, the EM algorithm is computationally intensive and the optimality depends on the initial values of the parameters chosen. We extend the idea of the EM test for homogeneity to extend this Bayesian approach to the change point problem. Our simulations studies show that the developed EM test procedure converges at a faster rate than the original EM approach. Our studies also show that the EM test with binomial prior distribution leads to solutions very close to the true values. We have applied our approach to two case examples.