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Control charts are widely used in statistical process control to detect changes in a production process and for monitoring a process to make sure that it is in control. In conventional statistical process control, the pattern of chance causes is often assumed to follow normal distribution. It is well known that the assumption of normality or any specific parametric form for the process distribution is too restrictive. In such situations, distribution-free or nonparametric control charts can serve the purpose better. In this paper, distribution-free control charts are developed based on a class of one-sample test statistics with sub-samples of size two due to Mehra, Prasad and Madhava Rao (Austral. J. Statist. 32: 373392, 1990). The control charts based on their statistic (-chart) are easy to understand and to use. The performance of the proposed procedures is studied through the average run length, which is the expected number of samples required by the procedure to signal out of control. It is observed that the performance of the proposed chart is better than the existing charts in the literature.

This study focuses on modeling the reliability of systems with multiple failure modes and imperfect repairs. Times to failure are exponentially distributed and repair times follow general distributions. Closed expressions are obtained for the steady state availability and Laplace transforms of the point-wise availability.

From 1st January 2010 the member states of the EU must guarantee effective product surveillance of their markets. According to the summary of Act No 765/2008 they are required to organise and carry out close monitoring so that the products covered by Community harmonisation legislation meet the requirements for protection of public interests such as health or safety. Furthermore market surveillance authorities must perform appropriate checks on the characteristics of products through documentary, physical and laboratory checks (. . . ). The article discusses potential sampling methods for market surveillance and evaluates their suitability to meet the legal requirements.

Control charts represent a very effective tool used for reducing process variability by early detection of the occurrence of assignable causes of variation. -charts are applied to detect changes in process mean whereas S -charts are used to detect the same in process variability. Both charts are generally based on the normality assumption. The S -chart utilizes an unbiased estimator of the population standard deviation . However, it is highly affected by any violation of the normality assumption. In this paper, we propose some alternatives of S -charts based on some robust estimate of scale parameters. We will also illustrate the performance of the proposed control chart.

In this article, a skewness parameter to a gamma distribution is introduced using an idea of Azzalini, which creates a new class of weighted gamma distributions. This new distribution has a probability density function with skewness representing a general case of weighted probability density function of the chi-square distribution, Erlang distribution, MaxwellBoltzmann distribution or skew-logistic distribution. It is observed that this distribution can also be obtained by hidden truncation. Different properties of this new distribution are discussed and the inference of the old parameters and the skewness parameter is studied.

In this paper the effect of truncation and measurement error on the operating characteristic (OC) and the average sample number (ASN) functions of a sequential test for the mean of the parent population with known variance is investigated.

This paper is concerned with the exact distribution of argmax (argmin) of a sequence of random variables. By argmax (argmin), we mean the random variable which attains the maximum (minimum) of the sequence. Change point estimators are of this type and the asymptotic distribution of this kind of estimator is studied extensively in literature. However, the exact distributions is generally not considered. Therefore, this paper is devoted to the exact distributions of the argmax in case of several examples. Finally, an approximation method is proposed.

This article proposes a hybrid economic group acceptance sampling plan for a truncated life test when the life time of the items follows an exponential distribution. For specified consumer's risk, test truncated time and group size, the minimum number of testers and acceptance number are determined. Tables of sampling plans are developed for the selection of sampling plans depending on different quality levels and given producer's risk. A comparative study of the proposed plan with existing plans is also performed. The results are illustrated by an example.

Acceptance sampling in quality control is a statistical methodology and consists of procedures for sentencing one or more incoming lots of finished products based on the inspection of sampled items drawn randomly from the lots. The theory of such procedures by attributes is often built upon the assumptions that the production process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, any production process exhibits quality variations, which occur due to random fluctuations. When the quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, for sentencing the processes generating the lots, Bayesian acceptance sampling plans, which use prior information on the process variation, can be employed as an alternative to conventional plans. This paper presents the concept of chain sampling inspection plans by attributes for continuous production using Bayesian methodology. The operating characteristic (OC) function of Bayesian chain sampling plans as a measure of performance is defined and the properties of OC curves of the plans with reference to their parameters are studied empirically. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed. The closed form expressions for the parameters of the plans are derived.

In this paper we consider the exponentiated modified Weibull distribution. The modified Weibull distribution, Weibull distribution and the exponentiated exponential distribution are found to be particular cases of this family. We derive the analytical shape of the corresponding density functions and hazard rate functions. The r th moment and the moment generating function are determined. Finally the distribution of order statistics and the least squares estimators of the parameters are discussed.

The present paper provides a new approach to study the problem of optimal control of a two-item inventory system with different types of deterioration. The total cost, which includes the sum of the holding costs of inventory levels, the holding costs of one item due to the presence of the other and the production costs, is minimized. The optimal solution is obtained based on Pontryagin's principle. The system is modeled by a system of non-linear differential equations and its solution is discussed numerically. It is also used for illustrating the system performance as function of the monetary and non-monetary input parameters.

In this note a moment inequality for the New is Better than Used in Laplace ordering (NBUL) class of lifetime distributions is derived. A simple test statistic for testing exponentiality against NBUL alternatives is constructed. The test statistic is proved to be asymptotically normal and consistent. Critical values obtained by a Monte Carlo simulation are tabulated for different sample sizes. The asymptotic relative efficiency of the test is also studied.