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Abstract. Industrial quality control is one of the most important activities in modern production systems. Each undetected quality flaw may have disastrous consequence not only for the functioning of products, but also from the view point of safety and financial losses. The methods used in quality control remained in principle the same for many decades and the question therefore arises, whether they are still appropriate. The applied methods in quality control are mainly taken from statistics and are hardly questioned by quality control specialists since there is often no deep understanding of aims and properties of the applied methods particularly if they are formulated as ISO standards. As a consequence the results obtained may be misunderstood leading to wrong decisions. The aim of this paper is therefore to introduce statistical methods by outlining their essential properties and weaknesses.

Abstract. The crossing point of two different distribution functions may be of interest for different reasons. The comparison of two different production processes with respect to failures may be one field of application, since the point of intersection of the corresponding distribution functions may be used for selecting the production process of superior quality. As a consequence, an estimator for the crossing point is needed. In this paper an estimator sequence is proposed by altering an approach that has been developed by Hawkins and Kochar in 1991. Using an approach suggested by Ferger in 2009, strong consistency and asymptotic normality of the proposed estimator sequence are derived by considering the argmax of a rescaled process which is selected as the scaled estimating error of the estimator sequence. Subsequently, weak convergence of this process to a limit process in the Skorokhod space is shown, where this limit argmax will turn out to satisfy a Gaussian distribution. A similar result has been obtained by Hawkins and Kochar in 1991, but by means of a different approach.

Abstract. The paper presents a model of multistage degraded system subject to L random failure modes and partial repairs. A transient analysis is performed and transient probabilities are calculated to find the availability, the mean of life times and of operational life times. Constant state dependent transition rates for the degradation process as well as for the failure process are considered. In contrast, the state dependent partial repair times follow distributions with the square of coefficient of variation greater than or equal to one. Moreover, the special case of Coxian-2 distributions for the partial repair times is investigated. A numerical example is provided to illustrate applicability of the expressions that are obtained throughout the paper.

Abstract. One-sided cumulative sum control charts are constructed for controlling the parameters of a random variable with doubly truncated binomial distribution. It is observed that the average run length (ARL) of the resulting control charts change considerably for a slight shift in the parameters of the distribution under study.

Abstract. This paper considers the problem of estimating the population mean of the study variable Y using systematic sampling in presence of an auxiliary variable X . A class of estimators is proposed and its properties are studied under large sample approximation. It is shown that the proposed class of estimators is more efficient under certain realistic conditions than the usual unbiased estimator, e.g., Swain's (1964) ratio estimator, Shukla's (1971) product estimator and modified estimators. The two phase sampling version of the suggested class of estimators in systematic sampling is introduced along with its properties. An empirical study is provided to illustrate the results of this paper.