Volume 20, Issue 1

Average run length is the most popular measure to assess the statistical performance of a control chart procedure. This paper discusses the limitations of the traditional average run length measure and introduces the concept of ‘unity’ average run length which is the ratio of the expected run length to the number of points plotted. The use of overall probability of acceptance for a set of plotted points is recommended as a supplementary performance measure. The background theory for using the overall probability acceptance is borrowed from the field of acceptance sampling. A discussion on how to improve the efficiency of the control chart signal rule is also made.

This paper discusses several designing procedures for chain sampling inspection plan (ChSP-1) for given values of AQL and LQL and with associated requirements with respect to the risks. Though, these procedures differ methodologically in arriving at solutions, their common primary aim refers to minimise the actual risks. This study reveals that too many procedures yield too many rather different solutions, thus confusing the user in choosing a plan. In this paper a procedure is developed to compare the seven different procedures in order to show the ambiguity of the procedures and their results. Moreover, some fundamental considerations concerning product control and process control lead to the conclusion that acceptance sampling and in particular chain sampling which was introduced more than 50 years ago might be out-of-time and should be replaced by efficient process control using the possibilities of modern IT technologies.

Reliable predictions by means of quantiles constitute one of the most important tasks not only in statistics but in entire science. Quantiles may be estimated by using Extreme- Value Theory (EVT). However, the properties of many estimators based on this theory depend heavily on the actual location. In this paper modified estimators for the quantiles are derived, the properties of which are less sensitive with respect to location. Moreover, these modified quantile estimators are also symmetric with regard to the mean for symmetric distributions, which is not the case for some of the estimators based on the EVT. The modified quantile estimators are a limiting result of an infinity shift of location of the estimators proposed by Dekkers et al. (The Annals of Statistics 17: 1833–1855, 1989). The results may be used in establishing control limits for Shewhart control charts.

Statistical tools are believed to be essential for competent quality judgements in the field of nuclear technology as well as in other branches of industry. In comprehensive quality management, these tools comprise not only well-known statistical procedures of quality control for fuel assembly production, but also methods for fuel rod design. Procedures which are set out in standards or directives are generally used in practice. This seems to be appropriate as in almost all statistical textbooks and publications the impression is given that in statistics some few standard methods are sufficient in practice just like cooking recipes in the kitchen. However, standard methods cannot take into due account the diversity and complexity of situations and, thus, lead almost inevitably to inappropriate results and false interpretations. It follows that in general statistical standard methods should not be part of a strategy of continuous quality improvement. This paper describes by means of several examples the problems which occur in the field of nuclear technology and illustrates the need that the different quality assurance measures must be organized so as to complement each other, thereby increasing the total efficiency.

A mine having five quarries needs at least 10 tippers out of 17 to be in running condition for a particular shift. However, with the poor availability of the tippers, the production was hampered. Substantial improvement of availability and utilisation of tippers under the existing infrastructure of the system was of primary concern to the plant management. Performance of all the tippers was evaluated through Mean Time-to-Failure (MTTF) and Mean Down Time (MDT) including the overall system performance. Based on Weibull( b, c ) and Exponential( λ ) distributions, the reliability of all the tippers (component reliability) along with the overall system reliability with respect to 10-out-of-17 structure was computed. Next, tippers were clustered, using k-means clustering algorithm, and the group reliabilities were obtained which led to different options for improving the overall system's reliability. The Pareto Principle was adopted to identify dominant failure modes. Using the matrix of interrelationship, five failure modes were found to be self-inducing in nature. The minimum number of repairmen required to keep the desired number of tippers running with a certain probability was determined, through simulation technique, using the classical repairmen model. The net effect of implementation of suitable preventive maintenance activities along with overhauling, training, ordering strategy of spare parts and maintenance crew restructuring was an increase in average utilisation of tippers from 66.8% to the level of 75%, whereas the system availability has improved to 85.75% from the earlier level of 78.34%.

The global competition requires and the improved possibilities of data collecting and data analysis enables implementation of so-called continuous improvement strategies . Such a strategy can be divided into two parts, one which identifies room for improvement and a second one which takes care of the improvement. Quantification is of utmost importance because it constitutes generally a necessary condition for improvement. In this paper two examples of quantification for subsequent improvement of two industrial processes are described. The first example deals with the manufacturing process of cast iron pipes and the problem of bending. After quantification an optimization problem is formulated and solved resulting in a considerable reduction of rework. In the second example an effectivity measure for training programs in the software industry is developed by means of which weaknesses in training courses can be identified in order to remove them. The scoring system provides a scale from 0 to 100 for rating a training programme. It turns out that the derived measure coincides with the well-known Mahalanobis distance.

Most of the commonly used control charts for variables have been developed under the assumption that the observations are coming from a normal population. One of them is ‘Group Runs’ GR control chart to detect shifts in the process mean proposed by Gadre and Rattihalli (Economic Quality Control 19: 29–43, 2004). In this article, we study the robustness of GR chart to violation of the assumption of normality. It is observed that, for moderate to large shifts in the process mean, GR chart is insensitive to the non-normality. It is also illustrated that, the GR chart performs better than the synthetic chart, when the process data are not coming from normal distribution.

In this paper recent results related to run and frequency quotas in time-homogeneous multi-state Markov chains are presented and their application in terms of the classical risk model is given.

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr( X <Y ). The algebraic form for R = Pr( X <Y ) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when ( X, Y ) follow a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate gamma. The calculations involve the use of special functions.

In [v. Collani, Theoretical Stochastics, Heldermann Verlag, 2004] the Bernoulli Space is introduced as fundamental model of uncertainty replacing Kolmogorov's probability space which though appropriate for defining a special branch of mathematics has hardly importance for describing real world. In [Stübner, Sans, Zhai, v. Collani, Economic Quality Control 19: 215-228, 2004] a general method for improving the variability function χ of a given Bernoulli Space is proposed. Subsequently this method has been applied to the case of uniform distributions in [Sans, Stübner, Sen, v. Collani, iapqr transactions 30: 2005]. In this paper the method is extended to cover the monotonic probability distributions.

In this paper, we propose a new bivariate Weibull regression model based on censored samples with common covariates. There are some interesting biometrical situations which motivate the study of a bivariate Weibull regression model of the proposed type. A procedure for obtaining the maximum likelihood estimators for the parameters in the model is derived and a test of significance for the regression parameters is sketched.