Volume 20, Issue 2

Without any particular notice of the worldwide scientific community, two anniversaries of one of the greatest - if not the greatest - heroes of humanity went by this year. 350 years ago the theologian, natural scientist and mathematician Jakob Bernoulli was born in Basel, and 300 years ago, Jakob passed away, again in his hometown. The 50 years of Jakob Bernoulli's life are full of outstanding achievements, which were crowned by the development of Stochastics . Unfortunately, his ideas were more than 300 years ahead of the rest of humanity and, therefore, could not be understood until our times. This contribution aims at honoring Jakob Bernoulli and amending the many misunderstandings and errors with respect to his life and work.

In the past years many companies in the US and Europe have embraced a quality management initiative based on the concept and metrics of “Six Sigma”. Developed as an internal company strategy at Motorola, it was put into action as a quality management program at General Electric and other big companies and nowadays Six Sigma is often being hailed as the new standard in quality for world class business. The creators of the approach call it “The Breakthrough Management Strategy Revolutionizing the World's Top Corporations.” However, a closer look at the rationale behind Six Sigma as presented in the original publications reveals that Six Sigma cannot keep its promise.

A procedure is derived for determining the values of the parameters of a multinomial distribution by means of the fiducial approach proposed by Fisher. By decomposing the involved probability (mass or density) functions, it is shown that the resulting fiducial distributions belong to the Dirichlet family.

In a production process, when quality of the product depends on more than one characteristic, ‘Multivariate Quality Control’ ( MQC ) techniques are used. Many MQC techniques have been developed to control multivariate variable processes, but not much work has been reported on multivariate attribute processes. In this article, we propose some group inspection based multi-attribute control charts to identify process deterioration. The charts proposed are the ‘Multi-Attribute np’ ( MA – np ) chart, the ‘Multi-Attribute Synthetic’ ( MA – Syn ) chart and the ‘Multi-Attribute Group Runs’ ( MA – GR ) chart. The charts are developed by using MP-test based on the exact distribution. It is numerically illustrated that, MA – GR chart performs better than the other two charts. Also in steady state MA – GR chart performs better than MA – np and MA – Syn control charts. A procedure of identifying the attributes causing signal is also proposed.

Control charts for high quality processes based on counting cumulative conforming items have attracted a lot of attention recently. However, such charting procedures usually apply when items are inspected one by one. There are situations that products are inspected sample by sample for practical or economic reasons. In such situations, the application of conventional cumulative conforming type of control charts based on the assumption of geometric or negative binomial distribution is challenged. To solve the related problem, in this paper we propose a new cumulative conforming type of control chart, called CCS (cumulative conforming samples) chart. The ANI (average number of items inspected) performance of CCS chart is examined. The advantage of CCS chart is discussed. Furthermore, the issue of correlation within samples is also addressed. The effect of correlation on the performance of CCS chart is investigated.

In this paper the use of Collani's statistic for monitoring simultaneously process mean and process variance is investigated by a comparison with the more popular chart and chart, respectively. The comparison is performed by means of an economic design of the charts assuming two different situations with respect to the occurrence of assignable cause. The criteria used for the comparison are the average total cost (ATC) and the average run lengths (ARLs), where the latter make sense only for equal sample sizes. Various cases with respect to the economic parameters and the distribution parameters are considered omitting the case of constant process variance, because in such a case a simple -chart is in any case superior. It turns out that a chart based on Collani's statistic is by far superior than the two popular charts. In order to have the superiority documented the numerical results are displayed in numerous tables.

The distribution of the ratio is derived when X and Y are logistic and Bessel function random variables distributed independently of each other. The distribution is of interest in econometrics, and ranking and selection problems.

In this paper, we propose a bivariate Weibull regression models for survival time derived from the bivariate exponential distribution of Freund [Freund, Journal of the Amer. Statist. Assoc. 56: 971-77, 1961]. There are some biometrical applications which motivated to study these particular models. We obtain estimators of regression parameters and develop a test procedure for testing the significance of regression parameters based on censored samples.

This article deals with estimation of the change-point in a sequence of independent random variables. It is based on a least squares process endowed with a weight function. For finite sample sizes we derive bounds of the error probability. They immediately yield rates of consistency which are known to be optimal. Our findings extend and sharpen earlier results of Antoch, Hušková and Veraverbeke (Journal of Nonparametric Statistics 5: 123-144, 1995).

Taguchi defined product quality in a universal way by adopting a quadratic quality loss function. In 1987, Kapur and Wang addressed the problem of setting economic specification limits for processes being not capable to meet given tolerances and, therefore, product quality has to be improved by inspection. Kapur and Wang selected for their investigations Taguchi's quadratic loss function. In this paper, we assume a asymmetrical linear quality loss function and show that the obtained optimal values differ greatly from those obtained by Kapur and Wang.

The well known inverse Rayleigh distribution is considered as a model for a life time random variable. The problem of acceptance sampling when the life test is truncated at a pre-assigned time is discussed. For various acceptance numbers, various confidence levels and various values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean life time is worked out. The operating characteristic functions of the sampling plans are obtained. Producer's risk is also discussed. A table for the ratio of the true mean life to a specified mean life that ensures acceptance with a pre-assigned probability is provided. The results are illustrated by an example.

In this paper, we present a simple proof of a result, which has useful applications in the context of shock models that are important in reliability theory. Though the result can be easily proved using properties of totally positive functions, we introduce a new idea which enables us to provide a proof that utilizes only elementary techniques of real variable calculus.

On 27 May 2005 the Draft International Standard ISO/DIS 2210: Milk and milk products - Sampling - Inspection by variables in the presence of measurement error was released. It is a so-called statistical standard aiming at deciding upon acceptance or rejection of incoming lots consisting of milk or milk products. In this paper we look critically at the draft standard and show that it does not meet any requirement, which should be demanded in order to have the standard achieve its purpose.