Volume 24, Issue 2

Uncertainty about the future constitutes the most difficult, but also by far the most important issue mankind is facing. The current state, which is characterized by the global warming, finance crisis and terror illustrates the fact that during the last centuries the future physical and social consequences of decisions for the whole global system have never been checked. One reason is that uncertainty is neglected in science and as a consequence has never been included in a rational way in the decision making processes. Contrary, science teaches that to be “rational”, human beings have to behave like a “homo oeconomicus” who acts to obtain the highest possible well-being for himself. In other words, only the consequences on an individual basis are considered in a shortsighted basis. As a result of the “individual” strategies, all vital systems exhibit an ever increasing instability that endangers individuals, nations and in fact the entire mankind. Dealing and handling appropriately uncertainty is therefore of utmost importance. Unfortunately, contemporary science cannot cope with the complexity of uncertainty because the reduction of complexity by assuming cause-effect relations constitute its foundation. There is only one established, but minor branch of science that pretends to deal with uncertainty namely statistics. Statistics however is an extremely ambiguous branch of science which can be seen from the fact that the question “What is statistics?” has not been answered so far in a satisfactory way (see for instance [Brown, Kass, The American Statistician 63: 105-123, 2009]). During the last two decades a new approach to model, handle and analyze uncertainty has been developed. This approach has been named “Bernoulli Stochastics”, and it represents a well-defined alternative to both traditional sciences such as physics based on determinism and statistics based on a probabilistic approach. Besides the problem of an appropriate approach there is the equally important problem of teaching how to handle uncertainty which raises the question whether or not there are sufficiently qualified teachers available to establish a comprehensive teaching system in the field of uncertainty. As to the newly developed Bernoulli Stochastics the answer must be definitely “no”! However, also for statistics the answer is not at all “yes” as can be seen from the doubtful question posed in a recent article written by a prominent statistician [Meng, The American Statistician 63: 202-210, 2009]: “Do we, as a discipline, even have a clear consensus on what constitutes qualifications for being the first quantitative trainers of future generations of scientists, engineers, policy makers, etc.?”. Fortunately, the advances of modern information technology have diminished the problem of lack of qualified teachers by the possibility of web-based E-Learning programs that can be accessed worldwide. This paper is devoted to E-Learning programs in statistics and Bernoulli Stochastics. Firstly, statistics and Bernoulli Stochastics are briefly introduced and subsequently some relevant E-Learning programs are described and compared in order to facilitate the choice for those who are interested in handling, controlling and reducing uncertainty.

Acceptance sampling plans by attributes involving sampling from the binomial distribution and the process average fraction nonconforming following a beta distribution are termed as Polya sampling plans. An iterative procedure of finding the parameters of a single sampling plan by attributes under Polya distribution satisfying given conditions with respect to producer's and consumers's risks is presented and tables are constructed for selecting the sampling parameters. The performance/discriminating power of the Polya single sampling plans is also discussed by determining the operating characteristic curve.

In this work, we discuss the steps for establishing a relationship between two time series in an industrial set up. The reheat furnace is the heart of the hot strip mill in a steel plant. In the hot strip mill, steel slabs are heated at high temperature at the reheat furnace before rolling. Furnace temperature depends upon the gas flow rate to burners of the furnace. We make an attempt to establish a relationship between furnace temperature and gas flow rate for controlling energy utilization at the furnace. The data collected on temperature and gas flow rate are time series in nature. We first check whether the order of the two time series are same or not by the Augmented Dickey-Fuller (ADF) unit root test. In the event of same order of the series, we establish the relationship between furnace temperature and gas flow rate by an ordinary least squares (OLS) regression method. The relationship is quite satisfactory and can be used for prediction and controlling energy utilisation.

In this paper we consider a cold standby system of two components with a single repair facility. The lifetime of a component is not necessarily independent of the repair time of the other component because there will be some pressure or load on the repairman if the working unit fails while repairing the other unit in order to reduce the length of down time. The lifetimes and repair times do not depend on the number of times that they have been repaired. But the reward per unit time (from a working unit) and the repair cost per unit time depend on the number of times they have been repaired. Also it is assumed that some extra amount has to be paid during the down time. The replacement policy considered here is to replace the system (both the components) as soon as the down time during any repair exceeds a given duration say ‘d’. A general expression of the cost function is derived by assuming that the joint distribution of the lifetime of a component and the repair time of the other component has Freund bivariate exponential distribution.

The theory of change point analysis finds applications in diverse fields such as stock market analysis, industrial quality control and reliability studies. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this expository paper we consider hazard models with a single jump in the hazard rate. We focus on inference problems concerning the change points. The approaches used by the different authors are critically examined. The models under parametric and non-parametric set ups are reviewed. Methods to handle censored data are also discussed. The use of different statistical techniques such as Weak Convergence Theory, TTT transform methods, Bayesian methods etc. are highlighted. Two examples using real life data sets illustrate the concepts.

The standard multivariate control chart usually employs fixed sample size at fixed sampling interval (FSI) to monitor a process. In this study, a multivariate exponentially weighted moving average (MEWMA) chart with variable sampling intervals (VSI) is investigated. The MEWMA chart with VSI varies the sampling interval from the process as a function of the data from the process. The performance measure of the VSI MEWMA chart is obtained through a Markov chain approach and it is compared with the corresponding standard FSI MEWMA chart in terms of average time to signal for different magnitude of shifts in the process mean. It is shown that the VSI MEWMA chart is more efficient than the corresponding standard FSI MEWMA chart in detecting shifts in the process mean.

Quartile Double Ranked Set Sampling (QDRSS) is investigated for estimating the population mean. The QDRSS estimators are compared to the simple random sampling (SRS), ranked set sampling (RSS) and quartile ranked set sampling (QRSS) estimators. It is shown that, the QDRSS estimators are unbiased for the population mean when the underlying distribution is symmetric, and have small biases when the underlying distribution is asymmetric. It turns out that the QDRSS is superior to the SRS, RSS and QRSS based on the same number of measured units. A real data set of “trees' olive yields” is used to illustrate the method.

In this paper an attempt is made to study control charts for the mean using the shrinkage technique. The operating characteristic (OC) function and probability of the error of first kind of the control chart with symmetrical limits are calculated. The OC curves for the shrinkage technique are also studied in the case of known value σ for the mean.

The main tool of information theory is the Shannon entropy introduced by C.E. Shannon in 1948. This paper, concentrates on obtaining probabilistic models for a queueing system using the principle of maximum entropy subject to certain constraints. Some properties of queueing systems following the maximum entropy approach are stated.

The concept of time-varying control limits with reference to EWMA charts is briefly introduced and for the asymptotic control charts proposed by Riaz and Abbasi [Interstat : 3, 2007], a proposal of time-varying control limits is made. The proposed limits are subsequently compared with those of Riaz and Abbasi [Interstat : 3, 2007] asymptotic charts and different time-varying EWMA control structures based on the sample range R , the sample standard deviation S and Downton's estimator σ*. The probability of detection of outliers is used as comparison criterion.

This paper is a continuation of the article “A Critical Note on the Guide to the Expression of Uncertainty in Measurement (GUM)” published in Economic Quality Control 23. Unfortunately, the critique expressed on the GUM in that paper has so far been ignored by the metrology community. This paper shall illustrate and discuss the flawed use of statistical terms and methods in metrology. The GUM was published more than a decade ago, and undergoes presently a revision. Therefore, it is to be hoped that the here discussed weak points might be avoided in a new version of the GUM. The IMEKO is a very important organization. On the IMEKO homepage one can read the following words: International Measurement confederation, IMEKO is a non-governmental federation of 39 Member Organizations individually concerned with the advancement of measurement technology. Its fundamental objectives are the promotion of international interchange of scientific and technical information in the field of measurement and instrumentation and the enhancement of international co-operation among scientists and engineers from research and industry. Founded in 1958, the Confederation has consultative status with UNESCO and UNIDO and is one of the five Sister Federations within FIACC: Five International Associations Co-ordinating Committee, further consisting of IFAC- International Federation of Automatic Control, IFIP - International Federation for Information Processing, IFORS - International Federation of Operational Research Societies and IMACS - International Association for Mathematics and Computers in Simulation. In September 2009, the IMEKO World Congress was organized in Lisbon, and the latest “scientific results” were exchanged by the leading metrologists. In this paper some of these results shall be examined and evaluated.