Volume 23, Issue 2

Stochastic measurement procedures have been proposed and developed in several articles published in EQC. In contrast to the traditional measurement procedures that use the obsolete error propagation formula for taking into account measurement uncertainty, stochastic measurement procedures include the entire uncertainty of the measurement process in a natural and rational way. In this paper the concept of stochastic measurement procedure is extended to the case that the measurement process is given by a stochastic process or more precisely said by a time series. This case appears often for economic phenomena. In this paper, only the feasibility of such measurement procedures shall be demonstrated and the considerations are therefore restricted to some simple and rather unrealistic examples. In a realistic case an appropriate stochastic model must be developed following the rules of stochastic modelling.

In the context of reliability the stress-strength model describes the life of a component which has a random strength X and is subject to a stress Y . The component fails at the instant the stress applied to it exceeds the strength and the component will work satisfactory in case of the event {( x , y ) | x > y }. Thus R = P X,Y ({( x , y ) | x > y }) is a measure of system reliability. In this paper, we obtain semi parametric estimators of the reliability under stress-strength model for the exponential distribution under complete and censored samples. We illustrate the performance of the estimators using a simulation study.

In this note we consider the performance of a new test of exponentiality against IFR alternatives. This test turns out to be an L -statistic. A table of critical values for some commonly used significance levels and different sample sizes is given. These critical values are based on the exact distribution of the test statistic for n ≤ 45 while for larger values of the sample size the critical values are based on simulation. The asymptotic relative efficiency of this new test is discussed. The test is applied to some real life data sets. A simulation experiment evaluates the empirical size and the empirical power against different alternatives. The proposed test competes favorably with other tests available in the literature.

Standard control charts are constructed under the assumption that the observations taken from the process of interest are independent over time; however, in practice the observations in many cases are actually correlated. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive model following a heavy tailed distribution. We propose a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case when the process quality characteristics follows a heavy tailed t -distribution. This chart has narrow control limits since the standard error of the least absolute deviation is smaller than that of the ordinary least square estimator in the case of heavy tailed distributions.

Many manufacturers produce and deliver large batches of small items. The delivery of an ordered number of pieces may be based on a manual count of the parts or by using scale counting. The pieces to be counted are weighted and the total weight (observed) is divided by an estimate of the average weight of the produced items. In this paper the design of the calibration step of a scale counting procedure is proposed for meeting a fixed precision requirement. Moreover, confidence intervals for the number of items to be counted are derived. Monte Carlo Simulation is run to evaluate the proposal.

This paper presents a continuous time Markov chain (CTMC) model to obtain closed form expressions of the mean time between system failures (MTBF) for K -out-of- N : G systems subject to M exponential failure modes and repairs. The results are obtained by using explicit matrix representations of the systems.

Control charts are used to identify the presence of an assignable cause of variation in the process. The non-parametric control chart is an emerging area of development in the theory of SPC. Its main advantage is that it does not require any knowledge about the underlying distribution of the variable. In this paper two non-parametric control charts for controlling variability are derived based on two non-parametric tests. Their in-control state performance is analyzed for different distributions by means of simulations. Furthermore, their efficiency in detecting shifts in the variability is evaluated.

The aim of this paper is to provide bounds for distorted risk measures when the joint distribution of the risk factors is unspecified but the marginal distributions are known. For convex distortion functions, a methodology to calculate the corresponding bounds is suggested and illustrated by several examples.

In this paper, we estimate the parameters using the EM algorithm of the bivariate exponential distribution of Marshall-Olkin when the samples are right censored. The advantage of using the EM algorithm is that the observed data vector is viewed as being incomplete but regarded as an observable function of complete data. Then the EM algorithm exploits the reduced complexity of maximum likelihood estimation for complete data. We also derive the standard deviations of the estimates for this bivariate exponential distribution. A simulation study is conducted to compare the estimated values with the true values. It turns out that the estimates based on EM algorithm are more better than estimates obtained without the EM algorithm.

The log normal distribution is as popular in engineering as the normal distribution is in statistics. However, there has been little work relating to order statistics from the log normal distribution. In this note, explicit expressions are derived for the moments of order statistics from the log normal distribution by using a formula due to Withers. The usefulness of the result is illustrated through two data sets.

This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some attribute. If the decision is made to accept complete absence, a probability statement may be required that the population is indeed free of the attribute. A partially specified prior is shown to be advantageous in making such statements realistic and useful.

In the last issue of EQC the “Guide to the Expression of Uncertainty in Measurement” (GUM) was critically discussed and it was shown that it is obsolete and should be replaced by a standard defining the rules for stochastic measurement procedures that in contrast to the GUM would express the inherent measurement uncertainty in an objective way, thus making reliable and accurate measurement procedures possible. Closely connected to stochastic measurement procedures are stochastic prediction procedures, as any measurement procedure is based on a corresponding prediction procedure. Furthermore, prediction procedures play a central role in any decision-making process. Prediction procedures are therefore the most important tool for human individuals as well as for the human community for solving problems and being able to survive. Having this in mind, mankind should be expected in its long history to have developed prediction procedures that, in an objective way, enable to look at the indeterminate future to prevent the occurrence of problems and to solve problems once they have occurred. Unfortunately, this is not the case. The technology of making predictions has not at all improved since the antiquity. In this paper, predictions procedures are dealt with, and the development of a prediction standard for the protection against misleading or even fraudulent prediction is proposed.