Volume 19, Issue 2

This article gives a survey on some important maintenance policies involving minimal repairs and replacements of technical systems. The main focus is on policies, which have been published after 1990. Based on a thinned nonhomogeneous Poisson process, repair cost limit policies with minimal repair are discussed in more detail. New results regarding the optimality of time dependent repair cost limits are presented.

Systems deteriorate over time and hence require maintenance. This paper discusses the operational performance of a repairable system subjected to several modes of failure. Unlike many models in the literature, where after each failure the system is perfectly repaired (replaced), it is assumed here that the system performance is declined after each failure, i.e., the performed repairs are imperfect. The paper presents a closed form expression for the long term probability that the system operates in the operational state.

This article provides an argument against the use of three sigma limits for control charts. An alternative proposal to use control limits narrower than three sigma control limits is made. The main reason for narrowing the control limits is to achieve a smaller variability in the frequency of process resetting as well as false alarms. An example is given illustrating why a good statistical design of control charts needs to avoid the use of three sigma control limits.

In a strength-stress interference model, we are interested in estimating the structural reliability of a system. Here we present Bayesian procedures to estimate the structural reliability and other relevant parameters when covariates are incorporated in the model. Numerical examples illustrate the proposed procedure.

Point estimation constitutes the heart of statistics. In this paper the corresponding methods are looked at from the viewpoint of a user and it is shown that point estimation procedures not only have major conceptual deficiencies, but that the corresponding methods offered and recommended in textbooks and journal articles are often confusing and misleading. To exemplify these claims reliability estimation assuming the log-logistic distribution is used. The reliability function is viewed as a parametric function. For certain values of the shape parameter, the scale parameter is estimated and used to obtain reliability estimates.

In this paper the problem is investigated how to prove that after a specified time t 0 of operation the conditional survival probability of an item is less than the corresponding survival probability of a new item. This problem occurs in various areas like for instance in industry, when designing a maintenance policy. For a randomly censored sample, test statistics are derived for testing the null hypothesis that a new item has stochastically the same residual life length as does a used item of specified age t 0 versus the alternative hypothesis that a new item has stochastically a longer residual life length as does a used item of specified age t 0 . The tests are based on the asymptotic distribution of the test statistics and selected using the Pitman asymptotic relative efficacy. Since small samples are prevailing in reliability testing, further research is needed, which omits the asymptotic derivation.

Stochastics investigates the relations between the determinate past and the indeterminate future, quantifies the structured connectivity of past and future and, thus, can be looked upon as a Science of Change . This reminds of the Book of Change , the ancient Chinese classics I Ging , which is considered as the oldest book of mankind. In the introduction of the 21st edition of Wilhelm Richard's famous translation [Ging, Text und Materialien, Eugen Diederichs Verlag, 1996], the late German sinologist Wolfgang Bauer writes: “The primary meaning of the word “I” is “exchange”, “change”, which corresponds to the basic character of the book. The non-static character constitutes its originality. Although a book of oracles it does not at all claim to predict the future as definite fate, but discloses the present situation, which, however, includes a “disposition” for the future development. And exactly this disposition is open to human actions by means of the permanently given advices. Not a single situation, but the tension between two situations is the topic of the I Ging , where the second emerges from the first.” In the view of Wolfgang Bauer's words the science of stochastics appears to be a modern quantitative fulfilment of ancient ideas of an acausal but structured stream of changes. In this paper one important aspect of the “disposition for the future development” is investigated namely the question which future developments are actually possible in a given situation. The proposed methods may be applied in so-called “zero-defects” situations arising in modern production environments, in cases where safety issues are of importance and in metrology.

The Least Cost Testing Sequence (LCTS) problem is a special case of the Weighted Shortest Processing Time (SPT) sequencing problem. A manufactured item has to pass each of n -tests at the final inspection, where the i th test has an associated cost C i of inspection and the item has a non zero probability p i of passing that test. The testing will be terminated if the item fails on any one test. When there is no constraint on the technical ordering of conducting the tests, it has been established that the optimal sequence that minimizes the expected inspection cost is obtained by sequencing the tests such that holds. The new aspect studied in this paper is the provision for rework. We admit a non-zero probability r i of rework for the i th test and a maximum of m − 1-reworks allowed for the item. The probability of termination of the testing process at the end of the i th test is the sum of probabilities of normal fail, fail after rework and that of reaching the m th rework. This probability will become the weight W i to be given for the i th test. An interesting probability structure is identified to derive W i under the condition that the probabilities are non identical. An array called Probability Position Matrix (PPM) is developed and a spreadsheet is designed to work out the W i and the sequence. This model may be applied to project evaluation studies, final testing in satellite launching cases etc.

In this paper a production process with a uni-variate quality characteristic is considered where the output is classified in three quality classes: good, marginal and bad. The process is subject to quality deterioration and, therefore, it is periodically monitored and according to the observed result a decision for one of four courses of action is made. The control procedure is represented by means of a GERT network and subsequently analysed using the so-called W -functions. Finally, the behaviour of the control scheme is investigated by some numerical examples.

Flour is the major ingredient for biscuit manufacturing. The selection of flour for a particular variety of biscuits is based on the performance of the Extensibility(E) and Resistance (R) properties, in general. However, the testing times of “E” and “R” led to an issue of 67% untested consignments of flour. In order to overcome these shortcomings, a new instrument, called Alveograph NG, was installed which can estimate Tenacity(P) and Extensibility(L) properties quickly and based on these values different types of flour should be discriminated. This study was undertaken to standardise the working norms of “P” and “L” properties of flour measured in the new instrument. Data collected on two types of flour showed that the tenacity(P) is the only significant discriminatory property of flour. In the event of this significant difference, the same data were subjected to ANOVA, using a two-way random effect model, which, however, yielded no useful result. Based on tenacity(P), operating rules for segregation of flour were developed allowing in a majority of cases a classification. Considering additionally Dry Gluten% as a further discriminating factor, the probability of successful classifications could be increased. There would be a significant improvement in cost with respect to enormous time saving for flour testing as well as selection of flour with high precision and accuracy. The entire methods of sampling, testing and decision making through Alveograph NG has become a routine practice in the organization.

Controlling uncertainty has an ever-increasing importance in all areas of industry. To meet the demand, the International Organisation of Standardization (ISO) developed and develops “statistical” standards. However, while success and failure of technical standards can be assessed rather easily, this is different with statistical methods because of randomness. Moreover, rationale and purpose of statistical methods are often vague. This paper analyzes one of the most frequently applied statistical standards namely ISO 2859-1 (1999). The aim of this investigation is to compare the purpose of ISO 2859-1 with industrial needs, to evaluate clearness and comprehensibility of its presentation, to check whether it represents the state of the art and a framework for future technological development. It turns out that the purpose of ISO 2859-1 is obsolete, that the formulation is ambiguous, that it does not represent the state of the art and finally that it hinders necessary future technological development in the field.