Volume 16, Issue 1

One widely used control chart, the -chart, is based on the assumption that means of samples drawn from the process are normally distributed. When the normality assumption is not valid, control chart users may choose from several different courses of action. These include using Box-Cox power transformations on the original data to yield an approximate normal distribution, increasing the size of the samples drawn from the process until the distribution of the sample means is considered normal, and modifying the -chart to employ asymmetric control limits instead of limits that are equidistant from the process target mean. Since none of the remedies for handling nonnormal processes is completely satisfactory, we build on previous neural network research by developing a neural network to control nonnormal processes. Comparison of the performance of our neural network model with that of traditional -control charts shows that the neural network model is superior to the traditional -control charts.

Consider a product with quality characteristic X . Assume that the product is composed of n parts each with quality characteristic X i , and and let X = X 1 + . . . + X n Assume that there is a lower specification L and an upper specification U for X . Then the problem arises how to select suitable specifications for the quality characteristics X i of the parts. If the type of distributions of the partial quality characteristics X i are known, then for solving the specification problem, the distribution of X = X 1 + . . . + X n is needed. In case of measurable quality features, usually the normal model is assumed for the X i and the problem of deriving the distribution of X is solved in the well-known way. However, generally the only feature of X i which is known with certainty is its bounded support, which follows from technical conditions. In such a case the normal approximation which is based on an unbounded support of each X i may lead to a distribution of X which does not reflect reality sufficiently well. In this paper, the uniform or a related distribution is assumed for the partial quality characteristics and an explicit expression for the distribution of the sum X is derived. The usefulness of the result is illustrated by an example taken from industrial practice.

In 1986 Taguchi presented the quadratic function for describing the loss of quality due to deviation from the production value. The objective then is to improve quality by minimizing the quadratic loss function which reflects the loss of both, the producer and the consumer. Subsequently, Kapur et al. (Wang, Economic design of specifications based on Taguchi's concept of quality loss function.: 23-36, 1987, Quality Engineering 1:63-77, 1988, Cho, Quality Engineering 6: 401-417, 1994) addressed the problem of deriving a loss function to be applied for determining the design of specification limits. This article further explores the problem of determining an integrated design of a Type I continuous sampling plan ( CSP -1) and the specification limits. By modifying Kapur and Wang's (Economic design of specifications based on Taguchi's concept of quality loss function.: 23-36, 1987) model, we not only obtain economic specification limits, but also obtaib an optimal CSP -1 plan for inspection.

Statistical process control is a major part of industrial statistics and consists not only of control charting, but also of capability analysis, of design of experiments and other statistical techniques. This paper reviews and comments some available techniques for the univariate as well as for the multivariate case from the viewpoint of industrial application.

A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment, when its long-run maintenance cost rate is minimal. The strict application of the economic lifetime does not take into account individual deviations of maintenance cost rates of single systems from the average cost development. To avoid this disadvantage, paper [Beichelt, Economic Quality Control 12: 173-181, 1997] proposes the total repair cost limit replacement policy: The system is replaced as soon as its total repair cost reaches or exceeds a given level. In that paper, the repair cost development is modeled by functions of the Wiener process. Here the same policy is considered assuming a repair cost process with nondecreasing samples paths and given one-dimensional probability distribution. Examples show that applying the total repair cost limit replacement policy instead of the economic lifetime may lead to cost savings between 4% and 30%. Finally, it is illustrated how to include the reliability aspect into the policy.

For deriving the steady state probabilities and the availability of K -out-of- N : G systems with constant failure rate and general repairs an imbedded Markov chain at repair completion epochs is used. The special cases of constant repair time, Coxian-2 and Erlang-2 repair time distributions are provided for illustrating the results.

This paper introduces a new designing methodology for Tightened Normal-Tightened ( TNT ) sampling schemes, indexed by an entry parameter called the crossover point ( COP ). The significance of the COP and the properties of the Operating Characteristic ( OC ) with respect to it are studied and the necessary tables constructed.

The average probability of acceptance ( APA ) is obtained for a single sampling plan assuming a Gamma prior distribution. Formula for inflection point and tangent at the inflection point are also derived. Tables are provided for selection of plan parameters.

Consider the following two situations which are characteristic for the application of statistical procedures. 1.) There is a deterministic variable of interest , whose actual value θ ∈ Θ is unknown. 2.) There is a random variable of interest with uncertain outcome . The aim in the first situation is to determine the unknown actual value θ of the quantity of interest . In the second situation the aim is to make a prediction about the uncertain outcome of the random variable of interest . Thus, measurement procedure and a prediction procedures are needed. In this paper it is shown that appropriately defined the two problems are equivalent in the sense that any solution of the one problem implies a solution of the second problem. Moreover, a quality indicator is derived reflecting the degree of “fitness for use” of a given procedure and enabling definition and determination of “optimal” statistical procedures. In agreement with general scientific practice, but in contrast to traditional statistics, the measurement and prediction procedures are developed for a suitably specified bounded range for the admissible values of the deterministic variable .

In this article, we survey the developments with respect to generalized models of repairable systems during the 1990s, particularly for the last five years. In this field, we notice the sharp fundamental problem that voluminous and complicated models are proposed without sufficient evidence (or data) for justifying a success in tackling real engineering problems. Instead of following the myth of using simple models to face complicated reality, and based on our own research experiences, we select and review some practical models, in the quickly growing areas: age models, condition monitoring models, and shock and wear models, including the delay-time models. Further, we also notice that there is an attempt to develop synthetical models from a different point of view. Therefore, we comment the relevant developments with strong emphasis on stochastic processes reflecting the intrinsic nature of the actual physical dynamics of those repairable system models.

A non-homogeneous Markov model is used to obtain closed form solutions of the state probabilities and the reliability of M modules in series where each module has N m components in parallel. The components have exponential time-varying failure rates which depend on the module. If the failure rates are independent of the modules the results are extended to a K -out-of- N : G system and series-parallel. Examples of assuming the Weibull distributions are presented to illustrate the results.