Ronald C. Suich

Simultaneous Optimization of Several Response Variables

A problem facing the product development community is the selection of a set of conditions which will result in a product with a desirable combination of properties. This essentially is a problem i...

k-out-of-n:G systems: some cost considerations

The authors provide a tool that an engineer designing a subsystem can use to decide between one subsystem and a more reliable but more costly one. The authors provide methods for selecting redundancy levels in k-out-of-n:G systems in order to minimize particular cost considerations where the k-out-of-n:G system is a subsystem of a major system. The n and k are chosen to minimize the total cost of the subsystem plus the average loss due to subsystem failure. A BASIC program is available to determine the n and k which find this minimum. Five loss functions are considered, and illustrations are given. >

Minimize system cost by choosing optimal subsystem reliability & redundancy

Both reliabilities and costs are used to find the subsystems with the lowest overall expected cost. The authors begin by reviewing some of the concepts of expected value. They then address the problem of choosing among several competing subsystems. These concepts are then applied to k-out-of-n: G subsystems. A basic program (CARRAC) enables the engineer to explore and graph various options. The use of this program is illustrated with several different cost models.<<ETX>>

Reliability and cost: Questions for the engineer

In designing a subsystem for a major system, a design engineer is often faced with a number of options, ranging from an inexpensive subsystem with low reliability to a highly reliable subsystem, usually costing considerably more. The basic question which we address in this paper is how to choose among these competing subsystems. This paper utilizes both reliabilities and costs to find the subsystems with the lowest overall expected cost. These concepts are then applied to k-out-of-n: G subsystems. A computer program has been developed to assist the design engineer in exploring and graphing the relative expected costs of competing subsystems over a range of values.

An exact test on the Goodman-Kruskal l for prediction on a dichotomy: power considerations

Turek and Suich (1983), through a reparametrization scheme, developed a test of H0:λ = 0 vs. H1:λ > 0 where λ is the Goodman-Kruskal λ for the case when the predicted variable is dichotomous, and sketched the method for the calculation of the power of the test. This paper presents the details of the algorithm for the computation of power and uses it to extensively investigate the power properties of the test. Examples are presented which demonstrate that the test has good power characteristics and that it has considerable power in detecting a non-zero λ.

An asymptotic partial correlation test for the Goodman-Kruskal λ

Goodman and Kruskal introduced a measure of predictive association when predicting the category of a variable A from a category of a variable B. This measure, denoted lambda, is the asymmetric proportional reduction in error measure in predicting an individuals A category that can be eliminated by using knowledge of the B classification. It takes values on the unit interval, with a zero value meaning no predictive gain, while a value of unity indicates a perfect predictive association between A and B. A test of H(0): lambda = 0 versus H(1): lambda > 0 is analogous to a test for the significance of the correlation coefficient. A test of the partial lambda coefficient, which is analogous to a test of the partial correlation coefficient, answers the question of whether knowledge of an additional third (or higher) classification or categorical variable results in a significant increase in predicting the variable A. Suich and Turek developed an exact test for the partial lambda coefficient, but only for the situation where the predicted categorical variable A is dichotomous. The present paper completes the previous work by developing an asymptotic test where the predicted category A is any polytomous variable.

Comment on: Determining Sample Size When Searching for Rare Items

Reliability and safety engineers must frequently search for rare items, often as part of a compliance sampling program intended to assure a good population of items. In this setting, Madsen & Holstein have provided a formula for approximating the minimum sample size to find at least one nonconforming item. They also indicate that the approximation is conservative in the sense that it may provide slightly larger sample sizes than actually required. This may lead the engineer, especially in situations where sampling costs are high, to wonder by how much the approximation errs on the conservative side. This note presents bounds on the minimum required sample size and shows that, when the number of nonconforming items in a population is small,the Madsen & Holstein approximation is very close.