Applying the Mahalanobis-Taguchi strategy for software defect diagnosis

The Mahalanobis-Taguchi (MT) strategy combines mathematical and statistical concepts like Mahalanobis distance, Gram-Schmidt orthogonalization and experimental designs to support diagnosis and decision-making based on multivariate data. The primary purpose is to develop a scale to measure the degree of abnormality of cases, compared to “normal” or “healthy” cases, i.e. a continuous scale from a set of binary classified cases. An optimal subset of variables for measuring abnormality is then selected and rules for future diagnosis are defined based on them and the measurement scale. This maps well to problems in software defect prediction based on a multivariate set of software metrics and attributes. In this paper, the MT strategy combined with a cluster analysis technique for determining the most appropriate training set, is described and applied to well-known datasets in order to evaluate the fault-proneness of software modules. The measurement scale resulting from the MT strategy is evaluated using ROC curves and shows that it is a promising technique for software defect diagnosis. It compares favorably to previously evaluated methods on a number of publically available data sets. The special characteristic of the MT strategy that it quantifies the level of abnormality can also stimulate and inform discussions with engineers and managers in different defect prediction situations.     

CF-GGA: A grouping genetic algorithm for the cell formation problem

In manufacturing, the machine-part cell formation (MPCF) problem addresses the issues surrounding the formation of part families based on the processing requirements of the components, and the identification of machine groups based on their ability to process specific part families. Past research has shown that one key aspect of attaining efficient groupings of parts and machines is the block-diagonalization of the given machine-part (MP) incidence matrix. This paper presents and tests a grouping genetic algorithm (GGA) for solving the MPCF problem and gauges the quality of the GGA's solutions using the measurements of efficiency (Chandrasekharan and Rajagopalan 1986a) and efficacy (Kumar and Chandrasekharan 1990). The GGA in this study, CF-GGA, a grouping genetic algorithm for the cell formation problem, performs very well when applied to a variety of problems from the literature. With a minimal number of parameters and a straightforward encoding, CF-GGA is able to match solutions with several highly complex algorithms and heuristics that were previously employed to solve these problems.     

APPLICATIONS OF THE DRAZIN INVERSE TO THE HILL CRYPTOGRAPHIC SYSTEM. PART III.

In this part it is shown how the scalar unit coefficient a appearing in the W key formula (see Part I) can be replaced by an invertible matrix coefficient Γ. (A similar discussion with respect to the V key will appear In Part IV.) Various examples illustrate in detail the different procedures involved. Some examples in the encipherment and decipherment calculations are left as problems for the reader. The Appendix contains a proof of the main theorem.     

On Jonckheere's k-Sample Test Against Ordered Alternatives

In this paper a k-sample non-parametric test for trend is considered. Given a sample of size n_i , i = 1, …, k respectively from each of k populations, the test rejects the hypothesis that the k populations are identical if S = Σ ^k _i=2 S_i ≥ S_i . Here Si is the Mann-Whitney statistic computed when each observation in the i-th sample is compared with the combined observations from the first (i – 1) populations. A recurrence formula is derived for computing the exact distribution of S. Tables of exact probabilities and critical values are given for nominal values of α = 0.5, 0.2, 0.1, 0.05, 0.025, 0.01, and 0.005 for k = 3 and all possible sample sizes from 2 to 8, and for equal sample sizes for values of n = 2(1)6, k = 4(1)6.     

Material Transfer Inside Head Disk Interface for Heat Assisted Magnetic Recording

Heat assisted magnetic recording (HAMR) promises to deliver higher storage areal density than the current perpendicular magnetic recording products. Laser heating is implemented in HAMR to achieve magnetic writing of the very high coercivity media. However, the high temperature environment creates several reliability challenges for the head disk interface (HDI). In this paper, material transfer within the HDI under HAMR recording conditions is studied. The mechanisms of material transfer are explored via experiments and modeling. This study revealed that temperature difference and mechanical interaction between the head and media are the main mechanisms for material transfer inside the HDI. Possible methods to remove the material are also discussed in this paper.