A critical look at some point process models for repairable systems

The use of a modeldriven approach to the analysis of repairable systems is considered and shown to be useful as a way of understanding the characteristics of such a system. However, considerable statistical problems arise from the use of a set of standard model-building elements. In particular, identification problems arise in many of the models. The argument is illustrated by examples from software reliability and mechanical reliability. The conclusion is that, in many cases, the exploratory data-analysis approach is as effective as the use of more sophisticated models

Methodology for Evaluating Reliability Growth Programs of Discrete Systems

The term Reliability Growth (RG) refers to the elimination of design weaknesses inherent to intermediate prototypes of complex systems via failure mode discovery, analysis, and effective correction. A wealth of models have been developed over the years to plan, track, and project reliability improvements of developmental items whose test durations are continuous, as well as discrete. This research reveals capability gaps, and contributes new methods to the area of discrete RG projection. The purpose of this area of research is to quantify the reliability that could be achieved if failure modes observed during testing are corrected via a specified level of fix effectiveness. Fix effectiveness factors reduce initial probabilities (or rates) of occurrence of individual failure modes by a fractional amount, thereby increasing system reliability. The contributions of this research are as follows. New RG management metrics are prescribed for one-shot systems under two corrective action strategies. The first is when corrective actions are delayed until the end of the current test phase. The second is when they are applied to prototypes after associated failure modes are first discovered. These management metrics estimate: initial system reliability, projected reliability (i.e., reliability after failure mode mitigation), RG potential, the expected number of failure modes observed during test, the probability of discovering new failure modes, and the portion of system unreliability associated with repeat failure modes. These management metrics give practitioners the means to address model goodness-of-fit concerns, quantify programmatic risk, assess reliability maturity, and estimate the initial, projected, and upper achievable reliability of discrete systems throughout their development programs. Statistical procedures (i.e., classical and Bayesian) for point-estimation, confidence interval construction, and model goodness-of-fit testing are also developed. In particular, a new likelihood function and maximum likelihood procedure are derived to estimate model parameters. Limiting approximations of these parameters, as well as the management metrics, are also derived. The features of these new methods are illustrated by simple numerical example. Monte Carlo simulation is utilized to characterize model accuracy. This research is useful to program managers and practitioners working to assess the RG program and development effort of discrete systems

Fault detection and correction modeling of software systems

Ph.DDOCTOR OF PHILOSOPH

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B