L. Sandamali Dharmasena

Resilience describes the capacity of systems to react to, withstand, adjust to, and recover from disruptive events. Despite numerous metrics proposed to quantify resilience, few studies predict these metrics or the restoration time to nominal performance levels, and these studies often focus on a single domain. This paper introduces three methods to model system performance and resilience metrics, which are applicable to various engineering and social science domains. These models utilize reliability engineering techniques, including bathtub-shaped functions, mixture distributions, and regression analysis incorporating event intensity covariates. Historical U.S. job loss data during recessions are used to evaluate these approaches’ predictive accuracy. This study computes goodness-of-fit measures, confidence intervals, and resilience metrics. The results show that bathtub-shaped functions and mixture distributions accurately predict curves possessing V, U, L, and J shapes but struggle with W and K shapes involving multiple disruptions or sudden performance drops. In contrast, covariate-based models effectively track all curve types, including complex W and K shapes, like the successive shocks in the 1980 U.S. recession and the sharp decline in the 2020 U.S. recession. These models achieve a high predictive accuracy for future performance and resilience metrics, evidenced by the low sum of square errors and high adjusted coefficients of determination.

This paper reports on the Failure To Attend (FTA) rate of appointments as well as patients following the implementation of SMS reminders in a public dental outpatient service. Given the ineffectiveness of the intervention and a highly representative patient’s profile, this paper identifies the demographic characteristics of patients who miss all of their appointments. Data on appointment attendance, patient demographics and dental service type was collected over a time period of 46 consecutive months. Using descriptive and inferential statistics (chi-square, two sample tests and Marascuilo procedure) we found the SMS intervention was ineffective in reducing the FTA rates. Further, patients associated with high rates of non-attendance exhibited one or more of the following characteristics: male; age 26 – 44; non-concession card holders; a person of Indigenous, local, Asian or African descent, and of refugee status, persons living in low socio-economic areas; and appointments in General Care and Student Clinics. Whilst the literature overwhelmingly attributes SMS reminders to improving the attendance rate of patients in outpatient clinics, our contradictory findings suggest a more targeted approach in settings whose patients exhibit strong characteristics associated with non-attendance.

This paper presents a new multivariate process capability index (MPCI) which is based on the principal component analysis (PCA) and is dependent on a parameter which can take on any real number. This MPCI generalises some existing multivariate indices based on PCA proposed by several authors when or . One of the key contributions of this paper is to show that there is a direct correspondence between this MPCI and process yield for a unique value of . This result is used to establish a relationship between the capability status of the process and to show that under some mild conditions, the estimators of this MPCI is consistent and converge to a normal distribution. This is then applied to perform tests of statistical hypotheses and in determining sample sizes. Several numerical examples are presented with the objective of illustrating the procedures and demonstrating how they can be applied to determine the viability and capacity of different manufacturing processes.

The use of sampling, randomized algorithms, or training based on the unpredictable inputs of users in Information Retrieval often leads to non-deterministic outputs. Evaluating the effectiveness of systems incorporating these methods can be challenging since each run may produce different effectiveness scores. Current IR evaluation techniques do not address this problem. Using the context of distributed information retrieval as a case study for our investigation, we propose a solution based on multivariate linear modeling. We show that the approach provides a consistent and reliable method to compare the effectiveness of non-deterministic IR algorithms, and explain how statistics can safely be used to show that two IR algorithms have equivalent effectiveness.

Several measures of process yield, defined on univariate and multivariate normal process characteristics, have been introduced and studied by several authors. These measures supplement several well-known Process Capacity Indices (PCI) used widely in assessing the quality of products before being released into the marketplace. In this paper, we generalise these yield indices to the location-scale family of distributions which includes the normal distribution as one of its member. One of the key contributions of this paper is to demonstrate that under appropriate conditions, these indices converge in distribution to a normal distribution. Several numerical examples will be used to illustrate our procedures and show how they can be applied to perform statistical inferences on process capability.

Software reliability growth models (SRGMs) are extensively employed in software engineering to assess the reliability of software before their release for operational use. These models are usually parametric functions obtained by statistically fitting parametric curves, using Maximum Likelihood estimation or Least -- squared method, to the plots of the cumulative number of failures observed N(t) against a period of systematic testing time t. Since the 1970s, a very large number of SRGMs have been proposed in the reliability and software engineering literature and these are often very complex, reflecting the involved testing regime that often took place during the software development process. In this paper we extend some of our previous work by adopting a nonparametric approach to SRGM modeling based on local polynomial modeling with kernel smoothing. These models require very few assumptions, thereby facilitating the estimation process and also rendering them more relevant under a wide variety of situations. Finally, we provide numerical examples where these models will be evaluated and compared.

Construction of a confidence interval for process capability index CPM is often based on a normal approximation with fixed sample size. In this article, we describe a different approach in constructing a fixed-width confidence interval for process capability index CPM with a preassigned accuracy by using a combination of bootstrap and sequential sampling schemes. The optimal sample size required to achieve a preassigned confidence level is obtained using both two-stage and modified two-stage sequential procedures. The procedure developed is also validated using an extensive simulation study.<br /

In nonparametric statistics the functional form of the relationship between the response variable and its associated predictor variables is unspecified but it is assumed to be a smooth function. We develop a procedure for constructing a fixed width confidence interval for the predicted value at a specified point of the independent variable. The optimal sample size for constructing this interval is obtained using a two stage sequential procedure which relies on some asymptotic properties of the Nadaraya--Watson and local linear estimators. Finally, a large scale simulation study demonstrates the applicability of the developed procedure for small and moderate sample sizes. The procedure developed here should find wide applicability since many practical problems which arise in industry involve estimating an unknown function. References E. F. Schuster. Joint asymptotic distribution of the estimated regression function at a finite number of distinct points. Ann. Math. Statist., 43, 1972, 84--88. http://www.jstor.org/stable/2239900 E. Isogai. The convergence rate of fixed-width sequential confidence intervals for a probability density function. Seq. Anal., 6, 1987, 55--69. doi:10.1081/SQA-100102647 E. A. Nadaraya. On estimating regression. Theory of Probab. Appl., 9, 1964, 141--142. doi:10.1137/1109020 M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995. G. S. Watson. Smooth regression analysis. Sankhya Series A, 26, 1964, 359--372. W. S. Cleveland. Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc., 74, 1979, 829--836. http://www.jstor.org/stable/2286407 J. Fan and I. Gijbels. Local Polynomial Modelling and its Applications. Chapman and Hall, London, 1996. T. Gasser, L. Sroka and C. Jennen-Steinmetz. Residual variance and residual pattern in nonlinear regression. Biometrika, 73, 1986, 625--633. http://www.jstor.org/stable/2336527 M. Ghosh, N. Mukhopadhyay and P. K. Sen. Sequential Estimation. Wiley, New York, 1997.