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The simultaneous testing of the two systems, both with an exponential distribution describing the times between failures, is presented. The effect of truncation of Wald's Sequential Probability Ratio Test (SPRT) on its characteristics is examined and the relationships are derived for calculating the coordinates of truncation apex (TA).

Confidence intervals are constructed for a cumulative distribution function and its inverse quantile function in order to study the reliability of parts and systems of space vehicles. The confidence intervals constructed on the basis of Jeffreys noninformative prior are found to be robust, with those based on a generalized gamma distribution outperforming nonparametric confidence intervals, and the approach is applied to evaluate the reliability of data from the Pad Hypergol Servicing System of NASA's Shuttle Orbiter.

Effects of parameter estimation are examined for the p-chart for fraction nonconforming based on attributes data. The results suggest that the performance of the p-chart could be highly degraded, particularly when p is estimated, unless the number of references observations is substantially large, much larger than what might be commonly used in practice.

A new approach for transforming a system's Availability expression to the corresponding Failure Frequency expression is presented. It showed that the computation problems for availability and failure frequency are reduced to only the problem for Availability when the system is s-coherent, and all component failures are s-independent.

The problem of determining optimal burn-in time is considered under the general failure model of two types namely Type I (minor failure) and Type II (catastrophic failure). In the ordinary burn-in models where systems have only catastrophic failures, the study of the shape of the failure rate (FR) is important for obtaining upper bounds for optimal burn-in time, while for the general failure model, the shape of FR and the Type II failure probability function are of significant importance.

An industrial scenario problem involving the potential failure of an element of building structure is discussed which had a warranty of several years. The idea of using hierarchical model to describe the degradation of strength with stress may have ramification beyond the physical science that have motivated it.

An analytical approach for the performance of fault tree analysis (FTA) with stochastic self-loop events is examined. It is possible to reduce the multiple self-loop basic events to the single-basic event by stepwise reduction of the FTA flow-graph and by usage of moment generating features (MGF).

In an effort to prioritize the repair, rehabilitation, and replacement of existing bridges, bridge management programs have been developed. In recent years, reliability-based optimum-maintenance planning strategies applicable to bridges have been proposed. Optimum inspection and repair times can be identified using these strategies. In this study, the effect of repair on time-variant failure probability is illustrated for several repair/replacement strategies. Time-variant reliability computations are performed using a combined technique of adaptive importance sampling and numerical integration. Several repair strategies are investigated for a typical bridge in Colorado. For this bridge, it is shown that for a single repair performed about halfway through the design life, the postrepair strength must be at least 80% of the original strength for the repair to have a significant influence on the system failure proability of the bridge during its remaining service life. Also, for maintenance using shotcrete, multiple repairs appear to have little influence on the lifetime system failure probability. Also presented are optimal maintenance strategies in which optimal inspection/repair times are identified based on minimum expected cost within prescribed reliability constraints. It is shown that the optimum repair time is dependent on the failure cost of the bridge and that the discount rate influences the optimum repair time and life-cycle cost. As the discount rate increases, the optimum repair time increases until it reaches an upper bound that is dependent on the system failure probability constraint. The results can be applied to the prediction of optimal lifetime maintenance planning strategies for concrete bridges under corrosion.

Proof for an additional T2 failure time dependence of the activation energy measured using Black's equation is provided. The investigation was conducted under the condition that the activation energy should be equal to the energy barrier needed for atomic hopping. Microscopic modeling , which offers an explicit connection between the microscopic parameters and macroscopic behavior of the model, is capable of providing a reliable technique of monitoring self-diffusion activation energies in pure metals.

Background. The standard approach for survival analysis of the elderly population is to define the survival time as the elapsed time from entry into the study until death, and to adjust by age using stratification and regression procedures. However, the interest is in the study of the aging process and the risk factors related to it, not in the use of time-on-study as the time scale. Here, we present methods to use age as the time scale and compare inferences and interpretations with those obtained using the standard approach. Methods. A total of 1,315 individuals aged 65 years or older from the city of Barcelona, Spain, were interviewed in 1986 (baseline). The vital status of the cohort was assessed in October 1994. To illustrate the usefulness of age as time scale (alternative approach) instead of time-on-study in the survival analysis of the elderly population, both methods were used to assess the relationship between baseline functional capacity and mortality. Results. Using the alternative approach, we observed that 50% of the sample died at age 80.6 years; this information could not be estimated with the standard approach. Using age as a covariate in the standard analysis with time-on-study as the time scale and using age as the time scale in the alternative analysis, the association of functional capacity at baseline and mortality was of similar magnitude under both analyses. Nevertheless, using the alternative approach, relative risks were slightly lower, and the adjustment by age was tight and was not subject to the inherent assumptions in regression models of the functional relationship of independent variables with outcome. We illustrated the methods with fixed covariates (i.e., gender) and baseline values of time-dependent covariates (i.e., functional capacity), but we discussed the extension of our methods for the analysis of time-dependent covariates measured at several visits in a cohort study. Methods proposed here are easily implemented with widely available statistical software packages. Conclusions. Although the use of standard survival analysis generally produces correct estimates, the use of age as time scale is deemed more appropriate for survival analysis of the elderly: Inferences are easier to interpret and final models are simpler. We therefore recommend the use of age as time scale for survival analysis of the elderly population.

The Weibull distribution, which is usually applied in modeling survival data, is embedded in a bigger family derived by adding another shape parameter. This generalized family not only has distributions with unimodal and bathtub hazard shapes, but also allows for a wider range of monotone hazard rates. Moreover, the distributions in this family are analytically tractable and easy to calculate. The modeling and analysis of survival data utilizing this family are presented and demonstrated in terms of a lifetime dataset and the results of a two-arm clinical trial., 1. INTRODUCTION The Weibull family is commonly used in statistical analysis of lifetime or response time data from reliability experiments and survival studies. It is generally adequate for modeling monotone [...]

A kernel estimate of the probability density function from bivariate data that have been randomly censored is derived. The large-sample characteristics of the proposed estimator are investigated by a strong approximation result. Consistency and asymptotic normality are established and a convenient representation of the kernel density estimator is provided. Simulations indicate that the suggested methodology provides a good estimate of the true density function even when the sample size is moderate., 1. INTRODUCTION Survival analysis studies often involve bivariate data subject to censoring. In the case of bivariate data, two dependent failure times of an experimental unit are of interest. This [...]

S is uniformly stochastically smaller than T if S and T are survival functions for two life distributions and theta(x) = S(x)/T(x) is nonincreasing in x on (x:T(x) > 0). Dysktra, Kochar and Robertson derived the restricted nonparametric maximum likelihood estimators (NPMLEs) of various unknown survival functions linearly ordered by uniform stochastic ordering. It is proven that these are inconsistent in general. Rojo and Samaniego provided excellent ad hoc estimators of S and T when the other is known. These are consistent, but lack some desirable qualities. A one-parameter family of estimators that have both of these estimators as extreme members is presented., 1. INTRODUCTION Nonparametric methods are finding increasing usage in reliability; see, for example, the survey article by Hollander and Proschan (1983). In accelerated life testing, if T is the survival [...]

State-space or dynamic models are suggested as a flexible method that allows simultaneous modeling and smooth estimation of hazard functions. The technique is based on a dynamic version of the piecewise exponential model and extensions to point processes investigated by Gamerman, and dynamic grouped survival models with only one terminating event where a generalized Kalman filter and smoother is suggested for estimating hazard functions and time-varying effects., 1. INTRODUCTION In many applications, duration or survival times are not observed continuously but are known to lie only between a pair of consecutive follow-ups. A typical example are data [...]

Transmission towers for major lines constitute a critical component because it is undesirable to lose any major transmission lines for longer than a few weeks. Since tower fabrication cannot be accomplished quickly on-demand, it is important to hold an adequate inventory of transmission towers. This paper discusses a statistical procedure to analyze failure data and estimate inventory requirements for transmission towers, using a Homogeneous Poisson Process model. Key Words: Transmission towers, inventory requirements, failure data, Homogeneous Poisson Process

A new method for analyzing the stochastic failure rates is introduced. The approach, which applies to series or parallel and series-parallel systems, characterizes the time-to-failure as an aggregate and/or product of several time series. This involves the use of recently-developed time-series techniques for estimating reliability decay, actual failure times, times-between-failures as well as the relationship between failure times and maintenance times.

The quality of life of patients is an important component of evaluation of therapies. We present an overview of a statistical method called Q-TWiST (Quality-Adjusted Time Without Symptoms and Toxicity) which incorporates quality-of-life considerations into treatment comparisons. Multivariate censored survival data are used to partition the overall survival time into periods of time spent in a set of progressive clinical health states which may differ in quality of life. Mean health state durations, restricted to the follow-up limits of the clinical trial, are derived from the data and combined with value weights to estimate quality-adjusted survival. The methodology emphasizes treatment comparisons based on threshold utility analyses that highlight trade-offs between different health state durations; it is not intended to provide a unique result combining quality and quantity of life. We also describe three recent extensions of the methodology: covariates can be included using proportional hazards and accelerated failure time regression models, restricted estimates can be projected beyond follow-up limits using parametric models, and meta-analyses can be performed incorporating quality-of-life dimensions. The basic methods are demonstrated in an analysis of data from a clinical trial comparing long versus short duration adjuvant chemotherapy regimens for the treatment of breast cancer. The clinical health states are defined by the following three outcomes: (1) end of treatment toxicity, (2) disease recurrence, and (3) death. The results allow one to evaluate the trade-off between the increased toxic effects and the increased recurrence-free interval associated with the long duration treatment. KEY WORDS: Clinical trials, Quality of life; Restricted means; Survival analysis; Utility., 1. INTRODUCTION The evaluation of treatments in terms of quality of life is becoming increasingly important in clinical research (Schumacher, Olschewski, and Schulgen 1991; Cox et al. 1992). In particular, [...]

The availability of powerful and inexpensive hardware and software for graphical computing makes the use of inter-active dynamic graphics feasible for the examination of survival data. The use of these approaches may help the clinical researcher formulate specific hypotheses and select appropriate models. This paper describes some simple techniques, which were implemented in the LISP-STAT environment. KEY WORDS: Exploratory graphics; Survival data, 1. INTRODUCTION Classic statistical methodology is designed to provide answers to specific questions; exploratory methodology is designed to uncover aspects of data that should generate questions. In collaborative research efforts, [...]

A tree-based methodology is further developed for the analysis of censored survival data based on concept of dissimilarity in survival distribution between groups of patients. The method utilized is based on maximizing the difference in survival between groups of patients represented by nodes in a binary tree. The research uses recursive partitioning procedures for survival analysis which proves to be very important in formulating a result.

Graphical methods for evaluating failure rate data are presented. The techniques exploit the relations between the maximum and minimum of the alpha-percentile residual life function and the minimum and maximum of the hazard rate, respectively, to aid in finding product burn-in for product warranties. Their use is demonstrated via several problems concerning a data set on the hazard rate of jet engine starters.

The reliability testing of fault-tolerant computer systems with multi-phased missions is investigated. Such systems are difficult to characterize due to the varying nature of their mean-time-before-failure and error handling property. Several approaches and a computer program for conducting efficient reliability analysis are presented along with Markov models for systems whose configuration or success criteria may be altered.

A variety of methods are in use for predicting upset rates. The predictions of several of these methods are compared with flight data from the microelectronics package on the CRRES satellite. The implications of current cosmic ray research relative to these results is discussed.

A procedure to predict the reliability of electrical insulators subjected to accelerated life testing is presented. A set of probability functions are derived and the best fit is used to describe the reliability data. The calculation of the minimum voltage stress level and the appropriate number of tests are also given. The technique permits the precise description of the probability distribution of the failure time data without adopting a Weibull distribution with a constant shape. A computer program allows for quick computation of the cumulative distribution function for the failure time data.

In this article, we estimate accelerated time-to-failure and proportional-hazard functions with about 100,000 members of the Dorn sample, finding greater hazards associated with smoking and some dependence on occupational variables that measure risk and physical activity. We answer three questions: (1) How sensitive are the estimates to sample length, using monthly data for the periods 1954-1969 and 1954-1980? The results differ somewhat between these sample periods. (2) How sensitive are the estimates to alternative functions for the hazard? Within a given time period, the estimates are fairly robust to specification changes in the distribution of the hazard in the accelerated time-to-failure models. (3) How sensitive are the estimates to alternative controls for unobserved frailty? Within a given sample period, the estimates are fairly robust to the allowance for parametric or nonparametric heterogeneity in the proportional-hazard models.

We consider a class of models that generalizes the popular Mixed Proportional Hazard (MPH) model for duration data: the Generalized Accelerated Failure- Time (GAFT) model. We show that the GAFT model is non-parametrically identified (up to a normalization). We then reconsider the non-parametric identification of the MPH model. We show that the class of MPH models is not close under normalization. This implies that a finite mean of the mixing distribution is a necessary condition for (no-paratemic) identification of the MPH model. It is impossible to test this hypothesis without imposing arbitrary restrictions on the base-line hazard and/or the regression function.

David W. HOSMER Jr. and Stanley LEMESHOW. New York: Wiley 1999. ISBN 0-471-15410-5. xiii + 386 PP. $79.95. This book is patterned after the text Applied Logistic Regression, by the [...]

We propose model selection procedures for bivariate survival models for censored data generated by the Archimedean copula family. In route to constructing the selection methodology, we develop estimates of some [...]

The estimation of survival distributions for radio-tagged animals is important to wildlife ecologists. Allowance must be made for animals being lost (or censored) due to radio failure, radio loss, or emigration of the animal from the study area. The Kaplan-Meier procedure (Kaplan and Meier 1958), widely used in medical studies to censoring, can be applied to this problem. We developed a simple modification of the Kaplan-Meier procedure that allows for new animals to be added after the study begun. We present 2 examples using telemetry data collected from nothern bobwhite quail (Colinus virginianus) to show the simplicity and utility of the Kaplan-Meier procedure and its modifications. The log rank test used to compare 2 survival distributions can also be modified to allow for additions during the study. Simple computer programs that can be run on a personal computer are available from the authors.

Structural evaluation and design have been dominated by component safety checks. In fact, current reliability-based codes for buildings and bridges are largely limited to individual structural component checks and do not generally include requirements for system reliability. Also, these codes do not consider the potential damaged states of a structural system and the ability of the damaged system to continue to carry loads. Furthermore, current codes do not entail the prediction of the failure time of deteriorating structural systems under time-varying loads. In this study, the reliability of deteriorating fail-safe structures is investigated using a time-variant parallel system reliability approach in which both load and resistance are time dependent. Monte Carlo simulation is used to find the cumulative-time system failure probability. Numerical examples are presented to illustrate the effects of various parameters such as variabilities in live loads, live load occurrence rate, live to dead load ratio, strength loss rate, resistance correlation, and number of degrading members on the cumulative-time failure probability of a deteriorating fail-safe system. Postfailure behavior of components and load redistribution effects are also considered. The results can be used to better predict the failure time of deteriorating fail-safe structures, such as redundant reinforced concrete bridges under corrosion attack, and to develop optimal lifetime reliability-based maintenance strategies for these structures.

Time to next failure (TTNF) can be a totally inappropriate method for evaluating software-reliability field data. Real software-reliability data are often noisy and too granular for the application of TTNF, and modelers seldom frame their models with reference to practical data-collection delays. Software-reliability modeling should focus on longer-range forecasting and estimation.