摘要:

Distributions of part life lengths are often seen to have a decreasing force of mortality during the early life of the part. This effect is known as theinfant mortalifyeffect. A similar decrease in the rate of occurrence of failures has been observed in field-failure data for repairable systems. In this article, we show how this improvement of system reliability can be understood as a consequence of heterogeneity in the quality of parts. We present a superimposed-renewalprocess model based on this assumption. The model results in a simple analytical expression for the rate of occurrence of failures with parameters that admit a direct physical interpretation. We compare the statistical properties of this model with models based on a postulated structure for the peril rate of a nonhomogeneous Poisson process, and in an example we illustrate the estimation of parameters in our model.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484765

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Interval estimation of component failure rates based on data from series systems having differing numbers of components of various kinds is addressed. Complete, Type I, and Type II censored observations from exponential lifetime distributions are considered. The cuberoot normalizing transformation is used to derive approximate confidence intervals for the component failure rates. Exact results and a simulation study show that the proposed method performs better than the standard application of maximum likelihood and a method stemming from Miyamura (1982). In fact, the proposed method is shown to be as accurate as the Wilson–Hilferty normal approximation to the chi-squared distribution in a limiting case. A data set on air-conditioner life-test results is used for illustration and comparison.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484766

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Although censored (including interval-censored) data may be easier or less costly to collect than complete data, they contain less information and are harder to analyze. Existing methodology is inadequate for analyzing such data from highly fractionated experiments. We propose an iterative method that provides a simple and flexible way to consider many models simultaneously. The method's simplicity makes it easy to implement with existing software, results in computational savings, and promotes experimenter involvement. We demonstrate the procedure by reanalyzing data from two real experiments. A simulation study also demonstrates its superiority over some existing methods, including Taguchi's minute accumulating analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484767

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

We consider a multivariate survival distribution derived from an inverse Gaussian mixture of exponential distributions. The variables of this multivariate distribution are shown to exhibit total positive dependence of order 2. A general formula for joint moments and the monotonicity properties of hazard rates are described. Inference methods—including derivation of a posterior distribution for the unknown exponential hazard rate, maximum likelihood estimation of the mixture distribution parameters, and derivation of a posterior predictive distribution for a new observation—are developed. Procedures for assessing model adequacy are also presented. The computational requirements of the methods are modest, and censored data are handled with ease. The inference methods and model assessment procedures are illustrated with several case examples, one of which exploits the connection between this multivariate distribution and the inverse Gaussian mixture of Poisson distributions.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484768

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

The Birnbaum–Saunders distribution was derived to model times to failure for metals subject to fatigue. In this article, we formulate and develop a log-linear model for the Birnbaum–Saunders distribution. The model may be used for accelerated life testing or to compare the median lives of several populations. Methods of analyzing data for this log-linear model are discussed, with maximum likelihood and least squares methods being compared. It is found that, for commonly occurring conditions, the notorious intractability of the Birnbaum–Saunders distribution is not a serious problem because least squares and normal-theory procedures provide a reasonable alternative.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484769

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

When performing quality control in a situation in which measures are made of several possibly related variables, it is desirable to use methods that capitalize on the relationship between the variables to provide controls more sensitive than those that may be made on the variables individually. The most common methods of multivariate quality control that assess the vector of variables as a whole are those based on the HotellingT2between the variables and the specification vector. AlthoughT2is the optimal single-test statistic for a general multivariate shift in the mean vector, it is not optimal for more structured mean shifts-for example, shifts in only some of the variables. Measures based on quadratic forms (likeT2) also confound mean shifts with variance shifts and require quite extensive analysis following a signal to determine the nature of the shift. This article proposes Shewhart and cumulative sum (CUSUM) controls based on the vectorZof scaled residuals from the regression of each variable on all others. Each component ofZis the (Neyman-Pearson) optimal single-test statistic for testing whether that variable is shifted in mean. The Shewhart charts plot the components ofZ, and the CUSUM charts are based on accumulation of components ofZ, leading one to anticipate good performance by the charts. This is verified by some average run length calculations. The vectorZalso has the valuable interpretive property that signals given are for shifts in the mean, or shifts in the variance, of particular variables rather than global signals indicating some unspecified departure from control.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484770

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Predicting values of a spatially distributed variable, such as the concentration of a mineral throughout an ore body or the level of contamination around a toxic-waste dump, can be accomplished by a regression procedure known as kriging. Kriging and other types of statistical inference for spatially distributed variables are based on models of stochastic processes {Yt:t∊D} called random-field models. A commonly used class of random-field models are the intrinsic models, for which the mean is constant, and half of the variance ofYt, –Ys. is a function, called the semivariogram, of the differencet–s. The type of kriging corresponding to an intrinsic model is called ordinary kriging. The semivariogram, which typically is taken to depend on one or more unknown parameters, must be estimated prior to ordinary kriging. Various estimators of the semivariogram's parameters have been proposed. For two Gaussian intrinsic random-field models, we compare, by a Monte Carlo simulation study, the performance of seven estimators—ordinary least squares (OLS), Cressie's weighted least squares (WLS-1 and WLS-2), Delfiner's weighted least squares (WLS-3). maximum likelihood (ML), restricted maximum likelihood (REML), and generalized minimum variance quadratic unbiased (GMIVQU) estimators. In addition, we compare the performance of the standard 95% confidence interval for the ordinary kriging predictor corresponding to each of the estimators. Our results indicate that the relatively easy-to-compute OLS, WLS-1, and WLS- 2 estimators and their corresponding prediction intervals perform as well or nearly as well as the more computationally demanding ML, REML, and GMIVQU estimators and their corresponding prediction intervals, but that the WLS3 estimator and its corresponding prediction interval perform poorly.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484771

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

This article presents a methodology for building measures of influence in regression models with time series data. We introduce statistics that measure the influence of each observation on the parameter estimates and on the forecasts. These statistics take into account the autocorrelation of the sample. The first statistic can be decomposed to measure the change in the univariate autoregressive integrated moving average parameters, the transfer-function parameters, and the interaction between both. For independent data, they reduced to theDstatistic considered by Cook in the standard regression model. These statistics can be easily computed using standard time series software. Their performance is analyzed in an example in which they are shown to be useful in identifying important events, such as additive outliers and trend shifts, in time series data.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484772

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Local-influence analysis of perturbations of the response vector is shown to be the same as the usual regression diagnostics in the fixed-effects model. This result provides a further justification for local-influence analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484773

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1991.10484774

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor