Estimation of system reliability using a semiparametric model (original) (raw)

Software Reliability Modeling with Software Metrics Data via Gaussian Processes

IEEE Transactions on Software Engineering, 2013

In this paper, we describe statistical inference and prediction for software reliability models in the presence of covariate information. Specifically, we develop a semiparametric, Bayesian model using Gaussian processes to estimate the numbers of software failures over various time periods when it is assumed that the software is changed after each time period and that software metrics information is available after each update. Model comparison is also carried out using the deviance information criterion, and predictive inferences on future failures are shown. Real-life examples are presented to illustrate the approach.

System reliability prediction based on historical data

Quality and reliability …, 1990

This paper describes the development and implementation of a computerized reliability prediction model at the IBM facility located in Research Triangle Park, North Carolina. Through the analysis of historical life-test data, the model provides maximum likelihood estimates of the assumed Weibull life distributions of various types of components. The resulting component life distribution estimates are used to predict the reliability of new system configurations. This approach is based upon the wellknown theory of competing risks. Our model, however, is unique in that it allows for the analysis of a pooled set of life data, i.e. life data from different types of systems, to obtain component estimates. This feature greatly generalizes the competing risks framework and hence offers advantages over the more traditional approach. We present the model and discuss various issues that were found to be critical to its successful implementation at IBM.

n-Steps ahead software reliability prediction using the Kalman filter

Applied Mathematics and Computation, 2014

This paper presents KSL, a new software reliability growth model (SRGM) based on the Kalman filter with a sub filter and the Laplace trend test. We applied the model to the Linux operating system kernel as a case study to predict the absolute and relative (per lines of code) number of faults n-steps ahead. The Laplace trend test is applied to detect when the series no longer follows a homogeneous Poisson process, improving the confidence level. An example is provided with a prediction of 13 months ahead on the number of faults with 8% error. The results (i.e. predictive capability) indicated that the proposed approach outperforms the S-shaped prediction model, Weibull, and Exponentiated Weibull distributions, as well as typical and OS-ELM Neural networks when the series has a short number of observations.

Flexible methods for reliability estimation using aggregate failure-time data

IISE Transactions, 2020

The actual failure times of individual components are usually unavailable in many applications. Instead, only aggregate failure-time data are collected by actual users due to technical and/or economic reasons. When dealing with such data for reliability estimation, practitioners often face challenges of selecting the underlying failure-time distributions and the corresponding statistical inference methods. So far, only the Exponential, Normal, Gamma and Inverse Gaussian distributions have been used in analyzing aggregate failure-time data because these distributions have closed-form expressions for such data. However, the limited choices of probability distributions cannot satisfy extensive needs in a variety of engineering applications. Phase-type (PH) distributions are robust and flexible in modeling failure-time data as they can mimic a large collection of probability distributions of nonnegative random variables arbitrarily closely by adjusting the model structures. In this paper, PH distributions are utilized, for the first time, in reliability estimation based on aggregate failure-time data. A maximum likelihood estimation (MLE) method and a Bayesian alternative are developed. For the MLE method, an expectation-maximization (EM) algorithm is developed for parameter estimation, and the corresponding Fisher information is used to construct the confidence intervals for the quantities of interest. For the Bayesian method, a procedure for performing point and interval estimation is also introduced. Numerical examples show that the proposed PH-based reliability estimation methods are quite flexible and alleviate the burden of selecting a probability distribution when the underlying failure-time distribution is general or even unknown.

Semiparametric smoothing of discrete failure time data

Biometrical Journal, 2012

An estimator of the hazard rate function from discrete failure time data is obtained by semiparametric smoothing of the (nonsmooth) maximum likelihood estimator, which is achieved by repeated multiplication of a Markov chain transition‐type matrix. This matrix is constructed so as to have a given standard discrete parametric hazard rate model, termed the vehicle model, as its stationary hazard rate. As with the discrete density estimation case, the proposed estimator gives improved performance when the vehicle model is a good one and otherwise provides a nonparametric method comparable to the only purely nonparametric smoother discussed in the literature. The proposed semiparametric smoothing approach is then extended to hazard models with covariates and is illustrated by applications to simulated and real data sets.

Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model

Journal of Statistical Theory and Applications, 2013

A semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability 1.  It is also assumed that the failure rate of unit i has the general form  

Sequential Bayesian technique: An alternative approach for software reliability estimation

Sadhana-academy Proceedings in Engineering Sciences, 2009

This paper proposes a sequential Bayesian approach similar to Kalman filter for estimating reliability growth or decay of software. The main advantage of proposed method is that it shows the variation of the parameter over a time, as new failure data become available. The usefulness of the method is demonstrated with some real life data.