• Communications for Statistical Applications and Methods
• /
• v.24 no.3
• /
• pp.227-240
• /
• 2017

In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

• Journal of Applied Reliability
• /
• v.14 no.1
• /
• pp.1-9
• /
• 2014

One important measure of performance for a repairable system is steady-state availability. In this paper, a method to estimate and establish confidence interval for the steady-state availability under Weibull lifetime and lognormal repair time distributions is proposed. Also, bias and mean squared error of a point estimator for an availability are investigated. In addition, a procedure to derive the sample size and critical value for availability demonstration test is presented and illustrated with a numerical example.

• KIEE International Transactions on Electrophysics and Applications
• /
• v.3C no.1
• /
• pp.1-4
• /
• 2003

This paper presents an attempt to develop probabilistic multistress life models to evaluate the lifetime characteristics of epoxy-encapsulated magnet wire with heavy build polyurethane enamel. A set of accelerated life tests were conducted over a wide range of pulsating voltages, temperatures, and frequencies. Samples of fine gauge twisted pairs of the encapsulated magnet wire were tested us-ing a pulse endurance dielectric test system. An electrical-thermal lifetime function was combined with the Weibull distribution of lifetimes. The parameters of the combined Weibull-electrical-thermal model were estimated using maximum likelihood estimation. Likewise, a generalized electrical-thermal-frequency life model was also developed. The parameters of this new model were estimated using multiple linear regression technique. It was found in this paper that lifetime estimates of the two proposed probabilistic multistress life models are good enough. This suggests the suitability of using the general electrical-thermal-frequency model to estimate the lifetime of the encapsulated magnet wire over a wide range of voltages, temperatures and pulsating frequencies.

• Journal of Applied Reliability
• /
• v.14 no.4
• /
• pp.220-224
• /
• 2014

A Bayesian zero-failure reliability demonstration test method for products with Weibull lifetime distribution is presented. Inverted gamma prior distribution for the scale parameter of the Weibull distribution is used to design the Bayesian test plan and selecting a prior distribution using a prior test information is discussed. A test procedure with zero-failure acceptance criterion is developed that guarantee specified reliability of a product with given confidence level. An example is provided to illustrate the use of the developed Bayesian reliability demonstration test method.

• Communications for Statistical Applications and Methods
• /
• v.24 no.2
• /
• pp.129-142
• /
• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.19 no.8
• /
• pp.1446-1452
• /
• 1994

In this paper, Weibull distribution is applied to the lifetme distribution of a device. The method of Bayesian estimate used to estimate requiring parameter in order to predict lifetime of device using accelerated lifetime test data, namely failure time of device. The method of Bayesian estimate needs prior information in order to estimate parameter. But this paper proposed the method of parameter estimate without prior information. As stress is temperature, Arrhenius model is applied and the method of linear estimate is applied to predict lifetime of device at the state of normal operation.

• Journal of the military operations research society of Korea
• /
• v.9 no.2
• /
• pp.39-43
• /
• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• Journal of Applied Reliability
• /
• v.14 no.3
• /
• pp.182-190
• /
• 2014

This paper presents new practical accelerated life test plans with different censoring times at three levels of stress for Weibull and lognormal lifetime distributions, respectively. The proposed plans are compared with the corresponding two-level statistically optimal plans and three-level compromise and practical plans. Computational results indicate that new practical plans have been more precise and effective than the existing three-level plans under a constraint of total testing time. In addition, a procedure to determine useful ALT plans is illustrated with a numerical example.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.2
• /
• pp.308-313
• /
• 2009

This paper presents a reliability analysis of S-bonds for AF track circuits, which detect train movement and transmit a speed control signal to the train. Field survey shows that S-bonds are exposed to very large vibrations transferred from rail, and suffer from frequent failures when they were installed on ballasted track. We collected the time-to-failure data of S-bonds from the maintenance field of Seoul metro line 2, and made a parametric approach to estimate the statistical distribution that fits the time-to-failure data. The analysis shows that S-bonds have time-to-failure characteristics described by Weibull distribution. The estimated shape parameter of Weibull distribution is 1.1, which means the distribution has constant failure rate characteristics like exponential distribution. The reliability function, hazard function, percentiles and mean lifetime are derived for maintenance support.

• Journal of Applied Reliability
• /
• v.4 no.2
• /
• pp.73-90
• /
• 2004

We performed the heat aging test to predict the useful lifetime of Elastomeric Bearing Chloroprene Rubber (CR) used for supporting bridge. During the test, we measured elongation that are influenced by temperature and aging time. The failure of a test piece is defined as the point at which the elongation reaches to 75% of the initial value. This failure criterion is based on KS F 4420: 1998 (Elastomeric Bearing for bridge). Through the accelerated heat aging test, we found that the Arrhenius relationship and the Weibull lifetime distribution are appropriate as the life-temperature relationship and lifetime distribution of the CR, respectively. Using the Arrhenius -Weibull model, the parameters of the model are estimated and the lifetime of the CR at use condition is predicted.