• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.41-53
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• 2006

The exact cause of the system's failure is often unknown in the masked system lifetime data. In such type of data, there are two observable quantities, namely (i) the systems time to failure and (ii) the set of systems components that contains the component, which might cause the system to fail. Our objective in this paper is to use the maximum likelihood procedure in the presence of masked data to make inference for the reliability of the system's components. We assume a multi-component series system where each component has a constant failure rate. Different cases that permit for closed form solutions of point estimates are considered. The results obtained in this paper generalize other published results.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.12
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• pp.971-982
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• 1989

An integrating position estimation algorithm has been developed for the navigation system of a free-ranging AGV system. The navigation system focused in this research work consists of redundant wheel encoders for the relative position measurement and a vision sensor for the absolute position measurement. A maximum likelihood method and an extended Kalman filter are implemented for enhancing the performance of the position estimator. The maximum likelihood estimator processes noisy, redundant wheel encoder measurements and yields efficient estimates for the AGV motion between each sampling interval. The extended Kalman filter fuses inharmonious positional data from the deadreckoner and the vision sensor and computes the optimal position estimate. The simulation results show that the proposed position estimator solves a generalized estimation problem for locating the vehicle accurately in space.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.433-438
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• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• Journal of Korean Society for Quality Management
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• v.40 no.2
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• pp.117-125
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• 2012

For the highly reliable products, an accelerated degradation test (ADT) is a useful tool which has been employed in industry to obtain reliability-related information within an affordable amount of time and cost. In an ADT, as all other reliability tests, it is important to carefully design the ADT beforehand to obtain estimates of the quantities of interest as precisely as possible. In this paper, optimal ADTs are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Under the constraint that the total cost does not exceed a pre-specified budget, the stress levels, the number of test units allocated to each stress level and the number of measurement (termination time) are determined such that the asymptotic variance of the maximum likelihood estimator of the q-th quantile of the lifetime distribution at the use condition is minimized.

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.53-70
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• 2008

In this paper, we discuss the plethora of uses for the software package R, and focus specifically on its helpful applications in reliability data analyses. Examples are presented; including the R coding protocol, R code, and plots for various statistical as well as reliability analyses. We explore Kaplan-Meier estimates and maximum likelihood estimation for distributions including the Weibull. Finally, we discuss future applications of R, and usages of quantile regression in reliability.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.187-201
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• 2006

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.65-82
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• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of Korean Society for Quality Management
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• v.37 no.4
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• pp.16-22
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• 2009

The inflection S-shaped software reliability growth model (SRGM) proposed by Ohba(1984) is one of the most commonly used models and has been discussed by many authors. The main purpose of this paper is to estimate the parameters of Ohba's SRGM within the Bayesian framework by applying the Markov chain Monte Carlo techniques. While the maximum likelihood estimates for these parameters are well known, the Bayesian method for the inflection S-shaped SRGM have not been discussed in the literature. The proposed methods can be quite flexible depending on the choice of prior distributions for the parameters of interests. We also compare the Bayesian methods with the maximum likelihood method numerically based on the real data.

• Journal of Korean Society for Quality Management
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• v.42 no.1
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• pp.1-14
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• 2014

Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.