• The Korean Journal of Applied Statistics
• /
• v.22 no.1
• /
• pp.205-220
• /
• 2009

For modeling skewed semicircular data, we derive new family of the exponential distributions. We extend it to the l-axial exponential distribution by a transformation for modeling any arc of arbitrary length. It is straightforward to generate samples from the f-axial exponential distribution. Asymptotic result reveals two things. The first is that linear exponential distribution can be used to approximate the l-axial exponential distribution. The second is that the l-axial exponential distribution has the asymptotic memoryless property though it doesn't have strict memoryless property. Some trigonometric moments are also derived in closed forms. Maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for goodness of fit test of the l-axial exponential distribution. We finally obtain a bivariate version of two kinds of the l-axial exponential distributions.

• Journal of Korean Society for Quality Management
• /
• v.24 no.4
• /
• pp.14-28
• /
• 1996

We consider optimal designs of partially accelerated life testing which is deviced for parallel systems with the considerably long life time. In partially step-stress life testing, test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. In partially constant-stress life testing, test items are run at either use or accelerated condition only until a specified censoring time. The optimal criterion for each test is to minimize either the generalized asymptotic variance of maximum likelihood(ML) estimators of the hazard rates at use condition and the acceleration factors or the asymptotic variance of the ML estimators of the acceleration factors.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.2
• /
• pp.15-21
• /
• 1993

This paper considers the optimal design of accelerated life test in which the stress is linearly increased. It discusses the special case when the life distribution under constant stress follows an exponential distribution and the accelerated equation satisfies the inverse power law. It is assumed that cumulative damage is linear, that is, the remaining life of test units depends only on the current cumulative fraction failed and current stress(cumulative exposure model). The optimization criterion is the asymptotic variance of the maximum likelihood estimator of the log mean life at a design stress. The optimal increasing rate is obtained to minimize the asymptotic variance. Table of sensitivity analysis is given for the prior estimators of model parameters.

• International Journal of Reliability and Applications
• /
• v.15 no.2
• /
• pp.99-110
• /
• 2014

Based on the kernel function, a new test is presented, testing $H_0:\bar{F}$ is exponential against $H_1:\bar{F}$ is UBACT and not exponential is given in section 2. Monte Carlos null distribution critical points for sample sizes n = 5(5)100 is investigated in section 3. The Pitman asymptotic efficiency for common alternatives is obtained in section 4. In section 5 we propose a test statistic for censored data. Finally, a numerical examples in medical science for complete and censored data using real data is presented in section 6.

• International Journal of Reliability and Applications
• /
• v.6 no.1
• /
• pp.53-64
• /
• 2005

In this paper, we propose a nonparametric test procedure for the multivariate, grouped and right censored data for two sample problem. For the construction of the test statistic, we use the linear rank statistics for each component and apply the permutation principle for obtaining the null distribution. For the large sample case, the asymptotic distribution is derived under the null hypothesis with the additional assumption that two censoring distributions are also equal. Finally, we illustrate our procedure with an example and discuss some concluding remarks. In appendices, we derive the expression of the covariance matrix and prove the asymptotic distribution.

• Journal of Korean Society for Quality Management
• /
• v.17 no.1
• /
• pp.89-106
• /
• 1989

For Weibull distributed lifetimes, this paper presents asymptotically optimal accelerated life test plans for practical applications under intermittent inspection and type-I censoring. Computational results show that the asymptotic variance of a low quantile at the design stress as optimal criterion is insensitive to the number of inspections at overstress levels. Sensitivity analyses indicate that optimal plans are robust enough to moderate departures of estimated failure probabilities at the design and high stresses as input parameters to plan accelerated life tests from their true values. Monte Carlo simulation for small sample study on optimal accelerated life test plans developed by the asymptotic maximum likelihood theory is conducted. Simulation results suggest that optimal plans are satisfactory for sample size in practice.

• Journal of the Korea Safety Management & Science
• /
• v.9 no.2
• /
• pp.123-134
• /
• 2007

This paper focuses on the in-house reliability assurance plan for the bulk materials of each company. The reliability assurance needs in essence a long time and high cost for testing the materials. In order to reduce the time and cost, accelerated life test is adopted. The bulk sampling technique was used for acceptance. Design parameters might be total sample size(segments and increments}, stress level and so on. We focus on deciding the sample size by minimizing the asymptotic variance of test statistics as well as satisfying the consumer's risk. In bulk sampling, we also induce the sample size by adapting the normal life time distribution model when the variable of the lognormal life time distribution is transformed and adapted to the model. In addition, the sample size for both the segments and increments can be induced by minimizing the asymptotic variance of test statistics of the segments and increments with consumer's risk met. We can assure the reliability of the mean life and B100p life time of the bulk materials by using the calculated minimum sample size.

• Communications for Statistical Applications and Methods
• /
• v.13 no.2
• /
• pp.419-428
• /
• 2006

The method of Reverse Ranked Ordering-Set Sampling(RROSS) as an opposed Ranked Ordering-Set Sampling(ROSS) and Ranked-Set Sampling(RSS) is discussed. We propose the test statistic using sign test on RROSS. This method is effective when observations are expensive and measurement is perhaps destructive or invasive. This method obtains more informations than ROSS and RSS. The asymptotic relative efficiencies of RROSS with respect to ROSS and RSS are always greater than 1 for all sample sizes. We consider a simple model to describe the effect of imperfect judgment errors.

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.669-690
• /
• 1998

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods having these properties and show in particular that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition we give a very simple test to identify the symmetric methods in practice.

• Journal of Korean Society for Quality Management
• /
• v.22 no.2
• /
• pp.166-176
• /
• 1994

Some rank score tests are proposed for testing the equality of all sampling distribution functions against ordered location-scale alternatives in k-sample problem. Under the null hypothesis and a contiguous sequence of ordered location-scale alternatives, the asymptotic properties of the proposed test statistics are investigated. Also, the asymptotic local powers are compared with each others. The results show that the proposed tests based on the Hettmansperger-Norton type statistic are more powerful than others for the general ordered location-scale alternatives. However, the Shiraishi's tests based on the sum of two Bartholomew's rank analogue statistics are robust.