• Industrial Engineering and Management Systems
• /
• 제9권1호
• /
• pp.54-59
• /
• 2010

A two-plan sampling system is proposed for a failure-censored life testing when the lifetime follows a Weibull distribution with known shape parameter. The proposed sampling system is based on a switching rule, for switching between the tightened and the normal inspection levels when lots are submitted for inspection in the order of production or in some other systematic way. The design parameters of the proposed sampling system are determined by the two-point approach considering the producer's risks and the consumer's at the specified acceptable reliability level and the lot tolerance reliability level, respectively. It has been observed that the proposed system requires only a single failure for the observation.

• Communications for Statistical Applications and Methods
• /
• 제17권3호
• /
• pp.319-326
• /
• 2010

In this paper, a new group sampling plan for the lot acceptance is proposed for the time truncated life test, which can be utilized when multi-item testers are implemented. The design parameters are found using the two-point approach such that the producer's and consumer's risks are satisfied simultaneously at the acceptable reliability level and the lot tolerance reliability level, respectively. The case of Weibull distribution is described to illustrate the procedure that can be used when the quality level is expressed by a multiple of the specified life. The advantage of the proposed plan is demonstrated by comparing with the existing plan in terms of the sample size required. The tables are constructed and some examples are given to illustrate the procedure developed here.

• Wind and Structures
• /
• 제28권6호
• /
• pp.369-380
• /
• 2019

Statistical distributions are very useful in describing wind speed characteristics and in predicting wind power potential of a specified region. Although the Weibull distribution is the most popular one in wind energy literature, it does not seem to be able to perfectly fit all the investigated wind speed data in nature. Thus, many studies are still being conducted to find flexible distribution for modelling wind speed data. In this study, we propose a new Odd-Burr Rayleigh distribution for wind speed characterization. The Odd-Burr Rayleigh distribution with two shape parameters is flexible enough to model different shapes of wind speed data and thus it can be an alternative wind speed distribution for the assessment of wind energy potential. Therefore, suitability of the Odd-Burr Rayleigh distribution is investigated on real wind speed data taken from different regions in the South Africa. Numerical results of the conducted analysis confirm that the new Odd-Burr Rayleigh distribution is suitable for modelling most of the considered real wind speed cases and it also can be used for predicting wind power.

• Journal of the Korean Statistical Society
• /
• 제28권4호
• /
• pp.399-413
• /
• 1999

• 품질경영학회지
• /
• 제22권3호
• /
• pp.111-118
• /
• 1994

In this paper we propose a parametric and a nonparametric small sample estimators for the mean residual life (MRL) under the random censorship model using the partial moment approximation. We also compare the proposed nonparametric estimator with the well-known nonparametric MRL estimator based on Kaplan-Meier estimator of the survival function, and present the efficiency of the nonparametric method relative to the Weibull model for small samples.

• 한국안전학회지
• /
• 제33권3호
• /
• pp.83-91
• /
• 2018

This paper suggests a weibull time delay model to evaluate failure risks in FMEA(failure modes and effects analysis). Assuming three types of loss functions for delayed time in failure cause detection, the risk of each failure cause is evaluated as its occurring frequency and expected loss. Since the closed form solution of the risk metric cannot be obtained, a statistical computer software R program is used for numerical calculation. When the occurrence and detection times have a common shape parameter, though, some simple results of mathematical derivation are also available. As an enormous quantity of field data becomes available under recent progress of data acquisition system, the proposed risk metric will provide a more practical and reasonable tool for evaluating the risks of failure causes in FMEA.

• Journal of the Korean Data and Information Science Society
• /
• 제7권2호
• /
• pp.263-272
• /
• 1996

임의의 기계에 대한 수명의 분포는 와이블분포를 하는 경우가 흔하다. 그리고 현실적으로 기계의 수명시간을 검정할 때, 시험시간및 여러 환경적인 제약에 의하여 표본으로 주어진 기계의 수명을 모두 관측하기는 어렵다. 그래서, 본 연구에서는 임의 중단모형 하에서 와이블분포의 모수를 최소제곱법(least squares method)을 이용하여 추정하고 기존의 최대우도추정량(maximum likelihood estimates)과 효율성의 측면에서 비교하고자 한다.

• Journal of the Korean Data and Information Science Society
• /
• 제28권3호
• /
• pp.659-668
• /
• 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.

• 품질경영학회지
• /
• 제24권3호
• /
• pp.37-49
• /
• 1996

For highly reliable devices it is often defined to "fail" when its performance degrades below a specified value. In this paper we consider a method for optimally designing accelerated degradation tests(ADTs) in which the performance over exposure time and stress has Weibull distribution. For the product whose performance has Weibull distribution, the optimum plan - low stress level and sample proportions allocated to each test condition - is obtained, which minimize the asymptotic variance of maximum likelihood estimator of a stated quantile at design stress. We also present compromise ADTs plan that can be used for the practical purpose.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2008년도 추계학술대회A
• /
• pp.173-174
• /
• 2008

The four-point bending test is a widely used method to determine material parameters. The aim of the present study was to evaluate the flexural strength (or modulus of rupture) and the Weibull modulus of cordierite ceramic substrate by means of four-point bending tests. The strength data from experiments followed Weibull statistics. These data indicate that the fatigue effects are more severe when the substrate temperature in the peripheral region is near $200^{\circ}$. At temperatures well above $200^{\circ}C$ the available design strength can be as high as 65% as substrate's initial strength.