• Title/Summary/Keyword: Mean Residual Life(MRL)

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A Nonparametric Small Sample Estimator of Mean Residual Life

  • Farrokh Choobineh;Park, Dong-Ho
    • Journal of the Korean Statistical Society
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    • v.19 no.1
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    • pp.80-87
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    • 1990
  • In reliability and life testing the mean residual life (MRL) of an item plays a significant role. While there has been a great deal of discussion on the theoretical aspects of the MRL, good estimators of MRL have been difficult to obtain. In this paper we propose a new estimator of the MRL of items at a given age, which is especially good for a small sample. The new estimator compares favorably with the empirical MRL estimator for small samples.

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Using Mean Residual Life Functions for Unique Insights into Strengths of Materials Data

  • Guess Frank M.;Zhang Xin;Young Timothy M.;Leon Ramon V.
    • International Journal of Reliability and Applications
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    • v.6 no.2
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    • pp.79-85
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    • 2005
  • We show how comparative mean residual life functions (MRL) can be used to give unique insights into strengths of materials data. Recall that Weibull's original reliability function was developed studying and fitting strengths for various materials. This creative comparing of MRL functions approach can be used for regular life data or any time to response data. We apply graphical MRL's to real data from tests of tensile strength of high quality engineered wood.

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Applying Novel Mean Residual Life Confidence Intervals

  • Guess, F.M.;Steele, J.C.;Young, T.M.;Leon, R.V.
    • International Journal of Reliability and Applications
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    • v.7 no.2
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    • pp.177-186
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    • 2006
  • Typical confidence intervals for a mean or mean residual life (MRL) are centered about the mean or mean residual life. We discuss novel confidence intervals that produce statements like "we are 95% confident that the MRL function, e(t), is greater than a prespecified $\mu_o$ for all t in the interval [0, $\hat{\theta})$)" where $\hat{\theta}$ is determined from the sample data, confidence level, and $\mu_o$. Also, we can have statements like 'we are 95% confident that the MRL of population 1, namely $e_1$(t), is greater than the MRL of population 2, $e_2$(t), for all t in the interval [0, $\hat{\theta}$)" where $\hat{\theta}$ is determined from the sample data and confidence level. We illustrate these one and two sample confidence intervals on internal bonds (tensile strengths) for an important modem engineered wood product, called medium density fiberboard (MDF), used internationally.

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The Study on the Mean Residual Life Estimation of Reliability Data under Random Censoring (임의절단 하에서 신뢰성 자료의 평균잔여수명 추정에 대한 연구)

  • Lee, Mi-Sook
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.11 no.6
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    • pp.1997-2003
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    • 2010
  • Mean Residual Life (MRL) function plays a very important role in the area of engineering, medical science, survival studies, social sciences, and many other fields. Specially, in the reliability study of technical systems, the MRL estimation of a component is very important because the sudden stop of a system brings a serious problem. So, many simulation studies of MRL estimation have been done considering various situation variables. In this paper, four estimators of MRL are proposed under random censoring and their performances re compared through bias and Mean Square Error (MSE) by Monte Carlo simulation.

A NEW UDB-MRL TEST WITH UNKNOWN CHANCE POINT

  • Na, Myung-Hwan
    • Journal of Korean Society for Quality Management
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    • v.30 no.3
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    • pp.195-202
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    • 2002
  • The problem of trend change in the mean residual life is great Interest in the reliability and survival analysis. In this paper, a new test statistic for testing whether or not the mean residual life changes its trend Is developed. It is assumed that neither the change point nor the proportion at which the trend change occurs is known. The asymptotic null distribution of test statistic is established and asymptotic critical values of the asymptotic null distribution is obtained. Monte Carlo simulation is used to compare the proposed test with previously known tests.

A NEW UDB-MRL TEST FOR WITH UNKNOWN

  • Na, Myung-Hwan
    • Journal of Korean Society for Quality Management
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    • v.30 no.4
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    • pp.78-85
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    • 2002
  • The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, a new test statistic for testing whether or not the mean residual life changes its trend is developed. It is assumed that neither the change point nor the proportion at which the trend change occurs is known. The asymptotic null distribution of test statistic is established and asymptotic critical values of the asymptotic null distribution is obtained. Monte Carlo simulation is used to compare the proposed test with previously known tests.

Estimation of Mean Residual Life under Random Censorship Model Using Partial Moment Approximation

  • Park, Byung Gu;Lee, Jae Man;Cha, Young Joon
    • Journal of Korean Society for Quality Management
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    • v.22 no.3
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    • pp.111-118
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    • 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.

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Estimator of the Mean Residual Life for Some Parametric Families (모수족에서 평균 잔여수명의 추정량)

  • Kuey Chung Choi;Kyung Hyun Nam
    • The Korean Journal of Applied Statistics
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    • v.7 no.2
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    • pp.89-100
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    • 1994
  • In this paper we consider a new estimator of mean residual life (MRL), based on the partial moment of the distribution. The parameters of a partial moment are estimated by its maximum likelihood estimators when the underlying distribution is known. Though the new estimator is not a consistent estimator of the MRL, it is shown to have smaller mean squared error than the well known empirical MRL estimator for certain parametric families. Numerical summaries of the mean squared errors of the new estimator are presented.

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Estimator of Mean Residual Life for Some Parametric Families Using Censored Data

  • Cho, Byung Yup;Choi, Kuey Chung;Choi, Sook Hee;Son, Young Nam
    • Journal of Korean Society for Quality Management
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    • v.23 no.2
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    • pp.80-90
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    • 1995
  • In this paper we consider a new estimator of mean residual life(MRL) under the random censorship model, based on the partial moment of the distribution. The parameters of a partial moment are estimated by its maximum likelihood estimators when the underlying distribution is known. Though the new estimator is not a consistent estimator of the MRL, it is shown to have smaller mean squared error than the well known empirical MRL estimator for a parametric family. We also compare the proposed estimator with some other estimators in terms of MSE for exponential and lognormal distributions using censored data.

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A Study on the Test of Mean Residual Life with Random Censored Sample (임의 절단된 자료의 평균잔여수명 검정에 관한 연구)

  • 김재주;이경원;나명환
    • Journal of Korean Society for Quality Management
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    • v.25 no.3
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    • pp.11-21
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    • 1997
  • The mean residual life(MRL) function gives the expected remaining life of a item at age t. In particular F is said to be an increasing intially then decreasing MRL(IDMRL) distribution if there exists a turing point $t^*\ge0$ such that m(s)$\le$ m(t) for 0$$\le s$\le$ t $t^*$, m(s)$\ge$ m(t) for $t^*\le$ s$\le$ t. If the preceding inequality is reversed, F is said to be a decreasing initially then increasing MRL(DIMRL) distribution. Hawkins, et al.(1992) proposed test of H0 : F is exponential versus$H_1$: F is IDMRL, and $H_0$ versus $H_1$' : F is DIMRL when turning point is unknown. Their test is based on a complete random sample $X_1$, …, $X_n$ from F. In this paper, we generalized Hawkins-Kochar-Loader test to random censored data.

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