• Title/Summary/Keyword: truncated Weibull distribution

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Jackknife Estimates for Parameter Changes in the Weibull Distribution

  • Jungsoo;Changsoo
    • Communications for Statistical Applications and Methods
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    • v.7 no.1
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    • pp.199-210
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    • 2000
  • We shall propose several estimators for the shape and scale parameters I the Weibull distribution based upon the complete or truncated samples when both parameters are functions of a known exposure level and study properties for proposed several estimators

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Truncated Sequential Test Plan under Weibull Distribution (와이블 분포에서의 종결형 축차시험방안)

  • 정해성;차명수;오근태
    • Journal of Applied Reliability
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    • v.3 no.2
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    • pp.137-143
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    • 2003
  • Sequential test plans are characterized by decision rules for accepting or rejecting compliance, or continuing the test at my test time. They are determined by selected values of risks and discrimination ratio. The sequential test plans in the international standard such as MIL-HDBK-781A are based on the assumption that the underlying distribution of times between failures is exponential. In this paper, sequential test plans are extended to the Weibull distribution case. Simulation studies are performed to examine the reasonability in this extension.

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Optimum failure-censored step-stress partially accelerated life test for the truncated logistic life distribution

  • Srivastava, P.W.;Mittal, N.
    • International Journal of Reliability and Applications
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    • v.13 no.1
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    • pp.19-35
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    • 2012
  • This paper presents an optimum design of step-stress partially accelerated life test (PALT) plan which allows the test condition to be changed from use to accelerated condition on the occurrence of fixed number of failures. Various life distribution models such as exponential, Weibull, log-logistic, Burr type-Xii, etc have been used in the literature to analyze the PALT data. The need of different life distribution models is necessitated as in the presence of a limited source of data as typically occurs with modern devices having high reliability, the use of correct life distribution model helps in preventing the choice of unnecessary and expensive planned replacements. Truncated distributions arise when sample selection is not possible in some sub-region of sample space. In this paper it is assumed that the lifetimes of the items follow Truncated Logistic distribution truncated at point zero since time to failure of an item cannot be negative. Optimum step-stress PALT plan that finds the optimal proportion of units failed at normal use condition is determined by using the D-optimality criterion. The method developed has been explained using a numerical example. Sensitivity analysis and comparative study have also been carried out.

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MOMENTS OF LOWER GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED CONTINUOUS DISTRIBUTIONS AND CHARACTERIZATIONS

  • Kumar, Devendra
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.3
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    • pp.441-451
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    • 2013
  • In this paper, we derive recurrence relations for moments of lower generalized order statistics within a class of doubly truncated distributions. Inverse Weibull, exponentiated Weibull, power function, exponentiated Pareto, exponentiated gamma, generalized exponential, exponentiated log-logistic, generalized inverse Weibull, extended type I generalized logistic, logistic and Gumble distributions are given as illustrative examples. Further, recurrence relations for moments of order statistics and lower record values are obtained as special cases of the lower generalized order statistics, also two theorems for characterizing the general form of distribution based on single moments of lower generalized order statistics are given.

A Time Truncated Two-Stage Group Sampling Plan for Weibull Distribution

  • Aslam, Muhammad;Jun, Chi-Hyuck;Rasool, Mujahid;Ahmad, Munir
    • Communications for Statistical Applications and Methods
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    • v.17 no.1
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    • pp.89-98
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    • 2010
  • In this paper, a two-stage group sampling plan based on the time truncated life test is proposed for the Weibull distribution. The design parameters such as the number of groups and the acceptance number in each stage are determined by satisfying the producer's and consumer's risks simultaneously when the group size and the test duration are specified. The acceptable reliability level is expressed by the ratio of the true mean life to the specified life. It was demonstrated from the comparison with single-stage group sampling plans that the proposed plan can reduce the average sample number or improve the operating characteristics.

An Improved Group Sampling Plan Based on Time-Truncated Life Tests

  • Aslam, Muhammad;Pervaiz, Muhammad Khalid;Jun, Chi-Hyuck
    • Communications for Statistical Applications and Methods
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    • v.17 no.3
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    • pp.319-326
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    • 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.

A study on estimating rifle ammunition RSR based on truncated Weibull model (우측중도절단된 와이블 분포를 이용한 소총 탄약 소요보급률 추정 연구)

  • Park, Jaeshin;Bang, Sungwan
    • The Korean Journal of Applied Statistics
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    • v.32 no.1
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    • pp.129-138
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    • 2019
  • Ammunition is an integral element of a weapon systems and in calculating fighting strength. The Korea Army utilizes the basic load (B/L) concept to supply ammunition smoothly. The required supply rate (RSR) is the basis of a B/L that is estimated from real combat data that includes a troop's mission and operation terrain. The current RSR is based on Korean War data and the sample mean has some problems in applications to modern combat. Therefore, this study used Korea Combat Training Center (KCTC) data that is similar to real combat to estimate rifle ammunition RSR. We used a quantile of truncated Weibull distribution to estimate rifle ammunition RSR considering that rifle ammunition consumption data in KCTC is truncated. As a result, we obtained a rifle ammunition RSR which covers most ammunition consumption by reflecting the individual consumption of rifle ammunition.

Sensitivity Analysis of Burn-in Model considering Bimodal-Mixed Weibull Distribution under Free Warranty Policy (무료보증정책하에서 이봉-혼합 와이블 분포를 고려한 Burn-in 모형의 민감도 분석)

  • Song Suh-Ill;Jo Young-Chan;Park Hyun-Kyu;Shon Han-Deak
    • Proceedings of the Korean Society for Quality Management Conference
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    • 1998.11a
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    • pp.544-555
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    • 1998
  • Although the bimodal mixed weibull distribution is used to developing burn-in model widely, the failure times for a component or a system is often truncated at some time, T, due to the obsolescence in the electronics industry. In this paper, we will determine minimum total cost and burn-in time by using the bimodal mixed weibull distribution and the truncated bimodal mixed weibull distribution under the free warranty policy. The results of this study are summarized as follows. First, when products or system is not repairable, the width of the change of burn-in time can be larger by ${\beta}_1,\;{\beta}_2$ Second, if burn-in time become longer, it will be impossible to consider the bum-in in a long time, and in this case, the burn-in time should be shorten by the acceleration burn-in. Third, in case that opportunity loss cost or repair cost is exceed the warranty cost, or the total cost of considering burn-in is larger than that of not considering burn-in, it is not existed burn-in time which makes total cost to minimize. Forth, the shorter life-cycle of product, the more burn-in times will be decreased and the cost in considering burn-in will be increased

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A Simulation Model for the Intermittent Hydrologic Process(I) - Alternate Renewal Process (ARP) and Continuous Probability Distribution - (간헐(間歇) 수문과정(水文過程)의 모의발생(模擬發生) 모형(模型)(I) - 교대재생과정(交代再生過程)(ARP)과 연속확률분포(連續確率分布) -)

  • Lee, Jae Joon;Lee, Jung Sik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.509-521
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    • 1994
  • This study is an effort to develop computer simulation model that produce precipitation patterns from stochastic model. A stochastic model is formulated for the process of daily precipitation with considering the sequences of wet and dry days and the precipitation amounts on wet days. This study consists of 2 papers and the process of precipitation occurrence is modelled by an alternate renewal process (ARP) in paper (I). In the ARP model for the precipitation occurrence, four discrete distributions, used to fit the wet and dry spells, were as follows; truncated binomial distribution (TBD), truncated Poisson distribution (TPD), truncated negative binomial distribution (TNBD), logarithmic series distribution (LSD). In companion paper (II) the process of occurrence is developed by Markov chain. The amounts of precipitation, given that precipitation has occurred, are described by a Gamma. Pearson Type-III, Extremal Type-III, and 3 parameter Weibull distribution. Daily precipitation series model consists of two models, A-Wand A-G model, by combining the process of precipitation occurrence and a continuous probability distribution on the precipitation of wet days. To evaluate the performance of the simulation model, output from the model was compared with historical data of 7 stations in the Nakdong and Seomjin river basin. The results of paper (1) show that it is possible to design a model for the synthetic generation of IX)int precipitation patterns.

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Tightened-Normal-Tightened Group Acceptance Sampling Plan for Assuring Percentile Life

  • Aslam, Muhammad;Azam, Muhammad;Jun, Chi-Hyuck
    • Industrial Engineering and Management Systems
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    • v.11 no.4
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    • pp.390-396
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    • 2012
  • The present paper extends the idea of tightened-normal-tightened sampling scheme to group acceptance sampling plans under the time truncated life tests. We consider three famous distributions that are widely used in the area of reliability such as the generalized exponential distribution, the Weibull distribution, and the Birnbaum-Saunders distribution in the proposed sampling plan. The plan parameters are determined such that the producer's risk and the consumer's risk are satisfied at the specified median life. Extensive tables showing plan parameters are provided at various values of the experiment time and the consumer's risk for each of three distributions for the practical use. Some examples are given to illustrate the procedure of the proposed plan.