摘要:

This study examines and develops new techniques for analyzing life test data. It obtains estimates for the life distribution in the use environment on based data from both the use and the accelerated environments. The techniques require only physically plausible assumptions, not the usual ones involving specification of a family of parametric probability distributions. Procedures are given for testing those assumptions that are made.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488761

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Suppose thatf(t; θ) is the density function of the time to failure random variable of a device under an environment defined by a vector of generalized stressesS. It is desired to predict θu, the value of θ at some low values of .the stress, saySu. The elements of θ are re-parameterized as a function ofS, such that θj=fi(S;aj), wherefjare known functions and the ai are unknown. Life tests are conducted atkdifferent accelerated values ofS,Si(i= 1, 2, …k), and estimates of the elements of θ, θji, are obtained from item censored samples. These estimates are then used to obtain point and interval estimates ofai, using either the method of least squares, or the method of maximum likelihood. Having obtained the estimates ofai, an inference about θu, can be made. Some problems in obtaining the least squares estimates ofaiare pointed out in this paper. To illustrate this, an unrealistic but simple case is treated and discussed in this paper. It is assumed thatf(t; θ) = λ exp (—λt), and that λi=BVi, where λiis the hazard rate under an environmentVi, andBis unknown. A weighted least squares estimator forBis obtained, and it is shown that asymptotically this estimator converges in distribution to that of a unit normal. The maximum likelihood estimator forBis shown to have an inverted gamma dist.ribution. Properties of the estimator of λuare discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488762

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this paper we consider the method of Johns and Lieberman (1966) for estimating the shape and the log of the scale parameters of the two parameter Weibull distribution. The estimates are linear, asymptotically jointly normal and efficient. The main thrust of the paper is that unlike most linear estimating procedures of the Weibull parameters, that require different sets (tables) of weights for the observations for each size and often for each different number of observations from the sample that are available, the present technique requires only the knowledge of the proportion of observations from the sample available for the estimates. Given this proportion and four numbers obtained from a table look-up, the weights of the observations are then expressible in simple closed forms. Further we include a simple scheme to update the estimates when more observations become available. Finally, small sample computations of mean squared errors indicate that these estimates compare very Pdvorably even here with other well known linear estimating procedures.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488763

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

LetX(1), …,X(k)be the firstkordered observations of a sample of sizemfrom the distribution with p.d.f.f(x; β1, θ) = (1/θ) exp [-(x– β1)/θ] forx≥ β1≥ 0, θ > 0 and zero elsewhere (2 ≤k≤m); letY(i), …,Y(l)be the firstlordered observations of a sample of sizenfrom the distribution with p.d.f.g(y; β2, θ) = (1/θ) exp [—(y– β2)/θ] fory≥ β2≥ 0, θ > 0 and zero elsewhere (2 ≤l≤n). It is assumed that θ is unknown. A test based on (X(1), …,X(k),Y(1), …,Y(l)) is proposed for the null hypothesis β1= β2against the alternative β1≠ β2. The distribution of the test statistic under the null hypothesis is derived. The significance points for various values ofk,I,m,nare tabulated for (α = .05 and .Ol.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488764

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The small sample performance of the bivariate two-sample Wilcoxon type rank sum testWis studied by Monte Carlo evaluation of power under shift alternatives in the bivariate normal distribution. Two types of alternatives are considered: (a) shift in only one coordinate and (b) equal amounts of shifts in both coordinates. The estimated power of theWtest is compared with the power of Hotelling'sT2test. Interestingly, it is found that the empirical power ofWsubstantially exceeds the power ofT2for some normal shift alternatives although the latter is the uniformly most powerful invariant test for the problem.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488765

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

It is noted that the Barlow-Scheuer estimation scheme is incomplete. The case in which all trials of a stage result in inherent failures is not covered. It is shown that the question is indeterminate in general. A policy to handle this case is proposed.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488766

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488767

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488768

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488769

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488771

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor