摘要:

There are given k Poisson processes with parameters (rates of occurrence) λ1, …, λk. Let λ(1)≤ λ(2)≤ … ≤ λ(k)denote the ordered set of values of the parameters. A procedure is given for selecting the process corresponding to λ(k)and estimating its parameter (λ(k)). The given procedure controls the joint risk of improper selection and of large error in the estimate. Let θ > 1 and 0 < α, β < 1 be given numbers, and let δ denote the estimate of λ(k). The joint probability that a correct selection is made and that |(δ/λ(k)) − 1| ≤ α is at least as large as β, for (λ(k)/λ(k−1)) ≥ θ. Two cases are considered, that is, when the processes are observed continuously in time, and when they are observed at successive intervals of time. Both the cases lead to the same theoretical results.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489113

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Several zone tests for quality-control charts are considered. One test calls for initiating a search for an assignable cause whenevernout ofNconsecutive points fall in some predetermined warning zone. An algorithm is given for obtaining the average-run-length of this procedure; and several alternative procedures, for which the average-run-lengths are explicitly given, are suggested. Also, a simple means is given for finding the average-run-length of procedures that combine a zone test with the standard 3σ-limit.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489114

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

TheWtransformation, a matrix transformation, is developed and applied for the mixed analysis of variance model to compute maximum likelihood estimates of the variance components and fixed parameters. This transformation not only eliminates the need for the explicit computation of then×ninverse matrix H−lbut permits handling the iterative calculations such that they do not depend uponn(the number of observations) in any way. Although not wedded to a particular numerical method, theWtransformation is implemented in conjunction with a modified Newton-Raphson method in which variance components are restricted to being non-negative.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489115

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

A modification of the “V”' mask control scheme for cusum charts is proposed. In this modified scheme, a parabolic section is included in the mask to provide better performance when the process undergoes a large change in the mean from goal conditions, It is shown that the modified “V” mask can be implemented either in conventional graphic form, or in an algorithmic form suitable for a digital computer. Average run lengths are given for a typical range of circumstances.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489116

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

As a practical solution to the estimation problem. it is suggested that the m.v.u.e. be calculated, and if this estimate is between 0.01 and 0.25, it should be replaced with the m.l.e. This combined estimator is shown to be nearly as efficient as the better of the m.v.u.e. and m.l.e. throughout the domain ofF(x).

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489117

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

The problem of estimatingY(1), the smallest of a future sample ofkobservations from the Weibull distribution, based on an observed sample from the same distribution, is considered. A conditional confidence interval solution is proposed for the estimation ofY(1). The results have direct application in reliability theory, where the time until the first failure in a group ofkitems in service provides a measure of assurance regarding the operation of the items.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489118

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

For combinations of parameter values ordinarily encountered in life testing and reliability data, the similarity of the Weibull with the Pearson Type III (gamma) distri-bution is well known. When the Weibull distribution is reflected about the vertical axisx= γ, we obtain a version with cumulative probability function

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489119

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489120

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Analytical and Monte Carlo results are used to investigate the robustness of the exact statistical test suggested by Nelson for testing the hypothesis of equality of two availabilities. A non-parametric test based on a generalized U-statistic is proposed which does not depend on the assumption that the times to failure and times to repair are exponentially distributed. Additional Monte Carlo results are used to point out the strengths and weaknesses of this test.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489121

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor

摘要:

Factors for constructing one-sided prediction intervals to containkout ofmfuture observations from normal and exponential populations are presented. An application involving prediction intervals is also given.

ISSN:0040-1706    

DOI:10.1080/00401706.1973.10489122

出版商:Taylor & Francis Group    

年代:1973

数据来源: Taylor