One-Sided β-Content Tolerance Factors for the Two Parameter Exponential Distribution

Guenther, William C.; Patil, S. A.; Uppuluri, V. R. R.

doi:10.2307/1268742

Cited by 23 publications

(22 citation statements)

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“…Notice that this is just a shifted version of the exponential distribution. Dunsmore (1978) and Guenther, Patil, and Uppuluri (1976) both discuss 2-parameter exponential tolerance intervals and the estimation procedure in greater detail. Engelhardt and Bain (1978) discusses how to modify the formulas when dealing with type II censored data.…”

Section: (2-parameter) Exponential Tolerance Intervalsmentioning

confidence: 99%

“…Evaluation of a 95%/90% upper 2-parameter exponential tolerance interval is found by implementing the exp2tol.int function: Note that the exp2tol.int function contains the argument method, which allows the user to specify which way to estimate k 2 . The two options are "GPU" (see Guenther et al 1976) and "DUN" (see Dunsmore 1978), where the latter has been shown to yield slightly improved estimates for n ≥ 8. Also note in the code above that the data was simulated using the function r2exp, which performs random generation from the 2-parameter exponential distribution.…”

Section: (2-parameter) Exponential Tolerance Intervalsmentioning

confidence: 99%

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tolerance: AnRPackage for Estimating Tolerance Intervals

Young¹

2010

J. Stat. Soft.

121

108

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The tolerance package for R provides a set of functions for estimating and plotting tolerance limits. This package provides a wide-range of functions for estimating discrete and continuous tolerance intervals as well as for estimating regression tolerance intervals. An additional tool of the tolerance package is the plotting capability for the univariate and regression settings as well as for the multivariate normal setting. The tolerance package's capabilities are illustrated using simulated data sets. Formulas used for the estimation procedures are also presented.

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Section: (2-parameter) Exponential Tolerance Intervalsmentioning

confidence: 99%

Section: (2-parameter) Exponential Tolerance Intervalsmentioning

confidence: 99%

tolerance: AnRPackage for Estimating Tolerance Intervals

Young¹

2010

J. Stat. Soft.

121

108

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“…It is well known that and independently. These results have been used by Guenther et al [4] to compute onesided tolerance factors in the case of the two-parameter exponential distribution.…”

Section: Preliminariesmentioning

confidence: 99%

One‐ and two‐sided sampling plans based on the exponential distribution

Kocherlakota

1986

Naval Research Logistics

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In this paper we examine the one-and two-sided sampling plans for the exponential distribution. Solutions are provided for several situations arising out of the assumptions on the knowledge of the parameters of the distribution. The values of the constants are tabled in the special case of p , = p 2 for the two-sided plans. PRELIMINARIESLet X have the two-parameter exponential distributionHere p is the location parameter (guarantee period) and u is the scale parameter (measuring the mean life). The maximum likelihood estimates of p and u are . n where X,,, < X ( z , < ... < X(,,) are the order statistics based on the random sample X , , . . . ,Xn from this population. It is well known that and independently. These results have been used by Guenther et al.[4] to compute onesided tolerance factors in the case of the two-parameter exponential distribution.While acceptance sampling plans for the normal distribution have received extensive attention (Owen [7]), little work has been done in the non-normal case. The present authors [5] have considered problems relating to the mixtures of normal populations. They have also suggested the use of robust estimators in symmetric distribution [ 5 ] . Rao et al. [lo] have examined the effects of non-normality on the tolerance limits based on samples from the Edgeworth series distribution. Owen [8] has given an excellent discussion of these problems relating to non-normality in acceptance sampling plans.

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“…From an economic point of view, the decision approach is probably a more scientific method since the sampling plan is determined by making an optimal decision on the basis of some economic considerations such as maximizing the return or minimizing the loss. Therefore, this method is widely used by many statisticians (see, e.g., Hald [7,8], Wetherill and Campling [23], Fertig and Mann [5], Wetherill and Köllerström [24], Guenther, Patil, and Uppuluri [6], Thyregod [21] Lam [13] and Hamilton and Lesperance [11]). …”

Section: Introductionmentioning

confidence: 99%

Designing acceptance sampling schemes for life testing with mixed censoring

Chen

Chou

et al. 2004

Naval Research Logistics

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Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time-consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed.

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One-Sided β-Content Tolerance Factors for the Two Parameter Exponential Distribution

Cited by 23 publications

References 0 publications

tolerance: AnRPackage for Estimating Tolerance Intervals

tolerance: AnRPackage for Estimating Tolerance Intervals

One‐ and two‐sided sampling plans based on the exponential distribution

Designing acceptance sampling schemes for life testing with mixed censoring

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