A New Decision Theoretic Sampling Plan for Type-I and Type-I Hybrid Censored Samples from the Exponential Distribution

Prajapati, Deepak; Mitra, Sharmistha; Kundu, Debasis

doi:10.1007/s13571-018-0167-0

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…In the literature, the quadratic loss function is the most popular one and is widely used to obtain the optimal sampling plan. Some key references are Lam, 4 Lin et al, 14 Chen et al, 7 Lin et al, 5 Liang et al, 15 Prajapati et al 12,13 Most of the authors consider the quadratic loss function to obtain an optimal sampling plan because of computational simplicity. Due to analytical tractability of the BJPC scheme, we are able to consider more general loss function capturing different aspects of the sampling plan.…”

Section: Model Construction and Assumptionsmentioning

confidence: 99%

“…Since n and k can take only integers values, similar algorithm which is proposed by Lam 4 and Prajapati et al 12,13 can be adopted to obtain the optimal DSP by minimizing the Bayes risk.…”

Section: Bayes Risk Of the Dsp Under The Bjpc Scheme And The Optimal Dspmentioning

confidence: 99%

“…These shrinkage estimators will exist even when no failure is observed from any one of the two samples. In the decision‐theoretic approach, this kind of shrinkage estimators are studied in Prajapati et al 12,13 We consider a very general loss function which contains the sampling cost, the cost per unit time of the experiment, the salvage value, the loss due to decision along with the precision of the shrinkage estimators. Due to analytical tractability of the BJPC scheme, the Bayes risk can be obtained in a simpler form under the assumption that the lifetime distributions are exponential.…”

Section: Introductionmentioning

confidence: 99%

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Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

Prajapati

Mondal

Kundu

2020

Appl Stoch Models Bus & Ind

Self Cite

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In statistical quality control, decision‐theoretic approach draws a significant amount of attention due to its economic considerations. In reliability life testing, decision‐theoretic approach has been used quite extensively under different censoring schemes. All these implementations are based on single sample of products coming from a particular source. In this work we study decision‐theoretic approach on two sample of products coming from two different sources under a joint censoring scheme when the life times are exponentially distributed. The major advantage of such implementation is to take decision on the acceptance or rejection of one or both the batches in a single life testing experiment. Decision making is performed based on minimizing the Bayes risk with respect to a given loss function. It is observed that under certain set‐ups, the joint censoring scheme is preferable over the two separate single sample censoring schemes in decision making.

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Section: Model Construction and Assumptionsmentioning

confidence: 99%

“…Since n and k can take only integers values, similar algorithm which is proposed by Lam 4 and Prajapati et al 12,13 can be adopted to obtain the optimal DSP by minimizing the Bayes risk.…”

Section: Bayes Risk Of the Dsp Under The Bjpc Scheme And The Optimal Dspmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

Prajapati

Mondal

Kundu

2020

Appl Stoch Models Bus & Ind

Self Cite

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“…Bartholomew (1957) [9] mentioned some problems and solutions that may arise during life testing. The exponential distribution is one of the widely used distributions for modeling life in reliability theory and practical reliability engineering [10].Many useful results on exponential distribution can be found in Balakrishnan and Basu (1995) [11]. The problem of estimating the problem of estimating the mean of the exponential distribution is very important and different maximum likelihood estimates exist depending on the truncated sample.…”

Section: Introductionmentioning

confidence: 99%

Order-preserving Property of One-parameter Expo nential Distribution MLE under Type-I Censoring

Liu,

Ren,

Bingliang

et al. 2023

Preprint

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Many researchers have studied various properties of maximum likelihood estimators as well as estimators for truncated samples.However,the order preserving properties of maximum likelihood estimation for censored samples have not been studied in the literature. This is precisely the subject of this paper. In this paper, we derive general necessary conditions under which the MLE has the general necessary conditions. In particular, the paper obtains conditions under which the one-parameter exponential, location, and scale families satisfy the order preserving property.

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“…The exponential distribution and its generalizations play an important role in many areas of science, including physics, chemistry, medical sciences and reliability engineering (see e.g. [1,2,16,19]). Dombi et al [6] introduced the epsilon distribution, which may be treated as an alternative to the exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

The Inverse Epsilon Distribution as an Alternative to Inverse Exponential Distribution with a Survival Times Data Example

et al. 2022

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This paper is devoted to a new flexible two-parameter lower-truncated distribution, which is based on the inversion of the so-called epsilon distribution. It is called the inverse epsilon distribution. In some senses, it can be viewed as an alternative to the inverse exponential distribution, which has many applications in reliability theory and biology. Diverse properties of the new lower-truncated distribution are derived including relations with existing distributions, hazard and reliability functions, survival and reverse hazard rate functions, stochastic ordering, quantile function with related skewness and kurtosis measures, and moments. A demonstrative survival times data example is used to show the applicability of the new model.

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A New Decision Theoretic Sampling Plan for Type-I and Type-I Hybrid Censored Samples from the Exponential Distribution

Cited by 11 publications

References 12 publications

Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

Optimal decision‐theoretic sampling plan for two exponential distributions under joint censoring scheme

Order-preserving Property of One-parameter Expo nential Distribution MLE under Type-I Censoring

The Inverse Epsilon Distribution as an Alternative to Inverse Exponential Distribution with a Survival Times Data Example

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