Assessing the lifetime performance index for Kumaraswamy distribution under first‐failure progressive censoring scheme for ball bearing revolutions

El-Monsef, M. E. Abd; Hassanein, W. A.

doi:10.1002/qre.2616

Cited by 11 publications

(9 citation statements)

References 20 publications

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“…It is well-known that the Bayes estimator δ𝐵𝑆 for the parameter 𝜃 under the squared error (SE) loss function 𝐿(𝛿, 𝜃) = (𝛿 − 𝜃) 2 is the mean of the posterior density of 𝜃. It follows that the Bayes estimate of 𝐶 𝐿 under the SE loss function, from Equations ( 5), (11) , and (12), is obtained as…”

Section: Point Estimationmentioning

confidence: 99%

“…Recently, Ahmadi and Doostparast 9 studied the statistical inferences about

C_L

on the basis of the progressively first‐failure censored data coming from a Pareto distribution with known scale parameter. Also, see Lee, 10 Wu and Hsieh, 11 Abd El‐Monsef and Hassanein 12 and Mahmoud et al. 13 …”

Section: Introductionmentioning

confidence: 98%

“…Recently, Ahmadi and Doostparast 9 studied the statistical inferences about 𝐶 𝐿 on the basis of the progressively first-failure censored data coming from a Pareto distribution with known scale parameter. Also, see Lee, 10 Wu and Hsieh, 11 Abd El-Monsef and Hassanein 12 and Mahmoud et al 13 It is known that the lifetime of industrial products have inherent stochastic behavior. In this paper, we consider the Pareto distribution as a probabilistic model for the lifetime of products.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

Ahmadi

Doostparast

2021

Quality & Reliability Eng

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Process capability indices has been widely applied in industry to assess the performance of industrial processes. For the larger‐the‐better lifetimes of products, the lifetime performance index CL$C_L$ is commonly considered by industrial managers. This paper confines itself to the the Bayesian statistical inferences about CL$C_L$ under the Pareto distribution with the progressively Type‐II censored samples. The Bayesian inferences are based on a conjugate continuous prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are given to demonstrate the sensitivity of results to the prior hyperparameters and the underlying distribution of the observations. Finally, a Monte Carlo simulation study is done to evaluate the behavior of the lifetime performance index CL$C_L$.

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Section: Point Estimationmentioning

confidence: 99%

“…Recently, Ahmadi and Doostparast 9 studied the statistical inferences about

C_L

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

Ahmadi

Doostparast

2021

Quality & Reliability Eng

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“…Improper use of these PCI‐based sampling methods might lead to misjudgments in applications. According to Epstein and Sobel, 15 Meyer, 16 Anderson et al., 17 Keller et al., 18 Abd and Hassanein, 19 Chakrabarty et al., 20 Johnen et al., 21 Lee et al., 22 and Limon et al., 23 the lifetime of parts and products usually follows an exponential distribution, gamma distribution, or Weibull distribution. Because the lifetime of a product is a longer‐the‐better type of quality characteristic, Montgomery 24 recommended the use of lifetime performance index (LPI)

{C_L}

to measure the lifetime performance of electronic products.…”

Section: Introductionmentioning

confidence: 99%

A repetitive group sampling plan based on the lifetime performance index under gamma distribution

Lee

Liu

2022

Quality & Reliability Eng

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As technology and living standards improve, people are becoming more concerned with the importance of quality. Quality, thus, becomes the key to company competitiveness, and process capability indices (PCIs) are effective means of measuring process performance. Most PCIs have been developed under the assumption that the quality characteristics are normally distributed; however, the lifetime of products generally possesses a non‐normal distribution. A lifetime performance index (LPI) CL has been proposed and used for measuring product lifetime performance. In this high‐quality era, the use of traditional testing methods incurs very high costs, so acceptance sampling plans have been widely used by industry to perform the inspection. This study considers the product lifetime with a gamma distribution and uses the uniformly minimum‐variance unbiased estimator (UMVUE) of the LPI to develop a repetitive group sampling plan (RGSP). For the practical purpose, this study presents a step‐by‐step procedure and tabulates the plan parameters for various combinations of acceptable and rejectable quality levels, producer's and consumer's risks, and shape parameter. Thus, practitioners can easily know the sample size and the corresponding critical values for decision making. This study also uses the results of the proposed plan to compare with the single sampling plan. Lastly, a practical example is used to illustrate how to apply this acceptance sampling plan.

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“…Therefore, Kumaraswamy distribution is considered as a substitutive model for Beta distribution in practical terms. For instance, Kumaraswamy distribution has an outstanding fitting effect on daily rainfall, individual heights, unemployment numbers, and ball bearing revolutions (see [3][4][5][6]).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inference for the Parameters of Kumaraswamy Distribution via Ranked Set Sampling

Jiang

Gui

2021

Symmetry

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In this paper, we address the estimation of the parameters for a two-parameter Kumaraswamy distribution by using the maximum likelihood and Bayesian methods based on simple random sampling, ranked set sampling, and maximum ranked set sampling with unequal samples. The Bayes loss functions used are symmetric and asymmetric. The Metropolis-Hastings-within-Gibbs algorithm was employed to calculate the Bayes point estimates and credible intervals. We illustrate a simulation experiment to compare the implications of the proposed point estimators in sense of bias, estimated risk, and relative efficiency as well as evaluate the interval estimators in terms of average confidence interval length and coverage percentage. Finally, a real-life example and remarks are presented.

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Assessing the lifetime performance index for Kumaraswamy distribution under first‐failure progressive censoring scheme for ball bearing revolutions

Cited by 11 publications

References 20 publications

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

A repetitive group sampling plan based on the lifetime performance index under gamma distribution

Bayesian Inference for the Parameters of Kumaraswamy Distribution via Ranked Set Sampling

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