Testing exponentiality against renewal new better than used in Laplace transform order: applications in reliability

Mahmoud, M. A. W.; Diab, L. S.; Radi, Davide

doi:10.1186/s42787-019-0044-7

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…Suppose that the following random sample 𝑋 1 , 𝑋 2 , … , 𝑋 𝑛 was taken from 𝐹 to apply this non-parametric testing. Several authors have introduced non-parametric hypothesis testing for a variety of life distributions (Bakr et al, 17 Mansour, 18 Abu-Youssef and El-Toony, 19 EL-Sagheer et al 20 and Mahmoud et al 21 From (1.1), The measure of departure can be written as: (assume that 𝜇 is equal one):…”

Section: Complete Data Testingmentioning

confidence: 99%

“…Several authors have introduced non‐parametric hypothesis testing for a variety of life distributions (Bakr et al., 17 Mansour, 18 Abu‐Youssef and El‐Toony, 19 EL‐Sagheer et al 20 . and Mahmoud et al 21 . From (1.1), The measure of departure can be written as: (assume that μ is equal one):

\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{\mathrm{\delta \;}}\left( {\mathrm{s}} \right) = \;\mathop \int \limits_0^\infty \mathop \int \limits_0^\infty \left( {{\mathrm{\bar F}}\left( {\mathrm{t}} \right){{\mathrm{e}}^{ - \frac{x}{{{\mu}}}}} - {\mathrm{\bar F}}\left( {x + {\mathrm{t}}} \right)} \right){e^{ - st}}dxdt}\\[16pt] { = \frac{1}{{{{\mathrm{s}}^2}}}\;\left( {\left( {1 + s} \right)\left( {1 - E\left( {{e^{ - sx}}} \right)} \right) - s{{\mu}}} \right)} \end{array} \end{equation}

…”

Section: Complete Data Testingmentioning

confidence: 99%

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On basic life testing issues in medical research using non‐parametric hypothesis testing

Bakr

2023

Quality & Reliability Eng

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The probability life distributions usually describe the time to event or survival time. Therefore, these life distributions play a crucial role in the analysis and projection of the maximum life expectancy using the Laplace transform technique for nonparametric hypothesis testing. A flexible framework for monitoring randomized clinical trials utilizing prior knowledge of certain phenomena under uncertainty is provided by the Laplace transform. By considering the previous data, medical professionals can also utilize these estimators to calculate the chance of tumor recurrence, cardiovascular death, and AIDS for HIV patients. However, censoring occurs in clinical trials and medical studies when the precise event's time of occurrence is unknown. The present study aims to propose a new test for exponential better than used (EBU). The suggested statistical test's efficiency and critical values are computed and compared with those of previous classes. Furthermore, the suggested test statistic is provided in bivariate form as well. Finally, the methodology is then tested using medical data in order to provide evidence that it is applied efficiently.

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Section: Complete Data Testingmentioning

confidence: 99%

\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{\mathrm{\delta \;}}\left( {\mathrm{s}} \right) = \;\mathop \int \limits_0^\infty \mathop \int \limits_0^\infty \left( {{\mathrm{\bar F}}\left( {\mathrm{t}} \right){{\mathrm{e}}^{ - \frac{x}{{{\mu}}}}} - {\mathrm{\bar F}}\left( {x + {\mathrm{t}}} \right)} \right){e^{ - st}}dxdt}\\[16pt] { = \frac{1}{{{{\mathrm{s}}^2}}}\;\left( {\left( {1 + s} \right)\left( {1 - E\left( {{e^{ - sx}}} \right)} \right) - s{{\mu}}} \right)} \end{array} \end{equation}

…”

Section: Complete Data Testingmentioning

confidence: 99%

On basic life testing issues in medical research using non‐parametric hypothesis testing

Bakr

2023

Quality & Reliability Eng

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“…Here, we create a test statistic to test if H 0 : F is exponential, against H 1 : F is UBA mgf . Nonparametric testing for classes of life distributions has been considered by many authors (see Abu-Youssef et al [ 16 , 18 ] and Mahmoud et al [ 19 ].…”

Section: The Statistic Testsmentioning

confidence: 99%

“…Take a look at the findings of Table 5 Mahmoud et al; see [ 19 ]. The year-ordered values are as follows.…”

Section: Applicationsmentioning

confidence: 99%

Statistical Modeling of Some Cancerous Diseases Using the Laplace Transform Approach of Basic Life Testing Issues

Bakr

Al-Babtain

Khosa

2022

Computational and Mathematical Methods in Medicine

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The purpose of the nonparametric statistical test used in this study is to compare different treatment options by looking at failure behavior in recorded survival data. Patients’ survival times are documented after using the proposed approach. The observed data’s behavior was assumed to be based on used better than aged in the moment generating function order (UBAmgf) characteristic or a constant failure rate in this study (exponential scenario). Suppose that the survival data is UBAmgf, then the treatment or the machine or system in use produces a better or a higher expected total present value than an older machine governed by an exponential survival function; if the data is exponential, the suggested treatment strategy is ineffective (the recommended treatment approach has neither positive or negative effects on the patients). To guarantee that the suggested statistical test is used correctly, the efficiency and critical values are calculated and compared to those of other tests, and the technique is then applied to medical data.

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“…Abu-Youssef et al [15] for used better than aged in increasing concave ordering (UBAC(2)) class. Mahmoud et al [16,17] for new better than renewal used in Laplace transform (NBRUL) class.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2022

Appl. Math. Inf. Sci.

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In this paper, we investigate the probabilistic characteristics for new better than renewal used in Laplace transform in increasing convex order class, the closure properties under various reliability operations such as convolution, mixture, homogeneous Poisson shock model are studied. A new hypothesis test is constructed to test exponentiality against, based on U-statistic. Pitman's asymptptic efficiency of the test are studied and compared with other tests. The percentiles of this test statistic are tabulated and the power of the new test statistics are calculated in case of censored and non-censored data. Finally, the right-censored data problem is given in some medical and engineering science applications to evaluate the performances of our test.

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Testing exponentiality against renewal new better than used in Laplace transform order: applications in reliability

Cited by 7 publications

References 15 publications

On basic life testing issues in medical research using non‐parametric hypothesis testing

On basic life testing issues in medical research using non‐parametric hypothesis testing

Statistical Modeling of Some Cancerous Diseases Using the Laplace Transform Approach of Basic Life Testing Issues

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