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Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution

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Abstract

This paper is devoted to estimating the reliability of a multi-component stress–strength model in an s-out-m (\(s \le m\)) system under progressively type-II censored modified Weibull data. This type of systems functions only if at least s out of m strengths exceed the stress. Maximum likelihood and Bayes estimators of the stress–strength reliability based on conjugate prior are obtained. The associated confidence and credible intervals are also developed. The Lindley’s approximation and Markov chain Monte Carlo methods are used to compute approximate Bayes estimates. Two real data sets representing the excessive drought of Shasta Reservoir in California, USA and failure times of software model are analyzed for illustrative purposes. Further, Monte Carlo simulations are performed to compare the so developed estimates.

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Abbreviations

AD:

Anderson−Darling

ACF:

Autocorrelation function

CDF:

Cumulative distribution function

CI:

Confidence interval

CM:

Cram\(\acute{\mathrm {e}}\)r-von Mises

CP:

Coverage probability

CS:

Censoring scheme

iid:

Independent and identically distributed

KS:

Kolmogorov–Smirnov

KME:

Kaplan and Meier estimator

MCMC:

Markov chain Monte Carlo

MLE:

Maximum likelihood estimator

MW:

Modified Weibull

PDF:

Probability density function

r.v.’s:

Random variables

SEL:

Symmetric error loss

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Acknowledgements

We would like to appreciate the constructive comments by an associate editor and two anonymous referees which improved the quality and the presentation of our results.

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Authors and Affiliations

  1. Department of Mathematics, Al-Azhar University, Nasr City, Cairo, 11884, Egypt

    M. S. Kotb

  2. Department of Mathematics, Albaha University, Albaha, Saudi Arabia

    M. S. Kotb

  3. Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

    M. Z. Raqab

  4. King Abdulaziz University, Jeddah, Saudi Arabia

    M. Z. Raqab

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  1. M. S. Kotb
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  2. M. Z. Raqab
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Correspondence to M. S. Kotb.

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Kotb, M.S., Raqab, M.Z. Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution. Stat Papers 62, 2763–2797 (2021). https://doi.org/10.1007/s00362-020-01213-0

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