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Statistical inference for a step-stress partially-accelerated life test model with an adaptive Type-I progressively hybrid censored data from Weibull distribution

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Abstract

In this paper, a new censoring scheme, namely, adaptive Type-I progressively hybrid censoring scheme under a step-stress partially accelerated test model is introduced. It has some advantages over the progressively hybrid censoring schemes already discussed in the literature. Based on this censoring scheme, the maximum likelihood estimations of Weibull distribution parameters and the acceleration factor are considered. The biases and mean squared errors of the maximum likelihood estimators of the model parameters are computed to evaluate their performances in the presence of censoring scheme developed in this paper through a Monte Carlo simulation study. The results obtained under the adaptive Type-I progressively hybrid censoring scheme are compared with those produced under the non-adaptive Type-I progressively hybrid censoring scheme using three different progressive censoring schemes. Moreover, the confidence intervals lengths and their associated coverage probabilities are obtained for both adaptive and non-adaptive Type-I progressively hybrid censoring scheme. In addition, Optimum test plans are also developed to improve/guarantee the quality of the statistical inference.

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Abbreviations

ALT:

Accelerated life test

PALT:

Partially accelerated life test

SSPALT:

Step-stress partially accelerated life test

WD:

Weibull distribution

MLEs:

Maximum likelihood estimates/estimators

pdf:

Probability density function

MSEs:

Mean squared errors

MTTF:

Mean time to failure

\(n\) :

Sample size (total number of test units in a SSPALT)

\(n_{u}\) :

Number of failed units at use condition

\(n_{a}\) :

Number of failed units at accelerated condition

\(m\) :

A pre-specified number of failures

\(\eta \) :

A pre-specified censoring time

\(k\) :

Number of failures occurred before time \(\eta \) (\(k\) is random)

\(y_{i}\) :

Observed lifetime of unit \(i\) tested under SSPALT

\(\tau \) :

Stress-change time

\(R_{i}\) :

Number of removed units at the ith failure

\(\wedge \) :

Denotes maximum likelihood estimate

\(\alpha \) :

WD shape parameter (\(\alpha >\) 0)

\(\lambda \) :

WD scale parameter (\(\lambda >\) 0)

\(\beta \) :

Acceleration factor (\(\beta >\)1)

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Acknowledgments

This project was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    Ali A. Ismail

  2. Department of Statistics, Faculty of Economics & Political Science, Cairo University, Orman, Giza, 12613, Egypt

    Ali A. Ismail

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  1. Ali A. Ismail
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Ismail, A.A. Statistical inference for a step-stress partially-accelerated life test model with an adaptive Type-I progressively hybrid censored data from Weibull distribution. Stat Papers 57, 271–301 (2016). https://doi.org/10.1007/s00362-014-0639-x

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  • DOI: https://doi.org/10.1007/s00362-014-0639-x

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