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Optimum plan and statistical inference for step-stress models based on censored samples

Optimum plan and statistical inference for step-stress models based on censored samples
Optimum plan and statistical inference for step-stress models based on censored samples
In lifetime data analysis, life testing for items under normal use conditions can often take a long time to obtain a reasonable number of failures. In this situation, accelerated life test (ALT) procedures are performed in order to obtain failure time data in a shorter time. In the step-stress accelerated life test (SSALT), which is a special class of ALT, the stress setting for survival units is changed step by step to higher stress levels at predetermined times during the experiment. In this way, information about the parameters of the life distribution is obtained quicker than would be possible under normal operating conditions. The censoring methodology is commonly used in planning the ALTs to reduce the cost and test time. Statistical inference of model parameters and optimum test plans are two main aspects in the SSALT studies. The main objectives of this thesis are to develop an optimal design for a simple SSALT model and to make statistical inferences for a simple SSALT model based on progressive type-II censoring schemes. It is assumed that the lifetimes at each stress level follow the generalized exponential distribution (GED) and a cumulative exposure model is assumed as a life-stress model. The study also compares the total test time of censored samples with complete samples. The maximum likelihood method is used to estimate three unknown parameters of the cumulative exposure model. Also, the asymptotic confidence intervals (CIs) for the parameters based on the observed Fisher information matrix are derived. Moreover, the bootstrap approach is used to obtain the CIs for the model parameters using two methods, percentile and bias-corrected and accelerated. The steps of obtaining asymptotic and bootstrap CIs based on two bootstrap methods are described. In ALT design, the optimal stress change time and optimal censoring schemes under the variance (V)-optimality criterion are studied in detail to provide the most precise estimates of percentile lifetime under the GED at the usage stress level. The optimal design is studied based on minimizing the asymptotic variance of the maximum likelihood estimate (MLE) of the 100p^thpercentile lifetime under the GED at the usage stress level. Different progressive censoring schemes are compared to find the optimal censoring scheme. Extensive simulation studies are conducted to investigate and compare the performance of the MLEs and CIs with associated precision for different values of sample size, failure percentage, stress change time and progressive censoring schemes using the Monte Carlo simulation technique. Also, numerical analysis is performed using the golden section search method to estimate the locally optimal stress change time. In addition, the optimal censoring scheme is also obtained and compared with the worst censoring scheme and the complete sample using relative efficiency and relative time.
University of Southampton
Mominkhan, Mariam Mohammed
da541607-6952-422d-9ee6-18bb493109f8
Mominkhan, Mariam Mohammed
da541607-6952-422d-9ee6-18bb493109f8
Overstall, Antony
c1d6c8bd-1c5f-49ee-a845-ec9ec7b20910
Kimber, Alan
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Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039

Mominkhan, Mariam Mohammed (2024) Optimum plan and statistical inference for step-stress models based on censored samples. University of Southampton, Doctoral Thesis, 190pp.

Record type: Thesis (Doctoral)

Abstract

In lifetime data analysis, life testing for items under normal use conditions can often take a long time to obtain a reasonable number of failures. In this situation, accelerated life test (ALT) procedures are performed in order to obtain failure time data in a shorter time. In the step-stress accelerated life test (SSALT), which is a special class of ALT, the stress setting for survival units is changed step by step to higher stress levels at predetermined times during the experiment. In this way, information about the parameters of the life distribution is obtained quicker than would be possible under normal operating conditions. The censoring methodology is commonly used in planning the ALTs to reduce the cost and test time. Statistical inference of model parameters and optimum test plans are two main aspects in the SSALT studies. The main objectives of this thesis are to develop an optimal design for a simple SSALT model and to make statistical inferences for a simple SSALT model based on progressive type-II censoring schemes. It is assumed that the lifetimes at each stress level follow the generalized exponential distribution (GED) and a cumulative exposure model is assumed as a life-stress model. The study also compares the total test time of censored samples with complete samples. The maximum likelihood method is used to estimate three unknown parameters of the cumulative exposure model. Also, the asymptotic confidence intervals (CIs) for the parameters based on the observed Fisher information matrix are derived. Moreover, the bootstrap approach is used to obtain the CIs for the model parameters using two methods, percentile and bias-corrected and accelerated. The steps of obtaining asymptotic and bootstrap CIs based on two bootstrap methods are described. In ALT design, the optimal stress change time and optimal censoring schemes under the variance (V)-optimality criterion are studied in detail to provide the most precise estimates of percentile lifetime under the GED at the usage stress level. The optimal design is studied based on minimizing the asymptotic variance of the maximum likelihood estimate (MLE) of the 100p^thpercentile lifetime under the GED at the usage stress level. Different progressive censoring schemes are compared to find the optimal censoring scheme. Extensive simulation studies are conducted to investigate and compare the performance of the MLEs and CIs with associated precision for different values of sample size, failure percentage, stress change time and progressive censoring schemes using the Monte Carlo simulation technique. Also, numerical analysis is performed using the golden section search method to estimate the locally optimal stress change time. In addition, the optimal censoring scheme is also obtained and compared with the worst censoring scheme and the complete sample using relative efficiency and relative time.

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More information

Submitted date: October 2023
Published date: April 2024

Identifiers

Local EPrints ID: 488845
URI: http://eprints.soton.ac.uk/id/eprint/488845
PURE UUID: d07c34af-e339-46a1-bacc-dbe58b38b661
ORCID for Antony Overstall: ORCID iD orcid.org/0000-0003-0638-8635
ORCID for Stefanie Biedermann: ORCID iD orcid.org/0000-0001-8900-8268

Catalogue record

Date deposited: 08 Apr 2024 16:41
Last modified: 22 May 2024 01:40

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Contributors

Author: Mariam Mohammed Mominkhan
Thesis advisor: Antony Overstall ORCID iD
Thesis advisor: Alan Kimber
Thesis advisor: Stefanie Biedermann ORCID iD

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