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Document Type |
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Thesis |
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Document Title |
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Planning Step Stress Accelerated Life Tests for Generalized Exponential Lifetime Model with Censoring دراسة الضغط المرحلي لإختبارات الحياة المعجلة للتوزيع الأسي العام للعينات المراقبة |
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Subject |
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Statistics department |
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Document Language |
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Arabic |
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Abstract |
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Modern technology is producing high reliability products. Life testing for such products under normal use condition takes a lot of time to obtain a reasonable number of failures. In this situation, an accelerated life test (ALT) procedure is performed in order to obtain failure-time data in a much shorter time with less cost. In step-stress accelerated life test (SSALT), which is a special class of ALT, the stress setting for survival units is generally changed step by step to a higher stress levels at a pre-determined times during the experiment, to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions.
The main focus of this thesis is to develop an optimum test plan, in which the stress change time should be optimality determined according to optimality criterion. This thesis studies the statistical inference of the unknown parameters on the SSALT model under type-II censoring. It is assumed that the failure times at each stress level follow the generalized exponential distribution with scale parameter that is a log linear function of the stress level. A cumulative exposure model is also assumed. First, simple SSALT model with two stress levels will be studied, then this model is extend to SSALT with 3 levels of stress and to more generalized model: k-step SSALT, which includes k levels (k 2) of one stress variable.
Under the assumption of a cumulative exposure model, the maximum likelihood method is used to obtain the estimators of the model parameters. Although the proposed estimators cannot be expressed in closed forms expressions, they can be easily evaluated by using appropriate numerical techniques. The performances of these estimators are studied using some statistical measures. The observed Fisher information matrix is derived for obtaining the asymptotic variance-covariance matrix of the estimates. Also, the approximate confidence intervals for the unknown parameters are deduced. In addition, test of hypothesis for the regression coefficient of the life-stress relationship is examined using the likelihood ratio test method. Moreover, the optimal allocation of the stress change time is determined using the D-optimality criterion, in the case of simple SSALT model. Simulation results are provided with discussion using “MathCAD-14” program, for the validation and illustration of the proposed inference method and the optimal test plan procedure discussed in this thesis. The simulation results showed that the relative absolute biases and mean squared errors are generally decreases with shortest confidence intervals as the sample size increases or as the censoring percentage decreases. Finally, numerical example is presented to numerically examine the inferential procedure discussed here. |
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Supervisor |
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Dr. Amal Soliman Hassan |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1433 AH
2012 AD |
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Added Date |
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Wednesday, September 26, 2012 |
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Researchers
| مريم محمد خان | Khan, Mariam Mohammed | Researcher | Master | |
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