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Document Type |
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Thesis |
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Document Title |
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Statistical Inference for the Parameters of A Lifetime Distribution with Various Types of Failure Rate الاستدلال الإحصائي حول معالم توزيع الحياة لأنواع متعددة من معدل الفشل |
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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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As a human attribute, reliability has been used for a long time for technical systems. However, the reliability concept has been applied for not more than 60 years. Reliability in the broad sense is the science aimed at prediction, analyzing, preventing and mitigating failures over time.
Quality control analysts and reliability engineers frequently face the problem to predict the results for future observations of certain products based on an initial sample. For example, in studies concerning the length of life of certain types of manufactured items, the prediction of the future life for an item is often wished based on available life testing information. More specifically, manufacturers would like to have the bounds for the life of their products so that their warranty limits could be more reasonably set, and consumers purchasing manufactured products would like to know the bounds for the life of the unit to be purchased. Statistical bounds to be obtained in the future sample based on a previous sample are known as prediction intervals (regions). An important search about the life testing was found by Epstein and Sobel (1953).
In many industrial applications, the failure rate function is observed to have the so-called bathtub shape is often high at the beginning phase. This can explain that there must be undiscovered defects in the items; these will show up when these items are activated. When this item has survived in an undiscovered defect phase, the failure rate often stabilizes at a level where it remains for a certain time until it starts to increase as the items start to wear out. From the shape of bathtub hazard carve; the lifetime of an item can be divided into three parts: the burn-in period, the useful period and the wear-out period.
During the burn-in period, the failure rate is expected to drop with age. In the second period, failure rate is approximately constant whereas components begin to reach the wear-out failure is the outcome of a depleted process due to abrasion, fatigue, and so on.
The objective of the thesis is to estimate the unknown parameters of Zhang's distribution based on Type II censoring. The problem will be discussed using the maximum likelihood method and Bayesian approach to estimate the parameters of the distribution. Since the estimation requires solving non liner equations, therefore, we using MathCAD (2001) package.
The thesis consists of 5 chapters and a list of references. It is organized as follows: Chapter I includes an introduction. Definitions and terminologies are given in Chapter II. Chapter III includes a literature review of the previous studies. Chapter IV includes the estimation of unknown parameters of the bathtub shape lifetime distribution using the maximum likelihood method and Bayesian method under type II censoring. Chapter V is devoted to conclusions and recommendations for future work. |
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Supervisor |
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Prof. Dr. Abdullah M. Abd-Elfattah |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1434 AH
2013 AD |
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Added Date |
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Tuesday, March 12, 2013 |
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Researchers
| فؤاد علي خلوي | Khalawi, Fouad Ali | Researcher | Master | |
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