الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
 |  | from | 114 |  |  |
| | | from | 114 | | |
Abstract
One of the attractions of the half-logistic distribution (HLD) in the context of reliability theory is that it has a monotonically increasing hazard rate for all parameter values, a property shared by relatively few distributions which have support on the positive half of the real line. Applications of the HLD to life-testing have been well demonstrated by Balakrishnan (1985). In terms of tail behavior, the HLD provides a degree of flexibility as its tail thickness lies between those of the half-normal and half-Cauchy distributions.
Prediction is an important problem in the statistical inference. It has many applications in the field of quality control, reliability, medical sciences, business, engineering, meteorology and other areas as well. It is the problem of inferring the values of unknown observables (future observations), or functions of such observables, from current available (informative) observations. One-sample and two-sample schemes are two commonly used schemes of prediction. A predictor could be a point or interval predictor.
Censoring is very common in life tests. It usually applies when the distribution of exact lifetimes are known for only a portion of the items and the remainder of the lifetimes are known only to exceed certain values under a life test. Type-I and type-II are the most common censoring schemes (CSs). There are many situations in life-testing and reliability studies in which the experimenter desires to remove functioning items at points other than the final termination. In such cases, the above two CSs are not appropriate to be used. This leads to consider a more general CS known as progressive type-II censoring.
The accelerated life tests (ALTs) are preferred to be used in manufacturing industries to obtain enough failure data, in a short period of time, to make inference regarding its relationship with external stress variables. In ALTs, the test items are subjected to higher than usual levels of stress (such as pressure, temperature, humidity, etc) to induce early failures. Data collected at such accelerated conditions are then extrapolated through a physically appropriate statistical model to estimate the lifetime distribution at normal use condition.
In medical studies or in the analysis of reliability data, the failure of individuals or items may be attributable to more than one cause of failure. These risk factors in some sense compete for the failure of the experimental unit. The data for these competing risks model consist of
failure time and an indicator variable denoting the specific cause of failure of the individual or
item.
The thesis consists of four chapters. Chapter 1 is an introductory chapter. In Chapter 2, we discuss one-sample Bayesian prediction using progressively type-II censored sample under progressive-stress ALT. The lifetime of a unit under use condition stress is assumed to follow the HLD with a scale parameter satisfying the inverse power law. Prediction bounds of future order statistics are obtained in the case of one and two unknown parameters. A simulation study is performed and numerical computations are carried out, based on two different progressive CSs. The coverage probabilities (COVPs) and average interval lengths (AILs) of the confidence intervals are computed via a Monte Carlo simulation.
In Chapter 3, one-sample Bayesian prediction bounds of order statistics based on progressively type-II censored competing risks data from a general class of distributions are obtained. The results are then applied to the HLD. Based on three different progressive type-II CSs, prediction intervals of the future order statistics are obtained. An illustrative example is pre- sented to show the procedure. A Monte Carlo simulation study is performed and numerical computations are carried out to obtain the COVPs and AILs of the prediction intervals.
In Chapter 4, two-sample scheme is used to predict the s-th order statistic in a future sample. The informative sample is assumed to be drawn from a general class of distributions. The informative and future samples are progressively type-II censored, under competing risks model, and assumed to be obtained from the same population. A special attention is paid to the HLD. Using three different progressive CSs, numerical computations are carried out to illustrate the performance of the procedure. An illustrative example based on real data is also considered. The COVPs and AILs of the prediction intervals are computed via a simulation study.