INFERENCE FOR A GAMMA STEP-STRESS MODEL UNDER CENSORING

Abstract

<p>In reliability and life-testing experiments, one of the popular and commonly used strategies, that allows manufacturers and designers to identify, improve and control critical components, is called the Accelerated Life Test (ALT). The main idea of these tests is to investigate the product's reliability at higher than usual stress levels on test units to ensure earlier failure than what could result under the normal operating conditions. Stress can be induced by such factors as voltage, pressure, temperature, load or cycling rate.</p> <p>ALT are applied using different types of accelerations such as high usage rate in which the compressed time testing is done through speed or by reducing off times. Another type of acceleration is the product design where the life of a unit can be accelerated through its size or its geometry. Stress loading is another type of acceleration that is applied using constant stress, step-stress, progressive stress, cyclic stress or random stress. Here, we discuss the step-stress model, which applies stress to each unit and increases the stress at pre-specified times during the experiment allowing us to obtain information about the parameters of the life distribution more quickly than under normal operating conditions.</p> <p>In this thesis, we present the simple step-stress model (the situation in which there are only two stress levels) when the lifetimes at different stress levels follow the gamma distribution when the data are (Chapter 2) Type-II censored, (Chapter 3) Type-I censored, (Chapter 4) Progressively Type-II censored, and (Chapter 5) Progressively Type-I censored, as well as a multiple step-stress model under Type-I and Type-II censoring. The likelihood function is derived assuming a cumulative exposure model with gamma distributed lifetimes. The resulting likelihood equations do not have closed-form solutions, and so they need to be solved numerically. We then derive confidence intervals for the parameters using asymptotic normality of the maximum likelihood estimates and the parametric bootstrap method. In each case, the performances of the methods of inference developed here are examined by means of Monte Carlo simulation study and are also illustrated with some numerical examples.</p>