The better mean residual life at $t_0\;(BMRL-t_0)$ class of life distribution is introduced by Kulasekara and Park (1987). They proved that the $BMRL-t_0$ class contains the DMRL class, but it is a proper subclass of the NBUE class. In this paper we develop a new family of tests for testing exponentiality against the $BMRL-t_0\;(WMRL-t_0)$ alternatives based on the goodness of fit approach. It is shown that the suggested test is better than the one introduced by Kulasekara and Park (1987) in the sense of Pitman asymptotic efficiency values.

A new class of life distributions is studied. This class is defined based on comparing the residual life time to the whole life in the moment generating function order giving 'the new better than used in the moment generating function order ageing class $(NBU_{mgf})$'. Fundamental properties of this class are given including some closure properties and characterizations. Finally, we consider new results about comparisons of age and block replacement policies when the underlying distribution belongs to $NBU_{mgf}$ aging classes.

Many real world cases in material failure analysis do not follow perfectly the normal distribution. Forcing of the normality assumption may lead to inaccurate predictions and poor product quality. We examine the failure process of the internal bond (IB or tensile strength) of medium density fiberboard (MDF). We propose a forced censoring technique that closer fits the lower tails of strength distributions and better estimates extremely smaller percentiles, which may be valuable to continuous quality improvement initiatives. Further analyses are performed to build an accelerated common-shaped Weibull model for different product types using the $JMP^{(R)}$ Survival and Reliability platform. In this paper, a forced censoring technique is implemented for the first time as a software module, using $JMP^{(R)}$ Scripting Language (JSL) to expedite data processing, which is crucial for real-time manufacturing settings. Also, we use JSL to automate the task of fitting an accelerated Weibull model and testing model homogeneity in the shape parameter. Finally, a package script is written to readily provide field engineers customized reporting for model visualization, parameter estimation, and percentile forecasting. Our approach may be more accurate for product conformance evaluation, plus help reduce the cost of destructive testing and data management due to reduced frequency of testing. It may also be valuable for preventing field failure and improved product safety even when destructive testing is not reduced by yielding higher precision intervals at the same confidence level.

The exact cause of the system's failure is often unknown in the masked system lifetime data. In such type of data, there are two observable quantities, namely (i) the systems time to failure and (ii) the set of systems components that contains the component, which might cause the system to fail. Our objective in this paper is to use the maximum likelihood procedure in the presence of masked data to make inference for the reliability of the system's components. We assume a multi-component series system where each component has a constant failure rate. Different cases that permit for closed form solutions of point estimates are considered. The results obtained in this paper generalize other published results.

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

The market for second hand products has been growing for a variety of reasons (e.g., new products appearing at a faster rate and the expected life of products increasing due to rapid advances in technology). The demand for warranties for second-hand products has been growing along with the growth of the market for second-hand products. Warranty for new products (consumer durables, industrial and commercial, and specialized defense products) has received a lot of attention. In contrast, warranties for second-hand product have received very little attention. Often, dealers of second-hand product such as cars offer 2D-warranties (Year and Kilometers). The expected warranty cost associated with a second-hand product for 2D-Policies is a function of the age of the item and its usage (as it affects failures over the warranty period), the warranty terms and the servicing strategy used by the dealer. This paper deals with development of models for warranty cost analysis along with the decision on sale price and warranty cover for 2D-Warranty policies associated with sale of second-hand products.

In this paper, some characterization results of the NBUCA class of life distributions are obtained. Behavior of the life distributions of the present class is developed in terms of the monotonicity of the residual life of k-out of-n systems given that the (n-k)th failure has occurred at time $t{\geq}0$. Similar conclusions based on the residual life of parallel system are also presented. Next, we focus upon the aging process of a system with independent but not necessarily identical NBUCA components. Finally, it is proved that if the lifetimes of a series systems with a random number of identical components have the NBUCA property then its units also have the same property.