Inference Based on Type-II Hybrid Censored Data from a Pareto Distribution

The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular failures to be observed by the end of the experiment. Maximum likelihood and Bayes estimation methods are used with their approximate confidence intervals. Proposed estimation methods are compared numerically based on simulation studies. A numerical example is also used to illustrate the theoretical outcomes.

Reliability Estimation for Hybrid System under Constant-stress Partially Accelerated Life Test with Progressively Hybrid Censoring

Background: Reliability analysis for the systems with masked data had been studied by many scholars. However, most researches focused on a system that is either series or parallel only, and the component in the system is mainly exponential or Weibull. In engineering practice, it is often seen that the structure of a system is a combination of series and parallel system, and other types of components are also used in the system. So it is important to study the reliability analysis of hybrid systems with modified Weibull components. Objective: For the hybrid system with masked data, the constant stress partial accelerated life test is performed under type-II progressive hybrid censoring. These data from life test are used to estimate unknown parameters and reliability index of system. The research results will not only provide theoretical basis and reference for system reliability assessment but also favor the patents on partial accelerated life test. Methods: Maximum likelihood estimates of unknown parameters are investigated with the numerical method. The approximate confidence intervals, and bootstrap confidence intervals for parameters are constructed by the asymptotic theory and the bootstrap method, respectively. Results: Maximum likelihood estimations of unknown parameters and reliability index of system are derived. The approximate confidence intervals and bootstrap confidence intervals for unknown parameters are proposed. The performance of estimation of unknown parameters and reliability index are evaluated numerically through Monte Carlo method. Conclusion: The performance on maximum likelihood estimation method is effective and satisfying. For the confidence intervals of parameters, bootstrap method outperforms the approximate method.

Assessing the Accuracy of Approximate Confidence Intervals Proposed for the Mean of Poisson Distribution

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Origin–Destination-Based Travel Time Reliability

Travel time reliability (TTR) is an important performance indicator for transportation systems. TTR can be generally categorized as either segment based or origin–destination (O-D) based. A primary difference between the two TTR estimations is that route information is implied in segment-based TTR estimations. Segment-based TTR estimations have been widely studied in previous research; however, O-D–based TTR estimations are used infrequently. This paper provides detailed insight into O-D–based TTR estimations and raises three new issues: ( a) How many routes do travelers usually take and what are the TTR values associated with these routes? ( b) Do statistical differences exist between route-specific and non-route-specific (NRS) TTR values? ( c) How can O-D–based TTR information be delivered? Two processes were proposed to address the issues. Three TTR measures—standard deviation, coefficient of variation, and buffer index—were calculated. The bootstrapping technique was used to measure the accuracy of the TTR measures. Approximate confidence intervals were used to investigate statistically the differences between route-specific and NRS TTR measures. A large quantity of taxicab GPS-based data provided data support for estimating O-D–based TTR measures. The results of O-D–based TTR measures showed that no statistically significant differences existed between route-specific and NRS TTR measures for most of the time periods examined. Statistically significant differences could still be found in some time periods. Travelers may take advantage of these differences to choose a more reliable route. Access to both numeric TTR values and route preference, instead of just to TTR information on segments of interest, can be beneficial to travelers in planning an entire trip.