Multi-Point and Multi-Interval Availabilities for Markov Repairable Systems with History-Dependent Up and Down States

A Markov repairable system with history-dependent up and down states is presented. The state space of the repairable system is divided into three sets, which are up states, down states and changeable states.Using aggregated stochastic processes, we can get the multi-interval availability and multi-point availability for the Markov repairable system. Finally, numerical examples are given to illustrate the obtained results.     

Memory based scheme to monitor non-random small shift patterns in manufacturing process

Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.     

Bayesian reliability assessment and degradation modeling with calibrations and random failure threshold

A degradation model with a random failure threshold is presented for the assessment of reliability by the Bayesian approach. This model is different from others in that the degradation process is proceeding under pre-specified periodical calibrations. And here a random threshold distribution instead of a constant threshold which is difficult to determine in practice is used. The system reliability is defined as the probability that the degradation signals do not exceed the random threshold. Based on the posterior distribution estimates of degradation performance, two models for Bayesian reliability assessments are presented in terms of the degradation performance and the distribution of random failure threshold. The methods proposed in this paper are very useful and practical for multi-stage system with uncertain failure threshold. This study perfects the degradation modeling approaches and plays an important role in the remaining useful life estimation and maintenance decision making.