International Journal of Reliability, Quality and Safety Engineering

It has been proposed in recent literatures that if replacement time is planned too early prior to failure time, a waste of operation cost, i.e., excess costs, would incur because the system might run for an additional period of time to complete critical operations; and if the replacement time is too late after failure, a great failure cost, i.e., shortage cost, is incurred due to the delay in time of the carelessly scheduled replacement. The above notion of shortage and excess costs are taken into consideration for the replacement first, replacement last and replacement overtime models in this paper. We obtain the expected cost rates and their optimum replacement times. Comparisons among these optimum times are made analytically and numerically.

In this paper, we propose a modified proximal gradient method for a class of sparse optimization problems, which arise in many contemporary statistical and signal processing applications. The new method uses a new scheme to construct the descent direction based on the proximal gradient method. It is proven that the modified proximal gradient method is Q-linearly convergent without the assumption of the strong convexity of the objective function. Numerical experiments have been conducted to evaluate the proposed method.

In this paper, the system reliability in a stress–strength model, when the distributions of the stress and the strength random variables are replaced by two distorted distributions, is considered. The conditions to increase the reliability under several distortion functions are studied. Furthermore, the changes in the residual stress–strength reliability, the mean remaining strength and the number of working components of a system are investigated when the original distributions have been affected by distortion functions. Some of the previous results in the literatures can be achieved as special cases of our results.

Preventive replacement policy conducted at a routine time $T^{\ast }$ has been surveyed extensively in literatures. Another two random replacement times $Y_1$ and $Y_2$ for time $T^{\ast }$ are jointly considered in this paper. We formulate the models of replacement first, replacement last and replacement middle, which are based on the respective assumptions of whichever occurs first, whichever occurs last and whichever occurs middle. Next, we modify replacement first and replacement last by using whichever occurs first and last jointly. Furthermore, we give the model of replacement overtime when the assumptions of whichever occurs first, whichever occurs last and replacing the unit over time $T$ are simultaneously considered. Comparisons among these replacement models are made to find which policy is more economical than the other.

In most statistical process control (SPC) applications, quality of a process or product is monitored by univariate or multivariate control charts. However, sometimes a functional relationship between a response variable and one or more explanatory variables is established and monitored over time. This relationship is called “profile” in SPC literature. In this paper, we specifically consider processes with compositional data responses, including multivariate positive observations summing to one. The relationship between compositional data responses and explanatory variables is modeled by a Dirichlet regression profile. We develop a monitoring procedure based on likelihood ratio test (lrt) for Phase I monitoring of Dirichlet regression profiles. Then, we compare the performance of the proposed method with the best method in the literature in terms of probability of signal. The results of simulation studies show that the proposed control chart has better performance in Phase I monitoring than the competing control chart. Moreover, the proposed method is able to estimate the real time of a change as well. The performance of this feature is also investigated through simulation runs which show the satisfactory performance. Finally, the application of the proposed method is illustrated based on a real case in comparison with the existing method.