A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

On entropy goodness-of-fit test based on integrated distribution function

In this study, we consider an entropy-type goodness-of-fit (GOF) test based on integrated distribution functions. We first construct the test for the simple vs. simple hypothesis and then extend it to the composite hypothesis case. It is shown that under regularity conditions, the null limiting distribution of the proposed test is a function of a Brownian bridge. A bootstrap method is also considered and is shown to be weakly consistent. A simulation study and real data analysis are conducted for illustration.     

Generalized anticipated backward stochastic differential equations driven by Brownian motion and continuous increasing process*

This article mainly considers a new class of anticipated BSDEs driven by Brownian motion and continuous increasing process, which are called generalized anticipated backward stochastic differential equations(GABSDEs). We first give the form of GABSDEs. Then, existence and uniqueness result for GABSDEs is established as well as a comparison theorem is obtained under the certain assumptions. At last, we give an application about the duality between SDDEs and GABSDEs.     

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

This article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on C_pk and the mixed variable lot size plan based on C_pk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.     

Generalized method of moments for an extended gamma process

In reliability theory, a widely used process to model the phenomena of the cumulative deterioration of a system over time is the standard gamma process (SGP). Based on several restrictions, such as a constant variance-to-mean ratio, this process is not always a suitable choice to describe the deterioration. A way to overcome these restrictions is to use an extended version of the gamma process introduced by Cinlar (1980), which is characterized by shape and scale functions. In this article, the aim is to propose statistical methods to estimate the unknown parameters of parametric forms of the shape and scale functions. We here develop two generalized methods of moments (Hansen 1982 Hansen, L. P. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50 (4):1029–54.[Crossref], [Web of Science ®] , [Google Scholar]), based either on the moments or on the Laplace transform of an extended gamma process. Asymptotic properties are provided and a Wald-type test is derived, which allows to test SGPs against extended ones with a specific parametric shape function. Also, the performance of the proposed estimation methods is illustrated on simulated and real data.     

A robust posterior preference multi-response optimization approach in multistage processes

Nowadays, many manufacturing and service systems provide products and services to their customers in several consecutive stages of operations, in each of which one or more quality characteristics of interest are monitored. In these environments, the final quality in the last stage not only depends on the quality of the task performed in that stage but also is dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. In this paper, a novel methodology based on the posterior preference approach is proposed to robustly optimize these multistage processes. In this methodology, a multi-response surface optimization problem is solved in order to find preferred solutions among different non dominated solutions (NDSs) according to decision maker's preference. In addition, as the intermediate response variables (quality characteristics) may act as covariates in the next stages, a robust multi-response estimation method is applied to extract the relationships between the outputs and inputs of each stage. NDSs are generated by the ?-constraint method. The robust preferred solutions are selected considering some newly defined conformance criteria. The applicability of the proposed approach is illustrated by a numerical example at the end.     

The estimation for Lévy processes in high frequency data

In this article, a generalized Lévy model is proposed and its parameters are estimated in high-frequency data settings. An infinitesimal generator of Lévy processes is used to study the asymptotic properties of the drift and volatility estimators. They are consistent asymptotically and are independent of other parameters making them better than those in Chen et al. (2010 Chen, S. X., Delaigle, A., Hall, P. (2010). Nonparametric estimation for a class of Lévy processes. Journal of Econometrics 157:257–271.[Crossref], [Web of Science ®] , [Google Scholar]). The estimators proposed here also have fast convergence rates and are simple to implement.     

Ruin problem of a two-dimensional fractional Brownian motion risk process

This paper investigates ruin probability and ruin time of a two-dimensional fractional Brownian motion risk process. The net loss process of an insurance company is modeled by a fractional Brownian motion. The two-dimensional fractional Brownian motion risk process models the surplus processes of an insurance and a reinsurance company, where the net loss is divided between them in some specified proportions. The ruin problem considered is that of the two-dimensional risk process first entering the negative quadrant, that is, the simultaneous ruin problem. We derive both asymptotics of the ruin probability and approximations of the scaled conditional ruin time as the initial capital tends to infinity.