ON THE EVALUATION OF CONTROL CHART LIMITS BASED ON PREDICTIVE DISTRIBUTIONS

ABSTRACT

We propose a Bayesian approach to obtaining control charts when there is parameter uncertainty. Our approach consists of two stages, (i) construction of the control chart where we use a predictive distribution based on a Bayesian approach to derive the rejection region, and (ii) evaluation of the control chart where we use a sampling theory approach to examine the performance of the control chart under various hypothetical specifications for the data generation model.     

Asymptotic behavior of RA-estimates in autoregressive 2D processes

In this work we study the asymptotic behavior of a robust class of estimators of the coefficient of a AR-2D process. We establish the precise conditions for the consistency and asymptotic normality of the RA estimator. The AR-2D model has many applications in image modeling and statistical image processing, therefore the relevance of knowing such properties. The adequacy of the AR-2D model is analyzed with real images; we also show the impact of contamination and the capability of the RA estimator to produce useful results even in the presence of spurious data.     

成组生产工序经济控制图的设计与应用研究

经济合理地利用控制图进行成组生产工序质量相对控制，必须先设计出经济控制图，并经济地运用控制图。因此，本文通过一案例阐述了成组生产工序经济控制图的设计方法和经济抽检间隔的确定方法，从而为企业经济合理地进行成组生产工序质量控制提供帮助。     

An NP Control Chart Using Double Inspections

The np control chart is used widely in Statistical Process Control (SPC) for attributes. It is difficult to design an np chart that simultaneously satisfies a requirement on false alarm rate and has high detection effectiveness. This is mainly because one is often unable to make the in-control Average Run Length ARL₀ of an np chart close to a specified or desired value. This article proposes a new np control chart which is able to overcome the problems suffered by the conventional np chart. It is called the Double Inspection (DI) np chart, because it uses a double inspection scheme to decide the process status (in control or out of control). The first inspection decides the process status according to the number of non-conforming units found in a sample; and the second inspection makes a decision based on the location of a particular non-conforming unit in the sample. The double inspection scheme makes the in-control ARL₀ very close to a specified value and the out-of-control Average Run Length ARL₁ quite small. As a result, the requirement on a false alarm rate is satisfied and the detection effectiveness also achieves a high level. Moreover, the DI np chart retains the operational simplicity of the np chart to a large degree and achieves the performance improvement without requiring extra inspection (testing whether a unit is conforming or not).     

Application of Multivariate Analysis to Increase the Yield of Dry Cell Batteries

In an organization, the manufacturing process of a dry cell battery was suffering from the problem of frequent stoppages in the assembly line. The complete battery manufacturing operation is highly automated and mechanized. It was suspected that excessive variation in overall height of bobbin was the major reason for such stoppages. The bobbin, the inside part of a dry cell battery acting as cathode, is formed by the battery extrusion process. A planned experiment was carried out on the extrusion process that identified the setting of extrusion machines and the amount of water content in the cathode mixture as the parameters causing variation in the bobbin characteristics. The problem of frequent stoppages was eliminated when appropriate action was taken on these two parameters. Finally, multivariate and univariate control schemes were developed for online control of the bobbin characteristics.     

Weighted Dickey–Fuller processes for detecting stationarity

Aiming at monitoring a time series to detect stationarity as soon as possible, we introduce monitoring procedures based on kernel-weighted sequential Dickey–Fuller (DF) processes, and related stopping times, which may be called weighted DF control charts. Under rather weak assumptions, (functional) central limit theorems are established under the unit root null hypothesis and local-to-unity alternatives. For general dependent and heterogeneous innovation sequences the limit processes depend on a nuisance parameter. In this case of practical interest, one can use estimated control limits obtained from the estimated asymptotic law. Another easy-to-use approach is to transform the DF processes to obtain limit laws which are invariant with respect to the nuisance parameter. We provide asymptotic theory for both approaches and compare their statistical behavior in finite samples by simulation.     

金属材料工程专业学生素质教育影响因素研究

对金属材料工程专业学生素质教育现状的调查结果,应用层次分析法与因果分析法相结合,得出素质教育影响因素的重要度因果分析图。从重要度因果分析图,可以直观地看出各个影响因素的排序,方便地找出其主要影响因素。此研究结果有较好的客观性、科学性和可靠性,对加强学生素质教育的途径和方法,有较大的参考价值。     

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t² units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t.     

Dual Nonparametric CUSUM Control Chart Based on Ranks

In this article, we provide a sequential rank-based dual nonparametric CUSUM (DNC) control chart for detecting arbitrary magnitude of shifts in the location parameter. It is a self-starting scheme and thus can be used to monitor processes at the start-up stages. Moreover, we do not require any prior knowledge of the underlying distribution. A simulation study demonstrates that the proposed control chart not only performs robustly for different distributions, but also is efficient in detecting various magnitudes of shifts. An illustrative example is given to introduce the implementation of our proposed DNC control chart. It is easy to construct and fast to compute.     

The double sampling S2 chart with estimated process variance

This paper proposes useful exact bounds for the parameters of the double sampling S² chart with known process variance and it also investigates the properties of the double sampling S² chart with estimated process variance, in terms of the average run length, the standard deviation of the run length and the average sample size, providing a numerical comparison with the known process variance case. It also provides guidelines to systematically design the double sampling S² chart both with known and estimated process variance and proposes two optimal design procedures with estimated process variance, for (a) minimizing the out-of-control average run length and (b) minimizing the out-of-control average sample size.