Self-adapting control charts

When the distributional form of the observations differs from normality, standard control charts are often prone to serious errors. Such model errors can be avoided by using (modified) nonparametric control charts. Unfortunately, these control charts suffer from large stochastic errors caused by estimation. In between these two types are the so-called parametric control charts. All three of them, as well as a combined chart, which chooses one of the three control charts according to the appropriate model assumption on the underlying distribution are discussed in this paper. The data indicate which of the three control charts to select. Readymade formulas for the several control charts are presented accompanied by an application on real data. Apart from bias removal, criteria based on exceedance probability and semi-variance are investigated.     

Economic Design of EWMA Charts with Variable Sampling Intervals

Control charting is a graphical expression and operation of statistical hypothesis testing. In the present paper, we develop the economic design of the variable sampling intervals (VSI) exponentially weighted moving average (EWMA) charts to determine the values of the six test parameters of the charts (i.e., the sample size, the long sampling interval, the short sampling interval, the warning limit coefficient, the control limit coefficient, and exponential weight constant) such that the expected total cost is minimized. The genetic algorithm (GA) is applied to search for the optimal values of the six test parameters of the VSI EWMA chart, and an example is provided to illustrate the solution procedure. A sensitivity analysis is then carried out to investigate the effects of model parameters on the solution of the economic design.     

Maximizing public value for subsidized non-profit firms: a mathematical economic model

In many public service industries, firms are assumed to maximize certain public goals and are not allowed to make any profits. These public service firms are financed by fixed and variable subsidies and fees-for-services paid by users. Standard economic models, such as the profit maximization and cost minimization model, are not suitable for describing the production structure and the economic behavior of these firms. Productivity and efficiency measures derived from these models therefore are not accurate. This paper derives a model that fits this type of firm and its economic context. It derives the exact mathematical relationships between public value, services delivered, (money) revenues, costs, service prices, resource prices and subsidies. In an empirical setting the model can be used as a reference to calculate productivity and efficiency scores. The usability of the model is demonstrated by an application to Social Labor Services in the Netherlands.     

Economically optimalc- andnp-control charts

In v. Collani (1981, 1986, 1987a and 1987b) simple procedures are developed to determine the approximately optimal economic design of control charts for measurements. Applying these procedures to the case of control charts for attributes, nomograms are obtained from which the approximately optimal design ofc-charts, i.e. charts for defects, is readily available. Furthermore it is shown that this method also provides good approximately optimalnp-charts, i.e. charts for defectives. Research supported by the DFG (Deutsche Forschungsgemeinschaft).     

Economic design of T<Superscript>2</Superscript> control charts with the VSSI sampling scheme

T ² charts are used to monitor a process when more than one quality variable associated with process is being observed. Recent studies have shown that the T ² chart with variable sampling size and sampling interval (VSSI) detects a small shift in the process mean vector faster than the traditional T ² chart. The paper considers an economic design of the VSSI T ² chart, in which the expected hourly loss is constructed and regarded as an objective function for optimally determining the design parameters (i.e. the maximum/minimum sample size, the longest/shortest sampling interval, and the warning/action limits) in sampling-and-charting. Furthermore, the effects of process parameters and cost parameters upon the expected hourly loss and design parameters are examined.     

A new procedure for monitoring the range and standard deviation of a quality characteristic

The Shewhart and the Bonferroni-adjustment R and S chart are usually applied to monitor the range and the standard deviation of a quality characteristic. These charts are used to recognize the process variability of a quality characteristic. The control limits of these charts are constructed on the assumption that the population follows approximately the normal distribution with the standard deviation parameter known or unknown. In this article, we establish two new charts based approximately on the normal distribution. The constant values needed to construct the new control limits are dependent on the sample group size (k) and the sample subgroup size (n). Additionally, the unknown standard deviation for the proposed approaches is estimated by a uniformly minimum variance unbiased estimator (UMVUE). This estimator has variance less than that of the estimator used in the Shewhart and Bonferroni approach. The proposed approaches in the case of the unknown standard deviation, give out-of-control average run length slightly less than the Shewhart approach and considerably less than the Bonferroni-adjustment approach.     

运用PCN分析法构建高铁互联网订餐服务模型

目的:为改善高铁餐饮服务体验,探讨PCN分析法在高铁餐饮服务设计中的应用。方法:运用PCN分析法梳理高铁互联网订餐服务中旅客同餐车服务、商家服务以及平台配送服务的多实体服务网络交互关系,分析现有流程环节中存在的问题。以配送环节的优化设计为例,采用PCN优化原则对其进行服务流程创新设计。结果:构建高铁互联网订餐服务的优化模型。结论:论文运用PCN分析法构建的高铁互联网订餐服务的优化模型,减少了顾客等待时间,节约商家的人力成本,有利于优化顾客的用餐体验,增加服务项目的经济效益。     

Optimal Processes Management for Over-Adjusted Process with Dependent Steps on Bank Industry

Process management is important for a company. An over-adjusted process may increase process quality variability, ultimately affecting the quality and cost of service or products. A two special-cause economic over-adjustment model is developed for controlling the service quality variation of the two-step process on a bank industry. The objective is to determine the optimal management policy for the two-step process, which minimizes the service quality variation and total quality control cost. A Markov chain approach is extended to derive the economi c adjustment model of the process, and the optimal management policy is obtained from optimization techniques. Application of the two special-cause over-adjusted model and the optimal management policy on the process management of a bank industry is demonstrated through an example.     

Monitoring the cross-covariances of a multivariate time series

In this paper sequential procedures are proposed for jointly monitoring all elements of the covariance matrix at lag 0 of a multivariate time series. All control charts are based on exponential smoothing. As a measure of the distance between the target values and the actual values the Mahalanobis distance is used. It is distinguished between residual control schemes and modified control schemes. Several properties of these charts are proved assuming the target process to be a stationary Gaussian process. Within an extensive Monte Carlo study all procedures are compared with each other. As a measure of the performance of a control chart the average run length is used. An empirical example about Eastern European stock markets illustrates how the autocovariance and the cross-covariance structure of financial assets can be monitored by these methods.     

Monitoring process mean level using auxiliary information

In this study, a Shewhart‐type control chart is proposed for the improved monitoring of process mean level (targeting both moderate and large shifts which is the major concern of Shewhart‐type control charts) of a quality characteristic of interest Y. The proposed control chart, namely the M_r chart, is based on the regression estimator of mean using a single auxiliary variable X. Assuming bivariate normality of (Y, X), the design structure of M_r chart is developed for phase I quality control. The comparison of the proposed chart is made with some existing control charts used for the same purpose. Using power curves as a performance measure, better performance of the proposedM_r chart is observed for detecting the shifts in mean level of the characteristic of interest.     

Run length distributions for estimated attributes charts

Attributes control charts, such as c and p charts, are popular methods for detecting out of control signals when it is practical only to obtain qualitative information about a process; in such cases, variables control charts, such as the , s and R charts, cannot be used. The run length distributions have previously been studied for variables charts when the control limits have been estimated. Little has been done in the case of attributes charts. In this paper, the run length distributions for the c chart and p chart are derived for the case when the control limits are estimated. It is shown that, as for variables charts, the effect of estimation on quantities such as the average run length (ARL) can be quite dramatic, but when the underlying process is in control, the ARL is potentially misleading as a basis for comparison. Received: September 1998     

CUMIN charts

Classical control charts are very sensitive to deviations from normality. In this respect, nonparametric charts form an attractive alternative. However, these often require considerably more Phase I observations than are available in practice. This latter problem can be solved by introducing grouping during Phase II. Then each group minimum is compared to a suitable upper limit (in the two-sided case also each group maximum to a lower limit). In the present paper it is demonstrated that such MIN charts allow further improvement by adopting a sequential approach. Once a new observation fails to exceed the upper limit, its group is aborted and a new one starts right away. The resulting CUMIN chart is easy to understand and implement. Moreover, this chart is truly nonparametric and has good detection properties. For example, like the CUSUM chart, it is markedly better than a Shewhart X-chart, unless the shift is really large.     

Multivariate statistical process control—recent results and directions for future research

The performance of a product often depends on several quality characteristics. These characteristics may have interactions. In answering the question “Is the process in control?”, multivariate statistical process control methods take these interactions into account. In this paper, we review several of these multivariate methods and point out where to fill up gaps in the theory. The review includes multivariate control charts, multivariate CUSUM charts, a multivariate MMA chart, and multivariate process capability indices. The most important open question from a practical point of view is how to detect the variables that caused an out-of-control signal. Theoretically, the statistical properties of the methods should be investigated more profoundly.     

Variables control chart limits and tests for special causes

Control charts are used to detect problems in control such as outliers, shifts in levels or excess variability in subgroup means that may have a special cause. This paper addresses itself to deriving control chart limits based on past data and based on initial samples in a current control situation. We present a general setting for control charts. Furthermore, an overview is given of tests for special causes. The tests are standardized so that the asymptotic type I error does not exceed a fixed level. The distributions of the run lengths of the tests and combinations of tests are also evaluated. We propose to use a low percen-tile of the run length distribution, instead of the average run length, to study the performance of the tests. These indicate that, in particular when tests are combined, the run length percentiles may be too small for practical purposes. It is shown that (nearly) exact control chart limits for observations from a normal distribution exist. The traditional limits differ considerably from the proposed ones and correspond to even smaller run length percentiles.     

辅助生产费用分配的通用模型分析

采用代数分配法来计算辅助生产车间单位成本,设计的关键是利用Excel提供的矩阵求值函数MDE-TERM()解联立方程。本模型使用一个专门的子过程来生成所需的各个数组,通过调用子过程来计算出各辅助生产车间的单位成本,分配结果直接生成表格。本模型使用方便,显示结果快捷准确,适应范围广,实用性很强。其最大的特点是灵活通用,可以用来处理任意多个辅助生产车间之间的费用交互分配问题。     

Why and how to use vector autoregressive models for quality control: the guideline and procedures

While quality control on multivariate and serially correlated processes has attracted research attentions, a number of very detailed problems need to be overcome in order to construct practical control charts. We suggest guidelines for construction of control charts based on vector autoregressive (VAR) residuals. We discuss why VAR model is reasonable for real processes in nature, the use of VAR models to approximate multivariate serially correlated processes, residual estimation, selecting the number of variables, and selecting appropriate orders, among other issues. In addition, we illustrate an example employing VAR techniques to approximate a multivariate process previously examined and construct a control chart to monitor residuals. Last, we illustrate the potential development and use of the VAR residual chart to assist quality control and improvement.     

Monitoring in service triads consisting of buyers, subcontractors and end customers

Organisations increasingly outsource service delivery to specialist subcontractors. These buyers, their subcontractors and their end customers operate in a triadic service relationship. In these triads, the buyer lacks direct control over service delivery and completely depends on the subcontractor for its performance towards its end customers. Subcontractors are confronted with two principals (buyer and end customer) who may have conflicting objectives.Although traditionally focusing on dyadic buyer–seller relationships rather than triads, Agency Theory provides valuable suggestions on the type of contract to be used and the type of monitoring to be employed. We adopt Agency Theory as a theoretical lens to look at the buyer–subcontractor–end customer triad and develop propositions on the design of contractual arrangements and monitoring activities. We use the results of two cases of service triads to provide some initial validation for these propositions.     

Run length distributions and economic design of [`(X)]\bar X charts with unknown process variance

The run length distribution of charts with unknown process variance is analized using numerical integration. Both traditional chart limits and a method due to Hillier are considered. It is shown that setting control limits based on the pooled standard deviation, as opposed to the average sample standard deviation, provides better run length performance due to its smaller mean square error. The effect of an unknown process variance is shown to increase the area under both tails of the run length distribution. If Hillier’s method is used instead, only the right tail of the run length distribution is increased. Collani’s model for the economic design of charts is extended to the case of unknown process variance by writing his standardized objective function in terms of average run lengths.     

Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.     

Apply 6-sigma methodology in measuring the competition quality of satisfaction performance—an example of ISP Industry

At present time the ISP (Internet Service Provider) already make a great impact to the human life as well as the economic society, everything has a close relation with the internet service and due to the fast development of information technology further lower the cost of ISP and improved the service speed as well as its quality. All of this make the customer layer of ISP more popular than before and thus bring up the fierce competition in this industry. Due to the entry barrier of high investment and high technology of ISP industry it has become as a monopoly market and the monopoly market is very respect the competition and cooperation relationship with competitors. Besides, most of the relevant literature in the past is focus on the measurement and analysis of customer to the self-company and few of them mention how to include the satisfaction of competitor’s customer into measurement and analysis. As golden strategy stated in the Sun-Tze Strategic: “Know yourself and know your competitor well, winning every war.” we must consider the strength, weakness, opportunity and threat on customer satisfaction of your company and competitors. Base on the above motivation, this article will apply the DMAIC (Define, Measure, Analyze, Improve, Control) methodology of 6-Sigma, focus on the viewpoint of customer satisfaction of ISP industry. At first we utilize the 5 equal scale measurement define the network quality item of ISP, which provided by the self-company and competitors. And measuring the degree of “satisfaction” and “importance” of these quality items, then use the performance evaluation matrix and strength and weakness matrix to analyze the Strength, Weakness, Opportunity and Threat of self and competitors, focus on the quality items that fall out of the 2 sigma and use the strength–weakness strategic chart to establish the improvement strategy. And at last, utilize the strength–weakness matrix chart as the control tool to verify and sustain the effectiveness of the improved performance. The complete and easy measurement improvement model provided in this article can be used by the enterprise to effectively and quickly evaluating and analyzing the service quality of self and competitors. And under the reasonable cost condition with considering the competing opportunity and threat of market to effectively improving the customer service quality and promoting the overall customer satisfaction and create powerful high value-added quality competition strength.