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1.
W. John Braun 《Metrika》1999,50(2):121-129
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 相似文献
2.
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. 相似文献
3.
Enrique Del Castillo 《Metrika》1996,43(1):189-201
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. 相似文献
4.
Majid Nili Ahmadabadi Yaghub Farjami Mohammad Bameni Moghadam 《Quality and Quantity》2012,46(4):1097-1111
The use of control charts in statistical quality control, which are statistical measures of quality limits, is based on several
assumptions. For instance, the process output distribution is assumed to follow a specified probability distribution (normal
for continuous measurements and binomial or Poisson for attribute data) and the process supposed to be for large production
runs. These assumptions are not always fulfilled in practice. This paper focuses on the problem when the process monitored
has an output which has unknown distribution, or/and when the production run is short. The five-parameter generalized lambda
distributions (GLD) which are subject to estimating data distributions, as a very flexible family of statistical distributions
is presented and proposed as the base of control parameters estimation. The proposed chart is of the Shewhart type and simple
equations are proposed for calculating the lower and upper control limits (LCL and UCL) for unknown distribution type of data.
When the underlying distribution cannot be modeled sufficiently accurately, the presented control chart comes into the picture.
We develop a computationally efficient method for accurate calculations of the control limits. As the vital measure of performance
of SPC methods, we compute ARL’s and compare them to show the explicit excellence of the proposed method. 相似文献
5.
Although statistical process control (SPC) techniques have been focused mostly on detecting step (constant) mean shift, drift
which is a time-varying change frequently occurs in industrial applications. In this research, for monitoring drift change,
the following five control schemes are compared: the exponentially weighted moving average (EWMA) chart and the cumulative
sum (CUSUM) charts which are recommended detecting drift change in the literature; the generalized EWMA (GEWMA) chart proposed
by Han and Tsung (2004) and two generalized likelihood ratio based schemes, GLR-S and GLR-L charts which are respectively
under the assumption of step and linear trend shifts. Both the asymptotic estimation and the numerical simulation of the average
run length (ARL) are presented. We show that when the in-control (IC) ARL is large (goes to infinity), the GLR-L chart has
the best overall performance among the considered charts in detecting linear trend shift. From the viewpoint of practical
IC ARL, based on the simulation results, we show that besides the GLR-L chart, the GEWMA chart offers a good balanced protection
against drifts of different size. Some computational issues are also addressed. 相似文献
6.
When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption
of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the
chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements
are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider
the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals
chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution
of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated
Burr, lognormal and exponential distributions. Some numerical calculations are generated for n = 2, 3, 4 by using MATLAB. 相似文献
7.
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. 相似文献
8.
在统计过程控制(SPC)中,对多元数据的监测仍然是一个重要且具有挑战性的问题。当缺乏或有限的关于潜在过程分布的认知时,特别是当过程测量是多变量的时候,非参数控制图在统计过程控制(SPC)中是有用的。文章基于Wilcoxon秩和检验结合广义加权移动平均(GWMA)控制方案来制定图表统计量,得到一个新的多元非参数控制图,用于监测多元数据的位置参数变化。文章的理论和数值研究表明,所提出的控制图能够为任意数据分布位置偏移检测提供令人满意的性能。 相似文献
9.
Engineering Process Controllers (EPC) are frequently based on parametrized models. If process conditions change, the parameter
estimates used by the controllers may become biased, and the quality characteristics will be affected. To detect such changes
it is adequate to use Statistical Process Control (SPC) methods. The run length statistic is commonly used to describe the
performance of an SPC chart. This paper develops approximations for the first two moments of the run length distribution of
a one-sided Shewhart chart used to detect two types of process changes in a system that is regulated by a given EPC scheme:
i) changes in the level parameter; ii) changes in the drift parameter. If the drift parameter shifts, it is further assumed that the form of the drift process changes
from a linear trend under white noise (the in-control drift model) into a random walk with drift model. Two different approximations
for the run length moments are presented and their accuracy is numerically analyzed.
Received: August 1998 相似文献
10.
Self-adapting control charts 总被引:2,自引:1,他引:2
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. 相似文献
11.
Monitoring the mean and the variance of a stationary process 总被引:3,自引:0,他引:3
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. 相似文献
12.
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. 相似文献
13.
A renewal equation approach is proposed to derive the multiple special-cause cost model for a system with two dependent subprocesses. The economic individual X control chart and simple cause-selecting control chart are thus constructed to monitor the two subprocesses. They may be used to maintain the whole process with minimum cost and effectively distinguish which component of the subprocesses is out of control. The economic design parameters of these two control charts can be determined by minimizing the cost model using a simple grid search method. An example of its application on controlling service quality in the bank industry is given to illustrate the design procedure and its application. It shows that these control charts may be used to control not only manufacturing dependent subprocesses but also service organisations with dependent subprocesses. 相似文献
14.
A statistical process control chart named the mixture cumulative count control chart (MCCC-chart) is suggested in this study, motivated by an existing control chart named cumulative count control chart (CCC-chart). The MCCC-chart is constructed based on the distribution function of a two component mixture of geometric distributions using the number of items inspected until a defective item is observed ‘n’ as plotting statistics. We have observed that the MCCC-chart has the ability to perform equivalent to the CCC-chart when number of defective items follows geometric distribution and better than the CCC-chart when the number of defective items produced by a process follows a mixture geometric model. The MCCC-chart may be considered as a generalized version of CCC-chart. 相似文献
15.
We are interested in detecting changes in the performance of a credit portfolio quickly and robustly. The portfolio is dynamic: customers can either default or pay the full amount, and new customers can be taken on. Robust detection means that changing the number of new customers taken on should not lead to either a false or delayed signal. We investigate the performances of monitoring schemes via a simulation study that uses several scenarios. We consider monitoring based on default rates estimated through a gliding window, cumulative sum (CUSUM) charts based on default rates, CUSUM charts based on defaults within a given follow-up time after arrival, and a survival analysis CUSUM chart. We conclude that using a survival analysis approach is preferable to using the other approaches. 相似文献
16.
Muhammad Riaz 《Statistica Neerlandica》2008,62(4):458-481
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 Mr 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 Mr 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 proposedMr chart is observed for detecting the shifts in mean level of the characteristic of interest. 相似文献
17.
Estimation in Shewhart control charts: effects and corrections 总被引:3,自引:0,他引:3
The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied.Acknowledgements. The authors would like to thank Sri Nurdiati for doing the Monte Carlo studies. 相似文献
18.
S. J. Wierda 《Statistica Neerlandica》1994,48(2):147-168
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. 相似文献
19.
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. 相似文献
20.
Alireza Faraz R. Baradaran Kazemzadeh M. Bameni Moghadam Aliasghar Bazdar 《Quality and Quantity》2010,44(5):905-914
In this paper we introduce a fuzzy chart for variables which is used in situations when uncertainty and randomness are combined.
It is showed that the Shewhart chart’s control limits must be adjusted in these situations. However, this chart is based on
a fuzzy acceptance region and this method arises when a decision should be made by referring to the grade of a sample statistic
belonging to the fuzzy acceptance region. 相似文献