=2), the difference of the ARL between the nonnormal and estimation case with the normal and known variance case decreases as m increases. (6) For the simultaneous effect of autocorrelation, nonnormality, and estimation: we conclude that the three-dimensional effect is nonmonotic on the mean and standard deviation of run length. For Subproblem 2, we propose an algorithm to compute values of the sample size n and control-limit factor k that minimize the out-of-control ARL while keeping the in-control ARL at a specified value. Simulation experiments are run to compare the proposed Xbar chart design with the EWMAST (Exponentially Weighted Moving Average STationary), SCC (Special Cause Control), and ARMAST (Auto-Regressive Moving-Average STationary) charts. When the data process is ARMA(1, 1) (AutoRegressive of order 1 and Moving Average of order 1) process, the ARMAST chart outperforms the proposed Xbar chart, EWMA, and SCC because the ARMAST chart is designed based on the ARMA(1, 1) process. When the data process is autocorrelated with nonnormal distribution, the proposed Xbar chart often performs better than the ARMAST chart. For Subproblem 3, we propose two distribution-free methods (denoted as Methods 1 and 2) to compute the sample size n and control-limit factor k that minimize the out-of-control ARL while keeping the in-control ARL at a specified value. Methods 1 and 2 are based on the assumptions that sample means are independently and normally distributed and that sample means follow an AR(1) (AutoRegressive of order 1) process, respectively. We further modify Methods 1 and 2 by setting the sample size to be at least 30 to meet the central limit theorem. The modified Method 2 outperforms the modified Method 1. We compare the modified Method 2 with R&W (Runger and Willemain) and DFTC (Distribution-Free Tabular CuSum) charts. The R&W and DFTC charts perform better when the autocorrelation is small to moderate and the shift is small or large. Our modified Method 2 performs better when the autocorrelation is high and the shift is moderate to large. For Subproblem 4, we propose a model-free Xbar chart design for unknown autocorrelated data processes, when M observations of in-control quality characteristic measurements are given. The standard deviation of Xbar is estimated by the NBM (nonoverlapping batch means) method. The Xbar chart design parameters n and k and the NBM batch size omega are determined to minimize the out-of-control ARL while keeping the in-control ARL at a specified value. During the search of n, k, and omega, the ARL values are computed assuming that the sample means and batch means are independently and normally distributed. The computed optimal values of n and omega are further modified to be at least 30 for meeting the central limit theorem. Simulation experiments are run to evaluate the performance of the proposed model-free Xbar chart using AR(1) processes and ARTA(1) (AutoRegressive To Anything of order 1) processes with t and exponential marginal distributions as testing examples. The experimental results show that our model-free method performs well in general; it performs better when the autocorrelation is small or when the autocorrelation is large but the shift is small or moderate. The proposed model-free Xbar chart performs worse when the data process is ARTA(1) with an exponential marginal distribution.' > Airiti Library
Search & Read at all times.
Your portable library is online!
3.227.247.17,Hello!
Search Symbol (Half-width) Description of Search Symbols
Space "AND" indicates the intertwining of key terms used in a search
Double Quotation Marks ("") ( " " ) Double quotation marks indicate the beginning and end of a phrase, and the search will only include terms that appear in the same order of those within the quotations. Example: "image process" : " image process "
? Indicates a variable letter. Entering two ? will indicate two variable letters, and so on. Example: "Appl?", search results will yield apple, apply… e , appl y … ( (often used to English word searches) )
* Indicates an unlimited number of variable letters to follow, from 1~n. Example: Enter "appl*", search results will yield apple, apples, apply, applied, application…(often used in English word searches) e , appl es , appl y , appl ied , appl ication … ( (often used to English word searches) )
AND、OR、NOT

Boolean logic combinations of key words is a skill used to expand or refine search parameters.
(1) AND (1) AND: Refines search parameters
(2) OR (2) OR: Expands search parameters (3) NOT: Excludes irrelevant parameters

close

DOI stands for Digital Object Identifier ( D igital O bject I dentifier ) ,
and is the unique identifier for objects on the internet. It can be used to create persistent link and to cite articles.

Using DOI as a persistent link

To create a persistent link, add「http://dx.doi.org/」 「 http://dx.doi.org/ 」 before a DOI.
For instance, if the DOI of an article is 10.5297/ser.1201.002 , you can link persistently to the article by entering the following link in your browser: http://dx.doi.org/ 10.5297/ser.1201.002
The DOI link will always direct you to the most updated article page no matter how the publisher changes the document's position, avoiding errors when engaging in important research.

Cite a document with DOI

When citing references, you should also cite the DOI if the article has one. If your citation guideline does not include DOIs, you may cite the DOI link.

DOIs allow accurate citations, improve academic contents connections, and allow users to gain better experience across different platforms. Currently, there are more than 70 million DOIs registered for academic contents. If you want to understand more about DOI, please visit airiti DOI Registrationdoi.airiti.com ) 。

Share
Abstract 〈TOP〉
Parallel Abstract 〈TOP〉
Reference ( 74 ) 〈TOP〉
  1. [20] Choobineh, F., Ballard, J. L. (1987). Control-Limits of QC Charts for Skewed Distributions Using Weighted-Variance. IEEE Transactions on Reliability 36}, 473-477.
    連結:
  2. [23] Darling, D. A. and A. J. F. Siegert. (1953). The First passage problem for a continuous Markov process. Annals of Mathematical Statistics 24}, 624-639.
    連結:
  3. [24] Del Castillo, E. (1996). Evaluation of Run Length Distributions for Xbar Charts with Unknown Variance. Journal of Quality Technology 28}, 116-122.
    連結:
  4. [29] Goldsman, D., M. S. Meketon, and L. W. Schruben. (1990). Properties of standardized time series weighted area variance estimators. Management Science 36, 602-612.
    連結:
  5. [44] Lucas, J.M. and M.S. Saccucci (1990). Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics 32, 1-12.
    連結:
Altmetrics 〈TOP〉
E-mail :
When an article is available to download, a notice will be sent to your mailbox address.
E-mail :

close

close