#### Title

Using Runs Rules to Monitor an Attribute Chart for a Markov Process

#### Document Type

Article

#### Publication Date

2012

#### Publication Title

Quality Technology and Quantitative Management

#### DOI

10.1080/16843703.2012.11673300

#### ISSN

1684-3703

#### Abstract

For some repetitive production processes, the quality measure taken on the output is an attribute variable. An attribute variable classifies each output item into one of a countable set of categories. One of the simplest and most commonly used attribute variables is the one that classifies an item as either "conforming" or "nonconforming." A tool used with a considerable amount of success in industry for monitoring the quality of a production process is the quality control chart. In this paper, a sequence of random variables, X* _{i}* ,

*i*= 1,2,… , is used to classify an item as conforming or nonconforming under a stationary Markov chain model and under 100% sequential sampling. The sequence of random variables to be plotted on the control chart is Y

_{i},

*i*= 1,2,… , where Y

_{1}counts the number of conforming items before the first nonconforming item and Y

_{i},

*i =*2,3,… counts the number of conforming items between the (

*i-1*)

^{th}and the

*i*nonconforming items. In the literature, Y

^{th}_{i}is called the CRL (Conforming Run Length). The contribution of this paper to the literature is to present runs rules for an attribute control chart of this type. The efficiency of these charts is evaluated using the average run length (ARL) of the charts. The supplemental runs rules that are presented are two out of three values of Y

_{i}, i 1,2, falling below determined lower limits, four out of five values of Y

_{i},

*i*=1,2,…falling below determined lower limits, and eight out of eight values of Y

_{i},

*i*=1,2,… falling below determined lower limits.

#### Recommended Citation

Shepherd, Deborah K., Steve E. Rigdon, Charles W. Champ.
2012.
"Using Runs Rules to Monitor an Attribute Chart for a Markov Process."
*Quality Technology and Quantitative Management*, 9 (4): 383-406.
doi: 10.1080/16843703.2012.11673300

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/20