TY - JOUR
T1 - Attribute Charts for Monitoring a Dependent Process
AU - Shepherd, Deborah K.
AU - Champ, Charles W.
AU - Rigdon, Steven E.
AU - Fuller, Howard T.
PY - 2007/4/1
Y1 - 2007/4/1
N2 - 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 which classifies an item as either 'conforming' or 'non-conforming'. A tool used with a considerable amount of success in industry for monitoring the quality of a production process is the quality control chart. Generally a control charting procedure uses a sequence, X1, X2..., Xt,... of the quality measures to make a decision about the quality of the process. How this sequence is used to make a decision defines the control chart. In order to design a control chart one must consider how the underlying sequence, X1, X2,..., Xt, ..., is modeled. The sequence is often modeled as a sequence of independent and identically distributed random variables. For many industrial processes, this model is appropriate, but in others it may not be. In this paper, a sequence of random variables, Xi, i = 1, 2,..., is used to classify an item as conforming or non-conforming under a stationary Markov chain model and under 100% sequential sampling. Two different control charting schemes are investigated. Both schemes plot a sequence of measures on the control chart, Yi, i = 1, 2, ... that count the number of conforming items before a non-conforming item. The first scheme signals as out-of-control if a value of Yi, i = 1, 2, ... falls below a certain lower limit. The second scheme signals as out-of-control if two out of two values of Y i, i = 1, 2, ... fall below a certain lower limit. The efficiency of both of the control charts is evaluated by the average run length (ARL) of the chart and the power of the chart to detect a shift in the process. The two out of two scheme is shown to have high power and a large ARL given certain parameter values of the process. An example of the two out of two scheme is provided for the interested reader.
AB - 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 which classifies an item as either 'conforming' or 'non-conforming'. A tool used with a considerable amount of success in industry for monitoring the quality of a production process is the quality control chart. Generally a control charting procedure uses a sequence, X1, X2..., Xt,... of the quality measures to make a decision about the quality of the process. How this sequence is used to make a decision defines the control chart. In order to design a control chart one must consider how the underlying sequence, X1, X2,..., Xt, ..., is modeled. The sequence is often modeled as a sequence of independent and identically distributed random variables. For many industrial processes, this model is appropriate, but in others it may not be. In this paper, a sequence of random variables, Xi, i = 1, 2,..., is used to classify an item as conforming or non-conforming under a stationary Markov chain model and under 100% sequential sampling. Two different control charting schemes are investigated. Both schemes plot a sequence of measures on the control chart, Yi, i = 1, 2, ... that count the number of conforming items before a non-conforming item. The first scheme signals as out-of-control if a value of Yi, i = 1, 2, ... falls below a certain lower limit. The second scheme signals as out-of-control if two out of two values of Y i, i = 1, 2, ... fall below a certain lower limit. The efficiency of both of the control charts is evaluated by the average run length (ARL) of the chart and the power of the chart to detect a shift in the process. The two out of two scheme is shown to have high power and a large ARL given certain parameter values of the process. An example of the two out of two scheme is provided for the interested reader.
KW - Attribute Charts
KW - Dependent Process
UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/493
UR - https://doi.org/10.1002/qre.793
U2 - 10.1002/qre.793
DO - 10.1002/qre.793
M3 - Article
SN - 0748-8017
VL - 23
JO - Quality and Reliability Engineering International
JF - Quality and Reliability Engineering International
ER -