Attribute Charts for Monitoring a Dependent Process

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Quality and Reliability Engineering International






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, 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, 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, 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, that count the number of conforming items before a non-conforming item. The first scheme signals as out-of-control if a value of falls below a certain lower limit. The second scheme signals as out-of-control if two out of two values of 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.