Single Attribute Control Charts for a Markovian-Dependent Process

Abstract

In a production process, sequence of observations related to the quality of a process need not be independent. In such situations, control charts based on the assumption of independence of the observations are not appropriate. When the characteristic under study is qualitative, the Markovian model serves as a simple model to account for the dependency of the observations. In this article, we develop two attribute control charts for a Markovian dependent process: the first is based on controlling the error probabilities; the second is based on minimizing the average time to get a correct signal.

The charts are developed under uniform sampling. Under uniform sampling, the two consecutive samples are far enough apart, so that for all practical purposes, two consecutive samples can be considered as if they are being independent. Optimal values of the design parameters of both the control charts are obtained. A procedure to estimate the values of the in-control parameters is also described. The chart's performance is evaluated using the probability of detecting shift. When we implement the proposed charts for the data simulated under given manufacturing environments, the charts exhibit the desired properties of error probabilities and average time to signal.

Keywords:

• Average time to signal
• Markovian dependence
• Transition probability matrix
• Serial correlation.

Mathematics Subject Classification:

• 62P30.