Suppose that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$Y_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>Y</mi> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> follows a simple AR(1) model, that is, it can be expressed as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$Y_t= \alpha Y_{t-1} + W_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>Y</mi> <mi>t</mi> </msub> <mo>=</mo> <mi mathvariant="italic">α</mi> <msub> <mi>Y</mi> <mrow> <mi>t</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>W</mi> <mi>t</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$W_t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>W</mi> <mi>t</mi> </msub> </math> </EquationSource> </InlineEquation> is a white noise with mean equal to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mu $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">μ</mi> </math> </EquationSource> </InlineEquation> and variance <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\sigma ^2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi mathvariant="italic">σ</mi> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation>. There are...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Few approaches for monitoring autocorrelated attribute data have been proposed in the literature. If the marginal process distribution is binomial, then the binomial AR(1) model as a realistic and well-interpretable process model may be adequate. Based on known and newly derived statistical...