Measurement Error Effect on the Power of Control Chart for the Ratio of Two Poisson Distributions

It is widely recognized that measurement errors often exist in practice and may considerably affect the performance of control charts in some cases. Measurement error variability has uncertainty which may be originated from several sources. Recently, Chakraborty and Khurshid [3] studied the effects of measurement error on control charts for zero-truncated Poisson distribution. In this paper, we study the effect of the two sources of variability on the power characteristics of control charts and obtain the values of average run length (ARL) for the binomial distribution based on the ratio of two Poisson distributions as studied by Sahai and Khurshid [20]. Expression of the power of the control chart under the standardized normal variable for the binomial distribution is also derived when the underlying distribution is the ratio of two Poisson distributions.