Measurement error effect on the power of control chart for Zero truncated Negative Binomial Distribution (ZTNBD)

Abstract

In the present article measurement error effect on the power of control chart for ZTNBD is investigated based on standardized normal variate.Numerical calculations are presented so as to enable an appreciation of the consequences of measurement errors on the power curve. To examine the sensitivity of the monitoring procedure, average run length is also considered.

Impact of Measurement Error on the Power Function of Average Control Chart under Non-Normal Population

“…In quality control applications measurement error often exists which is known to result in reduced power to detect a given change in the mean of a quality characteristic. The effect of measurement error on control chart is considered by many authors: Bennet [4], Linna and Woodall (2001), Duffua and Khan [5], Chakraborty et al [6], Singh and Mishra [7]. Noor-ul-Amin [8] studied the impact of measurement error on mixed EWMA-CUSUM control chart.…”

The performance of the adaptive EWMA median chart in the presence of measurement error

“…But, in practice, an exact measurement is a rare phenomenon in any of the situations where human involvement is evident. The effect of measurement errors has been intensively investigated for a number of mean‐ or variance‐type charts, and the conclusion is that the performance of these charts is always negatively affected in presence of such errors, see, for instance, Linna and Woodall,() Maravelakis et al, Shore, Chang and Nikzad, Chakraborty and Khurshid, Amiri and Nikzad, Khati Dizabadi et al, Ghashghaei et al, Tran et al, Daryabari et al, Sabahno and Amiri, Castagliola et al, and Salmasnia et al …”

“…But, in practice, an exact measurement is a rare phenomenon in any of the situations where human involvement is evident. The effect of measurement errors has been intensively investigated for a number of mean-or variance-type charts, and the conclusion is that the performance of these charts is always negatively affected in presence of such errors, see, for instance, Linna and Woodall, 25,26 Maravelakis et al, 27 Shore, 28 Chang and Nikzad, 29 Chakraborty and Khurshid, 30 Amiri and Nikzad, 31 Khati Dizabadi et al, 32 Ghashghaei et al, 33 Tran et al, 34 Daryabari et al, 35 Sabahno and Amiri, 36 Castagliola et al, 37 and Salmasnia et al 38 The measurement errors model the most commonly used in the literature is the linear covariate model, proposed by Linna and Woodall,25 ie, Y = A + BX + , where A and B are known constants and is a random error due to the measurement imprecision. In this paper, they investigated the properties of the ShewhartX and the S 2 charts with measurement errors, and they suggested taking multiple measurements to compensate for the effect of measurement errors, Maravelakis et al 27,39 evaluated the performance of the EWMAX and the CUSUMX charts, respectively, in the presence of measurement errors using the same linear covariate model.…”

Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

“…Chakraborty and Khurshid studied the effect of measurement error on the ability of zero truncated Poisson control chart. Haq et al .…”