Robustness ofR-Chart to Non Normality

Abstract

This study addresses the appropriate d 3 values for constructing range control charts (R-charts) when the distributions of the processes are the uniform, triangular, exponential, and Erlang. Comparisons of the range charts are based on Type I error probabilities obtained using simulations. The results reveal that inappropriate use of the d 3 values strongly affected the performance of the R-charts. Practitioners should be more careful in selecting suitable coefficients when using R-charts methods to process data. The distribution of the processes must be examined before the coefficients are chosen.

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

“…The simulated results as shown in Tables for the case of R and S are similar to those of exact results reported in most SPC books assuming normality of the quality characteristic (e.g., see tables of Ryan). For the case of non‐normal distributions, the results are also similar to the results reported for R chart by Mahoney, Kao and Ho, and Sim and Wong, which confirm the validity of our simulation routines. The power of control charts to detect shifts in process variability is used as a performance measure following Duncan, Nelson, and Riaz .…”

“…In most books on SPC, the control chart constants t 2 for R and S charts are provided under the assumption of normality of quality characteristics. When the assumption of normality is disturbed, the use of these constants no longer remains valid as shown by Mahoney and Kao and Ho . They considered several non‐normal distributions and examine their effect on the values of t 2 (commonly known as d 2 when σ is estimated using R ) for Shewhart and R charts and conclude that inappropriate use of d 2 values increases the false alarm rate of both and R charts.…”

Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

“…Mahoney studied the d 2 values for constructing the charts, and found out that the d 2 values seriously depend on the normal assumption. The results of Kao and Ho demonstrated that for four non‐normal distributions, the performance of range charts is worse than that under normal condition. Meanwhile, numerous papers show that the performance of the control charts with asymmetric control limits is better than those with symmetric control limits when the underlying distributions are skewed .…”

MDEWMA chart: an efficient and robust alternative to monitor process dispersion

“…When this assumption is violated, the use of these constants is no longer valid. This was shown by Mahoney [33] and Kao and Ho [34] forX and R charts. They considered several nonnormal distributions for the quality characteristic and concluded that the inappropriate use of d 2 and d 3 values to calculate control limits increases the false alarm rate of bothX and R charts.…”