Abstract:
Ranked set sampling prescribes the number of units from each rank order that are to be measured. Ranked set sampling is expected to be more efficient than Simple Random Sampling, when applicable regardless of how the ranking is done. Nonparametric or distribution-free charts using simple random sampling (SRS) has been found useful when there is no underlying process distribution but inefficient in monitoring process parameters. This study proposed a non parametric exponentially weighted moving average (EWMA) control chart based on sign test using ranked set sampling (RSS) to monitor small shifts in the process variability and detect assignable causes of variation (if any). Ranked set sampling technique is applied on random data generated using R package. Then, a computer programming code in R language was developed, to evaluate the performance of run lengths characteristics of the proposed chart, and it was compared with existing EWMA sign chart based on SRS using a fixed in-control ARL value (ARL0≅ 370) for the control limits coefficient (k) and different combination of sample sizes (n =3,4,5,6,7,8,9,10), cycle times (m=3,5,7) and smoothing parameter which 𝜆= 0.05 of the design parameters. The results shows that the performance of the proposed chart is better than the existing Exponentially Weighted Moving Average (EWMA) sign test based on simple random sampling (SRS) for monitoring process variability, since the values of the performances metrics observed for different combination of sample sizes (n) and cycle times (m) is smaller than the existing ones.
