In this paper, a new nonparametric control chart based on two EWMA statistics is proposed for monitoring process deviation from the target value. The performance comparison of the proposed chart with the existing nonparametric EWMA sign control chart and a nonparametric CUSUM mean control chart are made by using out-of-control average run length. The simulation study showed the superiority of the suggested chart over the four other parametric and nonparametric charts. An empirical illustration is also provided for performance evaluation of the proposed chart. By comparing the proposed chart with the existing charts, it is concluded that the proposed chart is more sensitive in detecting a small shift in the process.

Expectiles have gained considerable attention in recent years due to wide applications in many areas. In this study, the k-nearest neighbours approach, together with the asymmetric least squares loss function, called ex-$kNN$, is proposed for computing expectiles. Firstly, the effect of various distance measures on ex-$kNN$ in terms of test error and computational time is evaluated. It is found that Canberra, Lorentzian, and Soergel distance measures lead to minimum test error, whereas Euclidean, Canberra, and Average of $(L_1,L_{\infty })$ lead to a low computational cost. Secondly, the performance of ex-$kNN$ is compared with existing packages er-boost and ex-svm for computing expectiles that are based on nine real life examples. Depending on the nature of data, the ex-$kNN$ showed two to 10 times better performance than er-boost and comparable performance with ex-svm regarding test error. Computationally, the ex-$kNN$ is found two to five times faster than ex-svm and much faster than er-boost, particularly, in the case of high dimensional data.