BS ISO 7870-6:2016 pdf download – Control charts Part 6: EWMA control charts

5 Choice of the control chart 5.1 Shewhart control chart versus EWMA control chart Unlike the Shewhart control chart, it is not possible to find the probability of detecting a shift in the process on the basis of a sample because the probability is not constant. It depends on the number of the samples. One can calculate this probability for each sample, but these probabilities are too numerous to be used in practice. The effectiveness of the EWMA technique is therefore judged according to the ARL, i.e. the average number of successive samples required for detecting a shift. If the process is under control, it is expected that there be few false alarms, i.e. that the average number of samples prior to a false alarm be high (in general ARL 0 is taken between 100 and 1 000). On the other hand, in the event of a shift, it is expected that it be detected as quickly as possible, i.e. that the number of samples between the moment the shift occurred and that of the first point outside the control limits be the lowest possible (low ARL 1 ). Compared to the Shewhart control chart, the EWMA technique is extremely effective for minor or moderate shifts: the lower λ is, better is the effectiveness. On the other hand, the Shewhart control chart is more effective for sudden and high drifts. The effectiveness of the chart depends on the size of the sample: the higher n is, better is the effectiveness (see Annex D).

5.2 Average run length Table 3 gives the ARL and the MAXRL of the chart as a function of the drift, δ n . Therefore, the effectiveness for any value of n can be obtained. For example, the EWMA control chart with λ = 0,5, L z = 2,979 and n = 1 detects a shift of δ = 1 standard deviation in 14,5 samples on average because δ n = 1 . Whereas, the same chart with n = 4 detects it in 3,2 samples, because δ n = 2. In Table 3, the values of L z for the EWMA techniques have been chosen, so that the ARL (Average Run Length) = 370 (i.e. the same as that of the Shewhart control chart), with control limits established at ±3 σ n when the shift, δ , is equal to 0. Hence, you can compare the figures in the six columns directly since it is a question of control procedures, which have the same number of false alarms. Table 3 shows that the effectiveness for detecting minor shifts is better for small values of λ (e.g. the ARL goes from 14,9 to 7,6 for δ n = 1 ) ; and, is the contrary for major drifts (e.g. the ARL goes from 1,6 to 1,5 for δ n = 3 ). The choice of λ and L z is made so as to obtain an Average Run Length which one sets in an a priori manner as the quality objective. One can therefore thus obtain charts which correspond to the practical requirements of industry or services.

5.3 Choice of parameters for EWMA control chart

5.3.1 Choice of λ

The smaller λ is, the more the past is taken into account and the better minor drifts are detected; on the other hand, major, sudden drifts are less well detected;

The higher λ is, the less the past is taken into account and the better the reactivity to major, sudden drifts will be; on the other hand, minor drifts are less well detected.

The choice of λ shall be made on the basis of the experience that one has of the process. In general,0,05 ≤ λ ≤ 0,50 works well in practice,

— if slow drifts are expected, one should choose a value of λ between 0,05 to 0,25, and

— if one fears sudden, moderate magnitude shifts, one should choose rather a value of λ close to 0,5.

The most commonly used values of λ are between 0,25 and 0,5 inclusive. It is to be noted that one obtains the Shewhart control chart if one takes λ = 1.