Robust point location estimators for the EWMA control chart

Figures & data

Table 1. Phase I location estimators.

Estimator	Notation
Mean of the sample means	̿X
Trimmed mean of the sample means	̿X20
Median of the sample means	MXt)
Mean of the sample medians	M
Median of the sample medians	M (Mt)
Trimmed mean of the sample trimeans	TMM20

Figure 1. MSE of location estimators when contaminations are present in Phase I.

Figure 2. ARLs of the Phase II EWMA control chart when contaminations are present in Phase I.

Table 2. ARL and percentiles of the RL distribution of the EWMA control chart with estimated parameters for k = 50, n = 5 and δ_I = 1.5.

Phase I		ARL and percentiles
		δII = 0				δII = 0.1				δII = 0.3				δII = 0.5
Contaminations		ARL	10th	50th	90th	ARL	10th	50th	90th	ARL	10th	50th	90th	ARL	10th	50th	90th
In-control	̿X(Benchmark)	369	26	199	899	208	14	90	511	21	3	14	44	6	1	5	13
	̿X20	357	25	188	870	208	13	89	521	21	3	14	45	7	1	5	13
	M(Xt)	331	22	168	819	210	12	86	531	24	3	14	48	7	1	5	13
	M	332	22	172	814	211	12	87	530	23	3	14	48	7	1	5	13
	M(Mt)	297	18	141	748	210	11	80	536	28	3	14	55	7	1	5	14
	TM20	342	23	176	839	212	13	87	528	22	3	14	47	7	1	5	13
Localized	̿X	139	8	48	340	280	16	127	707	136	8	47	330	17	2	10	34
	X20	260	15	113	650	318	20	157	790	54	5	23	112	10	2	7	20
	M(Xt)	264	15	115	671	288	17	136	726	52	5	21	108	10	2	7	19
	M	144	7	47	360	265	15	116	672	142	8	46	351	19	2	10	37
	M(Mt)	233	12	93	603	270	15	120	683	71	5	23	153	11	2	7	22
	TM20	243	14	103	623	307	19	149	765	61	5	24	128	10	2	7	21
Diffuse	̿X	208	13	75	486	630	34	280	1552	234	13	74	538	20	4	13	40
	X20	237	13	79	560	633	33	277	1572	227	12	69	521	20	4	13	40
	M(Xt)	263	13	79	652	599	29	248	1513	248	11	67	584	21	3	12	42
	M	321	15	100	796	651	33	286	1626	193	10	54	418	18	3	11	36
	M(Mt)	365	14	106	936	584	27	233	1478	205	8	48	463	20	3	11	38
	TM20	320	15	103	788	668	35	300	1680	181	10	53	393	17	3	11	35
Structural	̿X	112	9	49	260	318	21	159	786	111	9	48	258	14	3	10	30
	X20	267	17	123	667	334	22	172	818	45	5	23	97	9	2	7	19
	M(Xt)	273	16	124	685	299	18	144	746	47	5	21	97	9	2	7	19
	M	126	8	48	294	298	19	142	742	125	8	48	296	15	3	10	31
	M(Mt)	239	13	98	615	280	16	128	707	66	5	23	138	11	2	7	22
	TM20	253	15	112	640	325	21	164	802	52	5	24	110	10	2	7	20
Random	̿X	171	6	46	457	209	9	76	546	134	6	36	344	39	2	10	64
	X20	242	10	94	636	257	13	111	658	77	5	23	165	18	2	7	27
	M(Xt)	253	12	103	650	257	14	111	657	68	4	21	143	14	2	7	22
	M	166	5	45	443	204	8	72	536	134	6	35	346	40	2	10	67
	M(Mt)	220	9	81	580	237	12	95	607	84	4	23	192	18	2	7	28
	TM20	233	9	88	610	251	13	106	644	83	5	24	183	20	2	8	29