EXTREME RANKED REPETITIVE SAMPLING CONTROL CHARTS

Amjad D. Al-Nasser ^**Corresponding author

Department of Statistics, Science Faculty, Yarmouk University, Irbid, Jordan - E-mail: amjadyu@yahoo.com

Enrico Ciavolino

Department of History, Society and Human Studies, University of Salento, Lecce, Italy - E-mail: enrico.ciavolino@unisalento.it

Amer Al-Omari

Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan - E-mail: alomari amer@yahoo.com

Shift	SRS	RSS	ERSS	Rep-RSS	Rep-ERSS
Shift	SRS	RSS	ERSS	k1= 3.03, k2= 2.09	k1= 3.18, k2= 1.2
0.0	369.68	340.56	340.4835	370.37	370.37
0.1	351.27	321.85	319.1829	318.58	285.71
0.2	305.25	254.77	247.5247	217.39	158.73
0.3	254.71	185.19	184.2978	163.93	163.93
0.4	202.47	128.51	133.7614	108.67	101.01
0.5	153.23	128.50	91.2909	86.95	90.09
1.0	43.31	18.89	18.87	14.99	12.09
1.8	8.67	3.27	3.2947	2.96	2.74
2.6	2.91	1.38	1.3774	1.24	1.36
3.4	1.52	1.04	1.05	1.00	1.01

Shift	SRS	RSS	ERSS	Rep-RSS	Rep-ERSS
Shift	SRS	RSS	ERSS	k1= 3.05, k2= 2.12	k1= 3.18, k2= 1.224
0.0	369.41	349.04	331.78	370.37	370.37
0.1	341.71	312.30	304.59	303.03	185.19
0.2	312.98	229.41	243.24	227.27	138.89
0.3	256.01	166.75	179.69	117.64	121.95
0.4	200.79	115.94	126.35	81.96	80.65
0.5	156.12	76.70	88.12	62.11	46.30
1.0	45.32	14.15	17.40	11.57	10.78
1.8	8.88	2.48	3.01	2.24	2.38
2.6	2.95	1.19	1.31	1.16	1.12
3.4	1.52	1.01	1.03	1.01	1.01

Shift	SRS	RSS	ERSS	Rep-RSS	Rep-ERSS
Shift	SRS	RSS	ERSS	k1= 3.06, k2= 2.51	k1= 3.21, k2= 1.84
0.0	369.41	356.76	350.7541	370.37	370.37
0.1	341.71	301.93	298.8643	292.61	200.00
0.2	312.98	225.83	229.8322	185.18	113.64
0.3	256.01	152.46	164.4466	136.98	80.65
0.4	200.79	98.42	107.1352	69.93	58.82
0.5	156.12	65.33	74.0631	51.81	44.25
1.0	45.32	11.05	13.5932	9.38	9.12
1.8	8.88	2.01	2.3922	1.84	2.08
2.6	2.95	1.10	1.1761	1.07	1.15
3.4	1.52	1.00	1.01	1.00	1.01

Shift	SRS	RSS	ERSS	Rep-RSS	Rep-ERSS
Shift	SRS	RSS	ERSS	K1= 3.07, k2= 2.73	K1= 3.2, k2= 1.98
0.0	370.52	346.14	331.12	370.37	370.37
0.1	349.41	300.84	309.88	285.71	232.56
0.2	309.02	218.77	232.66	212.55	169.49
0.3	248.04	137.12	158.40	107.52	92.59
0.4	198.89	87.00	110.60	62.50	64.52
0.5	154.94	55.95	75.03	40.81	45.45
1.0	45.57	9.00	13.66	7.73	9.57
1.8	7.69	1.71	2.39	1.58	2.02
2.6	2.93	1.05	1.17	1.04	1.12
3.4	1.52	1.00	1.01	1.00	1.01

{\overset{'}{x}}_{E R S S} = \{\begin{cases} \frac{1}{m n} \sum_{j = 1}^{m} (\sum_{i = 1}^{\frac{n}{2}} X_{[1 : n] i, j} + \sum_{i = \frac{n}{2} + 1}^{n} X_{[n : n] i, j}); n is even \\ \frac{1}{m n} \sum_{j = 1}^{m} (\sum_{i = 1}^{\frac{n}{2} - 1} X_{[1 : n] i, j} + \sum_{i = \frac{n}{2}}^{n - 1} X_{[n : n] i, j} + X_{[\frac{n + 1}{2} : i, j]}); n is odd \end{cases}

μ_{E R S S} = E ({\overset{'}{x}}_{E R S S}) = \{\begin{cases} \frac{1}{2} (μ_{(1)} + μ_{(n)}); n is even \\ \frac{n - 1}{2 n} (μ_{(1)} + μ_{(n)}) + \frac{1}{2} μ_{(\frac{n + 1}{2})}; n is odd \end{cases}

σ_{E R S S}^{2} = \{\begin{cases} \frac{1}{2 n} (σ_{(1)}^{2} + σ_{(n)}^{2}); n is even \\ \frac{(n - 1)}{2 n^{2}} (σ_{(1)}^{2} + σ_{(n)}^{2}) + \frac{1}{n^{2}} σ_{(\frac{n + 1}{2})}^{2}; n is odd \end{cases}

\hat{U C L_{1}} = {\hat{μ}}_{e r s s 0} + k_{1} {\hat{σ}}_{{\overset{'}{X}}_{E R S S}} \hat{U C L_{2}} = {\hat{μ}}_{e r s s 0} + k_{2} {\hat{σ}}_{{\overset{'}{X}}_{E R S S}} \hat{L C L_{2}} = {\hat{μ}}_{e r s s 0} - k_{2} {\hat{σ}}_{{\overset{'}{X}}_{E R S S}} \hat{L C L_{1}} = {\hat{μ}}_{e r s s 0} - k_{1} {\hat{σ}}_{{\overset{'}{X}}_{E R S S}}

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