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Economic Contro! Chart

109

LV Notation (Modlfied for Sampling by Attributes)

Table 2. Relating Earlier Model Notation to the Lorenzen-Vance "Unified" Model

Article	X	A	PO	P\	E	^tq	^Tl	h ...	a^1"^- ^T\+^T2	^51	09 I K) 8
1	X	NA	PO	Pl	0	*0	NA	NA	‘1	0	0
2	1	NA	PO	Ps	0	*0	NA	NA	<s	0	0
3^b	Notation matches Duncan (1956) for the single assignable cause model and Duncan (1971) for the multiple assignable cause model
4	X	5	NA	NA	e	NA	NA	NA	D	1	i
5(1)	*s	«s	NA	NA	g	NA	NA	NA	Ds	1	i
6	X	5	PO	Pl	g	NA	NA	NA	D	1	i
7(1)	X	NA	PO	Pl	g	*1	^X1	^x2	NA	0	0
7(2)	X	NA	Po	Pl	g	^X1	^X1	^x2	NA	1	0
8(1)	X	NA	Po	Pl	g	X	X	(1/X)£ Xjtj	NA	0	0
8(2)	X	NA	Po	Pl	g	X	X	(1/X)I Xjtj	NA	1	0
9	X	5	NA	NA	g	NA	NA	NA	D	1	1

LV Notation (Modified for Sampling by Attributes)

Article	,£jl	^C1	Y	W	a	b	n	h	L	d
1	0	< o 1	^0 ^+vo*o	Ai + V0ti	b	c	n	h	NA	d
2 3^b	0	< o i	Ao ^+ Vok)	A« ^+ v0*s	b	c	n	h	NA	d
4	0	M	T	W	b	c	n	h	k	NA
5(1)	0	^Ms	T	^Ws	b	c	n	h	k	NA
6	0	M	T	W	b	c	n	h	NA	d
7(1)	0	riP\~PQ>	(^cl+c2)xi	(^cl+c2)xi + (c2+c3)x2	h	b	n	V	NA	c
7(2)	0	*<P\-Pq)u	C,Xi	^cl^xl ^+(^c2^+c3)^x2	h	b	n	V	NA	c
8(1)	0	Kpi-po)^u	(s+d)x	(s+d)x + (l/X)EXjtj(d+Cj)	h	b	n	V	NA	c
8(2)	0	TiPl~P0)^u	sx	sx +(l/X)IXjtj(d+Cj)	h	b	n	V	NA	c
9	0	H	^a3	a3	^al	*2	n	h	k	NA

^ain several models a single parameter corresponds to Tj + 7^, the total time required to discover an gssignable cause and repair the process.

This article presents constrained versions of Duncan's X-chart models, where the constraint is on the out of control signal probability p.

NA, not appliable.