Calculations - Process Report
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See the notation used in the equations below:

Unbiasing constants for estimating long-term and short-term standard deviation
c4(LT)j	=		where:
c4(ST)j	=		where:
Short-term standard deviation with unbiasing constant (default)
Cum SD(ST)j	=		where:
Short-term standard deviation without unbiasing constant
Cum SD(ST)j	=		where:
Long-term standard deviation without unbiasing constant (default)
Cum SD(LT)j	=		where:
Long-term standard deviation with unbiasing constant
Cum SD(LT)j	=		where:
Long-term process mean
mLT	=		where:	mLT = cmLT,K
Long-term process standard deviation
sLT	=	Cum SD(LT)K

Short-term process mean

mST

=

T

If target given

(USL +LSL)

2

If no target given, both specs given

mLT

If no target given, only 1 spec given

Short-term process standard deviation

sST

=

Cum SD(ST)K

(See Centering values for short term statistics)

Capability statistics

CCpk

=

min	{	USL - mST	,	mST - LSL	}
		3sST		3sST

Cp

=

(USL - LSL) / (6sST)

Cpk

=

min	{	USL - mLT	,	mLT - LSL	}
		3sST		3sST

CPL

= (mST - LSL) / (3sST)

CPU

= (USL - mST) / (3sST)

Pp

=

(USL - LSL) / (6sLT)

Ppk

=

min	{	USL - mLT	,	mLT - LSL	}
		3sLT		3sLT

PPL

=

(mLT - LSL) / (3sLT)

PPU

=

(USL - mLT) / (3sLT)

Degrees of freedom

df(LT)j

=

df(ST)j

=

Proabilities

P.LSL(LT)j

=

1 - F(Z.LSL(LT)j )

P.LSL(ST)j

=

1 - F(Z.LSL(ST)j )

P.USL(LT)j

=

1 - F(Z.USL(LT)j )

P.USL(ST)j

=

1 - F(Z.USL(ST)jj )

P.Total(LT)j

=

P.USL(LT)j + P.LSL(LT)j

P.Total(ST)j

=

P.USL(ST)j + P.LSL(ST)j

Z bench statistics

Z.Bench(LT)j

=

F $image\MINUSONE.gif$ (P.Total(LT)j)

Z.Bench(ST)j

=

F $image\MINUSONE.gif$ (P.Total(ST)j)

Z.LSL(LT)j

=

(mLT - LSL) / Cum SD(LT)j

Z.LSL(ST)j

= (mST - LSL) / Cum SD(LT)j

Z.USL(LT)j

=

(USL - mLT) / Cum SD(LT)j

Z.USL(ST)j

= (USL - mST) / Cum SD(LT)j

Z.Shiftj

=

Z.Bench(ST)j - Z.Bench(LT)j

Note	Cp, Cpk, and CCpk represent the potential capability of the process. Therefore, these formulas use short-term variability. Pp and Ppk represent the actual process performance. Therefore, these formulas use long-term variability.