c4(LT)j

Unbiasing constant for long-term calculations at cumulative jth subgroup

c4(ST)j

Unbiasing constant for short-term calculations at cumulative jth subgroup

Cum SD(LT)j

Cumulative long-term standard deviation up to the jth subgroup

Cum SD(ST)j

Cumulative short-term standard deviation up to the jth subgroup

Cum SS(LT)j  

Cumulative long-term sum of squares up to the jth subgroup

Cum SS(ST)j

Cumulative short-term sum of squares up to the jth subgroup

cmLT,j

Cumulative mean up to the jth subgroup (Cum Meanj)

df(LT)j

Long-term degrees of freedom at jth subgroup

df(ST)j

Short-term degrees of freedom at jth subgroup

K

Number of subgroups

LSL

Lower specification limit

mj

Mean of the jth subgroup

mLT

Long-term mean or process mean    Note: mLT  =

mST

Short-term mean

nj

Size of the jth subgroup

P.LSL(LT)j

Long-term probability of less than or equal to lower spec at jth subgroup

P.LSL(ST)j

Short-term probability of less than or equal to lower spec at jth subgroup

P.USL(LT)j

Long-term probability of greater than or equal to upper spec at jth subgroup

P.USL(ST)j

Short-term probability of greater than or equal to upper spec at jth subgroup

P.Total(LT)j

Total (long-term) probability of out-of-spec at jth subgroup

P.Total(ST)j

Total (short-term) probability of out-of-spec at jth subgroup

F (z)

Standard normal cdf

F -1(p)

Inverse standard normal cdf

T

Target

USL

Upper specification limit

Long-term mean or process mean   Note: =  mLT

Z.Bench(LT)j

Benchmark Z (long-term) at jth subgroup

Z.Bench(ST)j

Benchmark Z (short-term) at jth subgroup

Z.LSL(LT)j

Z-value (long-term) for lower spec at jth subgroup

Z.LSL.(ST)j

Z-value (short-term) for lower spec at jth subgroup

Z.USL(LT)j

Z-value (long-term) for upper spec at jth subgroup

Z.USL(ST)j

Z-value (short-term) for upper spec at jth subgroup

Z.Shiftj  

Shift factor at jth subgroup