where:
Term  Description 

c_{4}(LT)_{j}  Unbiasing constant for longterm calculations at cumulative j^{th} subgroup 
c_{4}(ST)_{j}  Unbiasing constant for shortterm calculations at cumulative j^{th} subgroup 
df(LT)_{j}  Longterm degrees of freedom at j^{th} subgroup 
df(ST)_{j}  Shortterm degrees of freedom at j^{th} subgroup 
where:
Term  Description 

Cum SD(ST)_{j}  Cumulative shortterm standard deviation up to the j^{th} subgroup 
c_{4}(ST)_{j}  Unbiasing constant for shortterm calculations at cumulative j^{th} subgroup 
df(ST)_{j}  Shortterm degrees of freedom at j^{th} subgroup 
where:
Term  Description 

Cum SD(LT)_{j}  Cumulative longterm standard deviation up to the j^{th} subgroup 
c_{4}(LT)_{j}  Unbiasing constant for longterm calculations at cumulative j^{th} subgroup 
df(LT)_{j}  Longterm degrees of freedom at j^{th} subgroup 
Term  Description 

µ_{LT} 
Longterm mean or process mean μ_{LT} = cμ_{LT,K} Note

σ_{LT} = Cum SD(LT)_{K}
Term  Description 

µ_{ST}  Shortterm mean 
T  Target 
µ_{LT} 
Longterm mean or process mean Note

σ_{ST} = Cum SD(ST)_{K}
For more information, go to How Minitab chooses centering values for shortterm statistics for Process Report.
Cp, Cpk, and CCpk represent the potential capability of the process. Therefore, these formulas use shortterm variability.
Pp and Ppk represent the actual process performance. Therefore, these formulas use longterm variability.
Term  Description 

df(LT)_{j}  Longterm degrees of freedom at j^{th} subgroup 
df(ST)_{j}  Shortterm degrees of freedom at j^{th} subgroup 
Longterm probability of less than or equal to lower spec at j^{th} subgroup
P.LSL(LT) _{j} = 1 – Φ(Z.LSL(LT)_{j})
Shortterm probability of less than or equal to lower spec at j^{th} subgroup
P.LSL(ST) _{j} = 1 – Φ(Z.LSL(ST)_{j})
Longterm probability of greater than or equal to upper spec at j^{th} subgroup
P.USL(LT) _{j} = 1 – Φ(Z.USL(LT)_{j})
Shortterm probability of greater than or equal to upper spec at j^{th} subgroup
P.USL(ST) _{j} = 1 – Φ(Z.LSL(ST)_{j})
Total (longterm) probability of outofspec at j^{th} subgroup
P.Total(LT) _{j} = P.USL(LT)_{j} + P.LSL(LT)_{j}
Total (shortterm) probability of outofspec at j^{th}subgroup
P.Total(ST)_{j} = P.USL(ST)_{j} + P.LSL(ST)_{j}
Benchmark Z (longterm) at j^{th} subgroup
Z.Bench(LT)_{j} = Φ^{−1}(P.Total(LT)_{j})
Benchmark Z (shortterm) at j^{th} subgroup
Z.Bench(ST)_{j} = Φ^{−1}(P.Total(ST)_{j})
Zvalue (longterm) for lower spec at j^{th} subgroup
Z.LSL(LT)_{j} = (μ_{LT} – LSL) / Cum SD(LT)_{j}
Zvalue (shortterm) for lower spec at j^{th} subgroup
Z.LSL(ST)_{j} = (μ_{ST} – LSL) / Cum SD(ST)_{j}
Zvalue (longterm) for upper spec at j^{th} subgroup
Z.USL(LT)_{j} = (USL – μ_{LT}) / Cum SD(LT)_{j}
Zvalue (shortterm) for upper spec at j^{th} subgroup
Z.USL(ST)_{j} = (USL – μ_{ST}) / Cum SD(ST)_{j}
Shift factor at j^{th} subgroup
Z.Shift_{j} = Z.Bench(ST)_{j} – Z.Bench(LT)_{j}