TABLE I

Notation and Numerical Calculations for No Trend Over Time

Notation	Formula	Calculated Value
Confidence level	100(1 − α)%	95% (α = 0.05)
Percentage covered	100P%	99% (P = 0.99)
Standard normal quantile	Z_P (P is the area to the left)	Z_0.99 = 2.326
Number of lots	I	11
Lot degrees of freedom	s = I − 1	10
Error degrees of freedom	$\text{[math]}$	15
Harmonic mean of the number of values in each lot	$\text{[math]}$	1.454
Unweighted sample mean of lot means	$\text{[math]}$	71.206
Sample variance of lot means	$\text{[math]}$	5.917
Mean squared error	$\text{[math]}$	3.636
Estimated variance of Ȳ*	$\text{[math]}$	0.538
Estimated variance of Y = σ_A² + σ_E²	$\text{[math]}$	7.052
Effective sample size	$\text{[math]}$	13.110
Upper bound on variance of Y	$\text{[math]}$	16.232
Constants used to compute U where χ_α:s² and χ_α:r² are chi-squared percentiles with area α to the left and s and r degrees of freedom, respectively	H₁ = s/χ_α:s² − 1	1.538
	H₂ = r/χ_α:r² − 1	1.066
Lower bound on one-sided tolerance interval	Equation 2	L₁ = 60.63
Upper bound on one-sided tolerance interval	Equation 3	U₁ = 81.78
Lower and upper on two-sided tolerance interval	Equation 4	L₂ = 60.44 U₂ = 81.97
Lower and upper one-sided bounds using HK1 adjustment of two-sided tolerance interval	Equation 4 replacing $\text{[math]}$ with Z_P	L_1,HK1 = 61.48, U_1,HK1 = 80.92