Probability of Passing PPQ Test using Tolerance Interval

The function for calculating the probability of passing critical quality attributes (CQA) PPQ test .

ti_pp(Llim, Ulim, mu, sigma, n, n.batch, alpha, coverprob, side)

Arguments

Llim	lower specification limit
Ulim	upper specification limit
mu	hypothetical mean of the attribute
sigma	hypothetical standard deviation of the attribute
n	sample size (number of locations) per batch
n.batch	number of batches for passing PPQ during validation
alpha	significant level for constructing the tolerance interval
coverprob	coverage probability for constructing the tolerance interval
side	whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2, respectively).

Value

A numeric value of the passing/acceptance probability

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See also

rl_pp.

Author

Yalin Zhu

Examples

ti_pp(sigma=0.5, mu=2.5, n=10, n.batch=1, Llim=1.5, Ulim=3.5, alpha=0.05)
#> [1] 0.591041

sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = ti_pp, mu=97, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)
#> [1] 1.000000e+00 9.999914e-01 7.489382e-01 9.289979e-02 2.103286e-02
#> [6] 7.162916e-03 2.456487e-03 1.597179e-05
sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = ti_pp, mu=100, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)
#> [1] 1.000000e+00 1.000000e+00 1.000000e+00 9.018469e-01 2.971147e-01
#> [6] 5.696332e-02 1.110079e-02 2.462045e-05