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