norm.ss(x = NULL, alpha = 0.05, P = 0.99, delta = NULL, P.prime = NULL, side = 1, m = 50, spec = c(NA, NA), hyper.par = list(mu.0 = NULL, sig2.0 = NULL, m.0 = NULL, n.0 = NULL), method = c("DIR", "FW", "YGZO"))method = "YGZO".1-alpha is the confidence level.P) such that the tolerance interval of interest will only exceed P.prime by the probability given by delta.side = 1 or side = 2, respectively).integrate function, which is used for the underlying exact method for calculating the normal tolerance intervals.method = "DIR" or method = "YGZO". By default, the values are NA. The two elements of the vector are for the lower and upper specification limits, respectively. If side = 1, then only one of the specification limits must be specified. If side = 2, then both specification limits must be specified.method = "DIR" or method = "YGZO", then mu.0 and sig2.0 must be specified, which correspond to the assumed population mean and variance of the underlying normal distribution, which further pertains to the historical data for method = "YGZO". If method = "YGZO" and the sample size is to be determined using Bayesian normal tolerance intervals, then this is a required list consisting of the hyperparameters for the conjugate prior -- the hyperparameters for the mean (mu.0 and n.0) and the hyperparameters for the variance (sig2.0 and m.0)."DIR" is the direct method (intended as a simple calculation for planning purposes) where the mean and standard deviation are taken as truth and the sample size is determined with respect to the given specification limits. "FW" is for the traditional Faulkenberry-Weeks approach for sample size determination. "YGZO" is for the Young-Gordon-Zhu-Olin approach, which incorporates historical data and specification limits for determining the value of delta and/or P.prime in the Faulkenberry-Weeks approach. Note that for "YGZO", at least one of delta and P.prime must be NULL.norm.ss returns a data frame with items:
method = "DIR".method = "DIR".Young, D. S., Gordon, C. M., Zhu, S., and Olin, B. D. (2016), Sample Size Determination Strategies for Normal Tolerance Intervals Using Historical Data, Quality Engineering (to appear).
bayesnormtol.int, Normal, normtol.int
## Sample size determination for 95%/95% 2-sided normal
## tolerance intervals using the direct method.
set.seed(100)
norm.ss(alpha = 0.05, P = 0.95, side = 2, spec = c(-3, 3),
method = "DIR", hyper.par = list(mu.0 = 0,
sig2.0 = 1))
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