muEst {AccSamplingDesign} | R Documentation |
Estimate Mean \mu
Based on Specification Limits and Probability
Description
Computes the estimated mean \mu
for a given level of quality and specification limit under either a normal or beta distribution.
Usage
muEst(p, USL = NULL, LSL = NULL,
sigma = NULL, theta = NULL,
dist = c("normal", "beta"))
Arguments
p |
Level of quality (numeric, between 0 and 1). |
USL |
Upper specification limit (numeric). Only one of |
LSL |
Lower specification limit (numeric). Only one of |
sigma |
Standard deviation (numeric) for the normal distribution. Must be provided if |
theta |
Theta parameter (numeric) for the beta distribution. Must be provided if |
dist |
Distribution type. Either |
Details
The function estimates the mean \mu
corresponding to a given tail probability p
, assuming that the process output follows either a normal or beta distribution, and that the probability of being beyond the provided specification limit equals 1 - p
.
For the normal distribution, the mean is calculated using the inverse cumulative distribution function (quantile function) of the normal distribution.
For the beta distribution, the mean is solved numerically such that the CDF at the specified limit equals
p
, given the shape determined bytheta
.
Exactly one of USL
or LSL
must be provided to define whether the probability refers to the upper or lower tail.
Value
Returns the estimated mean \mu
as a numeric value.
Author(s)
Ha Truong
Examples
# Example for normal distribution with lower specification limit (LSL)
muEst(p = 0.95, LSL = 10, sigma = 2, dist = "normal")
# Example for beta distribution with upper specification limit (USL)
muEst(p = 0.95, USL = 0.7, theta = 500, dist = "beta")