README.md

In ULL-STAT/RepetPlan: Repetitive Design of Failure-Censored Sampling Plans with Prior Distribution

README

RepetPlan

RepetPlan is an R package developed to obtain failured-censored repetitive group sampling plans.

Installation

To install the current version of the code from Zenodo:

if(!require(zen4r)){install.packages("zen4r")}  #install if needed
zen4r::download_zenodo("10.5281/zenodo.5035779")
install.packages("RepetPlan-1.0.3.zip", repos = NULL) 

To install the current version of the code from GitHub:

if(!require(devtools)){install.packages("devtools")}  #install if needed
devtools::install_github("ULL-STAT/RepetPlan")

Load and Help

To load the RepetPlan package:

# load library and dependant libraries 
library(RepetPlan)

To see all available functions in the package use the command below

# To get index of help on all functions
help(package="RepetPlan")

Examples

Design of repetitive group sampling plans using conventional sampling risks

Suppose that T represents a lifetime variable and X = log (T) follows a log-location and scale distribution. This is an example which shows how to determine the designs of conventional censored repetitive sampling plans for the given requirements of maximum risks and quality levels

risks<-c(0.05,0.10)     #vector of producer and consumer maximum sampling risks
p<-c(0.00654, 0.0426)   #vector of acceptance and rejection quality levels
q<- 0.1                 #censoring degree
asvar<-asympt.var(q,"normal")    #asymptotical variance-covariance matrix of MLE estimators of location and scale paramters
designs<-rep.plan(risks,p,asvar) #designs satisfying the previous requirements

The first designs returned by the function rep.plan() are

q n kr ka termcd message p_alpha p_beta dist alpha beta asn_alpha asn_beta asn_avg p_asn_max asn_max 0.1 49 2.053225 2.055370 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 49.04823 49.06290 49.05557 0.0188643 49.16223 0.1 48 2.048891 2.060242 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 48.25590 48.32952 48.29271 0.0188293 48.84398 0.1 47 2.044397 2.065329 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 47.47311 47.60146 47.53728 0.0187927 48.52982 0.1 46 2.039733 2.070647 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 46.70045 46.87892 46.78969 0.0187547 48.22016 0.1 45 2.034888 2.076213 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 45.93857 46.16215 46.05036 0.0187151 47.91550 0.1 44 2.029850 2.082044 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1 45.18813 45.45141 45.31977 0.0186738 47.61636

The ASNavg-optimal design can be obtained as

optimal.design<-designs %>% group_by(q,dist,p_alpha,p_beta) %>%
  filter( (abs(alpha-risks[1])<1e-05) & (abs(risks[2]-beta)<1e-05) & (termcd==1)) %>%
  slice(which.min(asn_avg)) %>% arrange(q,p_alpha,p_beta) %>% as.data.frame()

q n kr ka termcd message p_alpha p_beta dist alpha beta asn_alpha asn_beta asn_avg p_asn_max asn_max 0.1 21 1.799825 2.3974 1 Function criterion near zero 0.00654 0.0426 normal 0.05 0.1000001 34.71139 32.27409 33.49274 0.0168694 46.02262

Design of repetitive group sampling plans using a generalized beta (GB) prior model of p and expected sampling risks

In this case, the censored repetitive sampling plans can be determined when a GB prior is assumed and there is available knowledge about the mean and variance of p. For given requirements of maximum expected risks and quality levels, the sampling plans are

risks<-c(0.05,0.10)     #vector of producer and consumer maximum sampling risks
p<-c(0.00654, 0.0426)   #vector of acceptance and rejection quality levels
q<- 0.1                 #censoring degree
asvar<-asympt.var(q,"normal")    #asymptotical variance-covariance matrix of MLE estimators of location and scale paramters
l<- p[1]/5              #lower limit of p
u<- p[2]+(p[1]-l)       #upper limit of p

# GB parameters for a knowledge of mean and variance of p distribution
know_p<-list(mean_p=p[1],var_p=((p[2]-p[1])/4)^2)
beta.parms<-beta.params(p,l,u, know_p)

designs<-repGBprior.plan(risks,p,asvar, beta.parms)

Then, the function repGBprior.plan() returns these designs. The first plans are

q n n_low n_up kr ka termcd message p_alpha p_beta a b l u mean_p var_p dist alpha beta asn_alpha asn_beta asn_avg easn p_asn_max asn_max 0.1 24 3 49 2.200833 2.200877 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500619 0.1000161 24.00090 24.00042 24.00066 24.00039 0.0121556 24.00107 0.1 23 3 49 2.187946 2.216942 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500908 0.1000238 23.58511 23.27324 23.42917 23.30382 0.0120410 23.69109 0.1 22 3 49 2.173528 2.234751 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500003 0.1000001 23.20269 22.56201 22.88235 22.63308 0.0119251 23.40886 0.1 21 3 49 2.158403 2.254219 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500319 0.1000146 22.82986 21.85480 22.34233 21.97611 0.0118011 23.12469 0.1 20 3 49 2.142068 2.275593 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500924 0.1000943 22.47555 21.15569 21.81562 21.34039 0.0116246 22.84847 0.1 19 3 49 2.123503 2.300221 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.0500073 0.1000022 22.18107 20.48217 21.33162 20.74946 0.0114847 22.62697

and the EASN-optimal design is obtained as

optimal.design<-designs %>% group_by(q,dist,p_alpha,p_beta) %>%
                 filter( (abs(alpha-risks[1])<1e-05) & 
                           (abs(risks[2]-beta)<1e-05) & (termcd==1)) %>%
                 group_by(q,p_alpha,p_beta,a,b,l,u,dist) %>%
                 mutate(easn_min=min(easn)) %>%
                 slice(which.min(easn)) %>% as.data.frame()

q n n_low n_up kr ka termcd message p_alpha p_beta a b l u mean_p var_p dist alpha beta asn_alpha asn_beta asn_avg easn p_asn_max asn_max easn_min 0.1 12 3 49 1.921685 2.611877 1 Function criterion near zero 0.00654 0.0426 0.1862234 1.469713 0.001308 0.047832 0.00654 8.13e-05 normal 0.05 0.1000001 21.7853 16.33357 19.05943 18.15345 0.0099061 22.38735 18.15345

ULL-STAT/RepetPlan documentation built on Dec. 18, 2021, 5:15 p.m.