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 ASN_avg-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