| Title: | Repetitive Group Acceptance Sampling Inspection Plans for Time Truncated Life Test |
|---|---|
| Description: | Designing repetitive group acceptance sampling inspection plans for time-truncated life tests. The package uses a distribution-free formulation in which the user supplies the failure probability. The functions compute operating characteristic probabilities and average sample numbers subject to a consumer's risk constraint. The package also provides graphical and comparative tools for comparing repetitive group, group and single sampling inspection plans. Sherman (1965) <doi:10.2307/1266124>; Aslam and Jun (2013) <doi:10.1007/s00170-013-4747-x>. Saha et al. (2025) <doi:10.1007/s41872-025-00305-w>; Tripathi et al. (2020) <doi:10.1080/02664763.2020.1759031>; Tripathi and Aslam (2024) <doi:10.1285/i20705948v17n3p636>; Tripathi et al. (2022) <doi:10.1007/s40745-020-00267-z>; Saha et al. (2021) <doi:10.1080/21681015.2021.1893843>; Tripathi et al. (2023) <doi:10.1007/s41872-023-00221-x>. |
| Authors: | Harsh Tripathi [aut, cre], Mahendra Saha [aut] |
| Maintainer: | Harsh Tripathi <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2026-09-30 14:23:13 UTC |
| Source: | https://github.com/cran/rReGSPTT |
Computes and compares the optimum sample sizes and average sample numbers of single, group and repetitive group acceptance sampling inspection plans.
compare_rgasip(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)compare_rgasip(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)
p |
Failure probability at the design condition. |
r |
Number of items inspected in each GSP group. |
c |
Acceptance number for SSP and GSP. |
c1 |
Acceptance number for RGASIP. |
c2 |
Rejection boundary for RGASIP. |
beta |
Producer's risk. |
n.max |
Maximum sample size considered for SSP and RGASIP. |
SSP and RGASIP sample sizes are optimized directly over n. For GSP, the group size r is supplied and the minimum number of groups is determined from the producer's risk constraint.
A data frame containing the computed SSP, GSP and RGASIP designs.
# User-supplied failure probability compare_rgasip( p = 0.10, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) # Generalized Exponential example a <- 0.5 b <- 1 alpha <- 2 p <- (1 - exp(-a / b))^alpha compare_rgasip( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) # Weibull example a <- 0.5 b <- 1 shape <- 2 p <- 1 - exp(-(a / b)^shape) compare_rgasip( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 )# User-supplied failure probability compare_rgasip( p = 0.10, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) # Generalized Exponential example a <- 0.5 b <- 1 alpha <- 2 p <- (1 - exp(-a / b))^alpha compare_rgasip( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) # Weibull example a <- 0.5 b <- 1 shape <- 2 p <- 1 - exp(-(a / b)^shape) compare_rgasip( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 )
Computes the minimum ASN for different termination ratios and plots the minimum ASN against the termination ratio.
plot_rgasip_asn(p, a, b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)plot_rgasip_asn(p, a, b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)
p |
A function with arguments |
a |
Vector of termination ratios. |
b |
Quality ratio. |
c1 |
Acceptance number. |
c2 |
Rejection boundary. |
beta |
Producer's risk. |
n.max |
Maximum sample size considered during optimization. |
For a time-truncated life test,
is the termination ratio and
is the quality ratio.
The supplied function p must return the failure probability
corresponding to the selected lifetime distribution.
A data frame containing a, b, p,
minimum n, probabilities and ASN.
#--------------------------------------------------------- # Example 1: Generalized Exponential distribution #--------------------------------------------------------- a <- c(0.5,0.75,1.5,2) alpha <- 2 b=1 p_GED <- function(a, b) {(1 - exp(-a / b))^alpha} plot_rgasip_asn( p = p_GED, a = a, b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Weibull distribution #--------------------------------------------------------- shape <- 2 a <- c(0.5,0.75,1.5,2) b=1 p_Weibull <- function(a, b) {1 - exp(-(a / b)^shape)} plot_rgasip_asn( p = p_Weibull, a = seq(0.2, 2, by = 0.2), b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 )#--------------------------------------------------------- # Example 1: Generalized Exponential distribution #--------------------------------------------------------- a <- c(0.5,0.75,1.5,2) alpha <- 2 b=1 p_GED <- function(a, b) {(1 - exp(-a / b))^alpha} plot_rgasip_asn( p = p_GED, a = a, b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Weibull distribution #--------------------------------------------------------- shape <- 2 a <- c(0.5,0.75,1.5,2) b=1 p_Weibull <- function(a, b) {1 - exp(-(a / b)^shape)} plot_rgasip_asn( p = p_Weibull, a = seq(0.2, 2, by = 0.2), b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 )
Produces a graphical comparison of the sample size or average sample number of SSP, GSP and RGASIP.
plot_rgasip_comparison(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)plot_rgasip_comparison(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)
p |
Failure probability at the design condition. |
r |
Number of items inspected in each GSP group. |
c |
Acceptance number for SSP and GSP. |
c1 |
Acceptance number for RGASIP. |
c2 |
Rejection boundary for RGASIP. |
beta |
Producer's risk. |
n.max |
Maximum sample size considered for optimization. |
The comparison data frame invisibly.
plot_rgasip_comparison( p = 0.10, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) #-----------Generalied Exponential Distribution a <- 0.5 alpha <- 2 b=1 p <- (1- exp(-a / b))^alpha plot_rgasip_comparison( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 )plot_rgasip_comparison( p = 0.10, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 ) #-----------Generalied Exponential Distribution a <- 0.5 alpha <- 2 b=1 p <- (1- exp(-a / b))^alpha plot_rgasip_comparison( p = p, r = 5, c = 0, c1 = 0, c2 = 2, beta = 0.25 )
Computes a repetitive group acceptance sampling inspection plan for a time-truncated life test. The procedure is distribution-free because the failure probability p is supplied by the user.
repetitive_group_asip(p, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)repetitive_group_asip(p, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)
p |
Failure probability before the termination time. It must be
a numeric value between 0 and 1. For a time-truncated life test,
|
c1 |
Acceptance number. The lot is accepted when the number of
failures satisfies |
c2 |
Rejection boundary. The lot is rejected when the number of
failures satisfies |
beta |
Producer's risk constraint. The optimum plan satisfies
|
n.max |
Maximum sample size considered during optimization. |
In each sampling round, a random sample of size n is selected from the lot and placed on a life test for a fixed time t0. Let d denote the number of failures observed during the test.
The lot is accepted if d <= c1, rejected if d > c2, and the sampling procedure is repeated if c1 < d <= c2.
If d follows a binomial distribution with failure probability p, the probability of acceptance in one sampling round is
and the probability of rejection in one sampling round is
The probability of repeating the sampling procedure is
The operating characteristic probability of the repetitive plan is
The average sample number is
The optimum sample size is obtained by minimizing ASN subject to the producer's risk constraint
A data frame containing the failure probability, optimum sample size, acceptance number, rejection boundary, one-round acceptance probability, repetition probability, one-round rejection probability, eventual acceptance probability and average sample number.
#--------------------------------------------------------- # Example 1: User-supplied failure probability #--------------------------------------------------------- p <- c(0.05, 0.10, 0.15, 0.20) repetitive_group_asip( p = p, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Generalized Exponential distribution #--------------------------------------------------------- a <- c(0.5,0.75,1.5,2,2.5) b <- 1 alpha <- 2 p_GED <- function(a, b) {(1 - exp(-a / b))^alpha} p <- p_GED(a, b) repetitive_group_asip( p = p, c1 = 0, c2 = 2, beta = 0.25 ) #--------------------------------------------------------- # Example 3: Repetitive acceptance sampling plans for burr type XII percentiles #--------------------------------------------------------- q=.10 al=2; k=0.5; u=( ((1/(1-q))^(1/k)) - 1)^(1/al) a=c(0.5,1); ### a=t/the0 b=1; ### b=the/the0 p= 1- ( 1+ ((u*a/b)^(al)) )^(-k) repetitive_group_asip( p = p, c1 = 0, c2 = 1, beta = 0.25 )#--------------------------------------------------------- # Example 1: User-supplied failure probability #--------------------------------------------------------- p <- c(0.05, 0.10, 0.15, 0.20) repetitive_group_asip( p = p, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Generalized Exponential distribution #--------------------------------------------------------- a <- c(0.5,0.75,1.5,2,2.5) b <- 1 alpha <- 2 p_GED <- function(a, b) {(1 - exp(-a / b))^alpha} p <- p_GED(a, b) repetitive_group_asip( p = p, c1 = 0, c2 = 2, beta = 0.25 ) #--------------------------------------------------------- # Example 3: Repetitive acceptance sampling plans for burr type XII percentiles #--------------------------------------------------------- q=.10 al=2; k=0.5; u=( ((1/(1-q))^(1/k)) - 1)^(1/al) a=c(0.5,1); ### a=t/the0 b=1; ### b=the/the0 p= 1- ( 1+ ((u*a/b)^(al)) )^(-k) repetitive_group_asip( p = p, c1 = 0, c2 = 1, beta = 0.25 )
Calculates operating characteristic values for different quality ratios using the RGASIP design obtained at b = 1.
rgasip_oc(p_design, a, p_oc, b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)rgasip_oc(p_design, a, p_oc, b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)
p_design |
Failure probabilities at the design condition b = 1. |
a |
Vector of termination ratios corresponding to
|
p_oc |
Matrix of failure probabilities for different
quality ratios. Each row corresponds to a value of |
b_oc |
Numeric vector of quality ratios corresponding to
the columns of |
c1 |
Acceptance number. |
c2 |
Rejection boundary. Rejection occurs when d > c2. |
beta |
Producer's risk. |
n.max |
Maximum sample size considered during the design optimization. |
For each termination ratio, the optimum sample size is first determined at b = 1 by minimizing ASN subject to the producer's risk constraint. The resulting sample size is then kept fixed while calculating the operating characteristic for different quality ratios.
The lot is accepted when d <= c1, rejected when d > c2, and the sampling procedure is repeated when c1 < d <= c2.
A data frame containing the termination ratio, quality ratio, failure probability, design sample size, acceptance probability, repetition probability, rejection probability, eventual acceptance probability and ASN.
#--------------------------------------------------------- # Example 1: User-supplied failure probabilities #--------------------------------------------------------- a <- c(0.5, 1, 1.5, 2) # Failure probabilities at b = 1 p_design <- c(0.05, 0.10, 0.15, 0.20) # Quality ratios b_oc <- 2:6 # Example failure probabilities for different b values p_oc <- sapply( b_oc, function(b) p_design / b ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Generalized Exponential distribution #--------------------------------------------------------- alpha <- 2 a <- c(0.5, 0.75, 1, 1.5, 2) b_oc <- 2:6 # Design failure probabilities at b = 1 p_design <- (1 - exp(-a))^alpha # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) (1 - exp(-a / b))^alpha ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 3: Weibull distribution #--------------------------------------------------------- shape <- 2 a <- c(0.5, 0.75, 1, 1.5, 2) b_oc <- 2:6 # Design failure probabilities at b = 1 p_design <- 1 - exp(-(a^shape)) # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) 1 - exp(-((a / b)^shape)) ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 4: Repetitive acceptance sampling plans for burr type XII percentiles #--------------------------------------------------------- q=.10 al=2; k=0.5; u=( ((1/(1-q))^(1/k)) - 1)^(1/al) a <- c(0.5, 1) b_oc <- 2:3 # Design failure probabilities at b = 1 p_design <- 1- ( 1+ ((u*a)^(al)) )^(-k) # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) 1- ( 1+ ((u*a/b)^(al)) )^(-k) ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 )#--------------------------------------------------------- # Example 1: User-supplied failure probabilities #--------------------------------------------------------- a <- c(0.5, 1, 1.5, 2) # Failure probabilities at b = 1 p_design <- c(0.05, 0.10, 0.15, 0.20) # Quality ratios b_oc <- 2:6 # Example failure probabilities for different b values p_oc <- sapply( b_oc, function(b) p_design / b ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 2: Generalized Exponential distribution #--------------------------------------------------------- alpha <- 2 a <- c(0.5, 0.75, 1, 1.5, 2) b_oc <- 2:6 # Design failure probabilities at b = 1 p_design <- (1 - exp(-a))^alpha # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) (1 - exp(-a / b))^alpha ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 3: Weibull distribution #--------------------------------------------------------- shape <- 2 a <- c(0.5, 0.75, 1, 1.5, 2) b_oc <- 2:6 # Design failure probabilities at b = 1 p_design <- 1 - exp(-(a^shape)) # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) 1 - exp(-((a / b)^shape)) ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 ) #--------------------------------------------------------- # Example 4: Repetitive acceptance sampling plans for burr type XII percentiles #--------------------------------------------------------- q=.10 al=2; k=0.5; u=( ((1/(1-q))^(1/k)) - 1)^(1/al) a <- c(0.5, 1) b_oc <- 2:3 # Design failure probabilities at b = 1 p_design <- 1- ( 1+ ((u*a)^(al)) )^(-k) # Failure probabilities at different quality ratios p_oc <- sapply( b_oc, function(b) 1- ( 1+ ((u*a/b)^(al)) )^(-k) ) rgasip_oc( p_design = p_design, a = a, p_oc = p_oc, b_oc = b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 100 )