Package {rReGSPTT}

Compare SSP, GSP and RGASIP

Description

Computes and compares the optimum sample sizes and average sample numbers of single, group and repetitive group acceptance sampling inspection plans.

Usage

compare_rgasip(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)

Arguments

Details

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.

Value

A data frame containing the computed SSP, GSP and RGASIP designs.

Examples

# 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
)

Plot Minimum ASN Against Termination Ratio

Description

Computes the minimum ASN for different termination ratios and plots the minimum ASN against the termination ratio.

Usage

plot_rgasip_asn(p, a, b = 1, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)

Arguments

Details

For a time-truncated life test,

a = t/\theta_0

is the termination ratio and

b = \theta/\theta_0

is the quality ratio.

The supplied function p must return the failure probability corresponding to the selected lifetime distribution.

Value

A data frame containing a, b, p, minimum n, probabilities and ASN.

Examples

#---------------------------------------------------------
# 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
)

Plot Comparison of SSP, GSP and RGASIP

Description

Produces a graphical comparison of the sample size or average sample number of SSP, GSP and RGASIP.

Usage

plot_rgasip_comparison(p, r, c = 0, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)

Arguments

Value

The comparison data frame invisibly.

Examples

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
)

Repetitive Group Acceptance Sampling Inspection Plan

Description

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.

Usage

repetitive_group_asip(p, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)

Arguments

Details

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

P_a = \sum_{i=0}^{c_1} {n \choose i} p^i(1-p)^{n-i}

and the probability of rejection in one sampling round is

P_r = 1 - \sum_{i=0}^{c_2} {n \choose i} p^i(1-p)^{n-i}.

The probability of repeating the sampling procedure is

P_{rep} = 1-P_a-P_r.

The operating characteristic probability of the repetitive plan is

P_A = \frac{P_a}{P_a+P_r}.

The average sample number is

ASN = \frac{n}{P_a+P_r}.

The optimum sample size is obtained by minimizing ASN subject to the producer's risk constraint

P_A \leq \beta.

Value

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.

Examples

#---------------------------------------------------------
# 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
)

Operating Characteristic Values for a Repetitive Group Acceptance Sampling Inspection Plan

Description

Calculates operating characteristic values for different quality ratios using the RGASIP design obtained at b = 1.

Usage

rgasip_oc(p_design, a, p_oc, b_oc, c1 = 0, c2 = 2, beta = 0.25, n.max = 500)

Arguments

Details

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.

Value

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.

Examples

#---------------------------------------------------------
# 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
)