mds_oc: Operating Characteristic Values for an MDS Plan

In rMDSPTT: Multiple Dependent State Sampling Inspection Plan for Time Truncated Life Test

Operating Characteristic Values for an MDS Plan

Description

Calculates the operating characteristic (OC) values for a Multiple Dependent State Sampling (MDS) plan.

Usage

mds_oc(
  p_design,
  a,
  p_oc,
  b_oc,
  i = 1,
  beta = 0.25,
  c1 = 0,
  c2 = 1,
  n_max = 10000
)

Arguments

p_design	Failure probability at the design condition. It must lie strictly between 0 and 1.
a	Termination ratio, defined as 'a = t/theta0'.
p_oc	Matrix or data frame of failure probabilities used for OC calculation. Rows correspond to 'a' and columns correspond to 'b_oc'.
b_oc	Quality ratios used for OC calculation.
i	Number of preceding lots considered in the MDS plan.
beta	Consumer's risk.
c1	First acceptance number.
c2	Second acceptance number.
n_max	Maximum sample size searched at the design condition.

Details

The sample size is first determined at the design condition using 'p_design' and the constraint 'Pa <= beta'. This sample size is then kept fixed while the failure probabilities in 'p_oc' are used to calculate the probability of acceptance for the quality ratios in 'b_oc'.

Let

A=P(D\leq c_1)

and

B=P(c_1<D\leq c_2).

The MDS probability of acceptance satisfies

P_a=A+B A^i.

The resulting 'Pa' values are the OC values for the specified quality ratios in 'b_oc', using 'Pa = A + B A^i'.

Value

A data frame containing 'a', 'b', 'p', fixed 'n', 'ASN', 'A', 'B', and 'Pa'. The 'Pa' values are the OC values.

Examples

# ----------------------------------------------------------
# Example 1: User-defined failure probabilities
# ----------------------------------------------------------

a <- c(0.5, 1, 1.5, 2)

p_design <- c(
  0.05, 0.10, 0.15, 0.20
)

b_oc <- 2:12

# User-defined probabilities for OC calculation.
# Rows correspond to a and columns correspond to b.
p_oc <- outer(
  a,
  b_oc,
  function(a, b) pmin(0.95, a / (10 * b))
)

# The n values are determined using p_design and then
# kept fixed for all b values.
#
# The Pa values represent the OC values.

mds_oc(
  p_design = p_design,
  a = a,
  p_oc = p_oc,
  b_oc = b_oc,
  i = 3,
  beta = 0.25,
  c1 = 0,
  c2 = 1
)


# ----------------------------------------------------------
# Example 2: Weibull distribution
# ----------------------------------------------------------

shape <- 2

a <- c(0.5, 1, 1.5, 2)

# Design quality ratio
b_design <- 1

# Failure probabilities at b = 1
p_design <- 1 - exp(
  -((a / b_design)^shape)
)

# Quality ratios for OC calculation
b_oc <- 2:12

# Failure probabilities for each a and b
p_oc <- sapply(
  b_oc,
  function(b)
    1 - exp(-((a / b)^shape))
)

mds_oc(
  p_design = p_design,
  a = a,
  p_oc = p_oc,
  b_oc = b_oc,
  i = 3,
  beta = 0.25,
  c1 = 0,
  c2 = 1
)


# ----------------------------------------------------------
# Example 3: Generalized Exponential distribution
# ----------------------------------------------------------

alpha <- 2

a <- c(0.5, 1, 1.5, 2)

# Design quality ratio
b_design <- 1

# Failure probabilities at b = 1
p_design <- (
  1 - exp(-a / b_design)
)^alpha

# Quality ratios for OC calculation
b_oc <- 2:12

# Failure probabilities for each a and b
p_oc <- sapply(
  b_oc,
  function(b)
    (1 - exp(-a / b))^alpha
)

mds_oc(
  p_design = p_design,
  a = a,
  p_oc = p_oc,
  b_oc = b_oc,
  i = 3,
  beta = 0.25,
  c1 = 0,
  c2 = 1
)

rMDSPTT documentation built on Oct. 2, 2026, 5:09 p.m.