Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology

ISSN No:-2456-2165

Group Acceptance Sampling Plan for Truncated

Life Test using Generalized
Exponential-Poisson Distribution
Dr. V. Kaviyarasu1and S. Sivasankari2
1
Assistant Professor and 2 Research scholar
Department of Statistics, Bharathiar University,
Coimbatore-641046,Tamilnadu

Abstract:- A Group Acceptance Sampling Plan (GASP) observing the lifetime of the products until it fails is not
is designedto study the truncated life testplan when the possible. The truncated life test is intentionally used to save
lifetime of an item follows a new compound distribution the time and cost of the experiment in such a way that life
called as Generalized Exponential-Poisson (GEP). In this test can be studied at the specified time period.
article the design parameters are developed for the
group size, its acceptance numbers, OC curve, minimum In an attribute single sampling planbased on the
number of groups are determined through the specified truncated life testa decision of acceptance or rejection of the
consumer’s confidence level and test termination ratio. lot is made based on the single sample which is the
Two points on the OC curve approach is incorporated to traditional procedure in sentencing the lot. Epstein. B (1954)
design the proposed plan. The OC values are calculated discussed truncated life test in the exponential case. Goode
when the ratio of specified average life and the actual H.P and Kao J.H.K (1961) have studied sampling plan based
average life is given. The minimum mean ratio for the on the weibull distribution. Balamuarali S. and Lee S.H
proposed plan are determined at the fixed producer’s (2006) discussed variable sampling plans for Weibull
risk. The obtained plan parameters are illustrated with distribution under sudden death testing. Kaviyarasu and
areal time example with the simulation study which are fawaz (2007) has studied reliability sampling plan to ensure
exhibited in the tables. percentiles through Weibull Poisson Distribution.
Kaviyarasu, V. and Sivasankari, S. (2020) studied the Single
Keywords:- Generalized Exponential-Poisson distribution, sampling plan for life testing under the Generalized
consumer’s confidence level, producer’s risk, operating Exponential-Poisson Distribution. Every single item in the
characteristic function, truncated life test. sampling units are required single tester however in practice
a tester may accommodate multiple number of items
I. INTRODUCTION simultaneously hence it saves more time and the cost of the
experiment. Here the items in a tester can be regarded as a
In the competitive global market, quality product group and the number of items in the group is called as
always seeks more attention and demand to meet the group size such as study is called as Group Acceptance
standards prescribed by the manufactures. In industry Sampling Plan (GASP). In this method many items can be
outgoing or incoming products are widely inspected to tested on the basis of few items are tested from the lot size
control the quality of the products which are essential of infinite. Hence this GASP elevate the ordinary plan to
activities in industries. Statistical quality control may inspect many items with multiple tester. Also it improves the
categorized into process control and product control. precision of the testing because various sampling units are
Product control plays a vital role when the product is in distributed to multiple testers. In a life test experiment, a
finished mode and helps to identify the reliable product and sample of size n is tested from a lot of products is put on the
eliminate the manufacturing errors.The statistical techniques test when the corresponding acceptance number is fixed
are usually employed to remove the defective products in with the test assigned time. Probability of rejecting a good
the production process as an offline product control lot is called the producer’s risk and probability of accepting
techniques at any stage of the manufacturing process as an a bad lot is called the consumer’s risk. Here the confidence
incoming raw materials, semi-finished products or a finished level is p* then the consumer risk will be 1-p*. The main
products can be tested.Product control is equally important objective of any acceptance sampling plan procedure is to
techniques however sampling plans for attributes and reduce both the risk simultaneously.
variables are widely studied, however sampling plan by
attributes is easy to perform in industrial shop floor Therefore many researchers prefers the GASP than any
conditions. Acceptance sampling plan is one of the other plans and have done their researchwith various
important techniques adopted in quality control towards distributions such as Aslam and Jun (2009)designed the
inspection and testing the sampling units in which decision group acceptance sampling plans based on the truncated life
about the lot can be made. In the acceptance sampling test when the life time of products follows an Gamma
procedure the life test plan is carried out when the quality Distribution and Weibull distributions. Rao (2011)
characteristics of the product is defined by its lifetime. In introduced a hybrid group acceptance sampling plans for
particular, truncated life test is adopted at which the test will lifetimes based on generalized exponential distribution and
terminated at a certain point of time in the sense that log logistic distributions. Aslam et al.(2010) introduced an

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
improved group sampling plan based on time truncated life increasing and also upside-down bathtub shaped model.
tests. Kaviyarasu and Suresh (2011)proposed a new plan and These applications of the proposed distribution can be seen
designated as quick switching multiple repetitive group the toys and crafts manufacturing sectors are widely used.
sampling plan of type QSMRGSP-1 in which disposition of
lot is determined on the basis of normal and tightened GEP distribution characterized by the parameter α (>0)
sampling schemes. Sudamani Ramaswamy and and the random sample 𝑌1 . . . . . . . 𝑌∝ from the EP distribution.
Sutharani(2012) designed Weighted Group Sampling Plan So that X = max{𝑌𝑖 }α𝑖=1 is GEP distributed. Hence this model
Based on Truncated Life Tests under various distribution can be applicable for the maximum lifetimes of EP random
using Minimum Angle Method. Muhammad Aslam et al. samples. GEP is more suitable distribution for the physical
(2013)proposed a multiple state Repetitive Group Sampling interpretation. If the n components are connected in a
plan by considering the processloss. Aslam et al. (2015) parallel system, the lifetimes of the components are
proposed two stage group acceptance sampling plan for half identically and independently GEP distributed random
normal percentiles. Rosaiah et al. (2016) developed a group variables. Also the whole system lifetime follows the GEP
acceptance sampling plan for truncated life tests when the law.The Probability density function of GEP is
lifetime of items follows the Type-II generalized log logistic 𝛼𝜆𝛽
distribution (TGLLD). f(x;𝜃) = {1 −
(1−𝑒 −𝜆 )𝛼
−𝜆+𝜆 exp(−𝛽𝑥) }𝛼−1 −𝜆−𝛽𝑥+𝜆 exp (−𝛽𝑥)
II. OPERATING PROCEDURE 𝑒 𝑒 -----(1)

Here our interest in determining the number of group’s The Cumulative Distribution Function of the GEP is
‘g’ with the various values of acceptance number c and the given as
test termination time t0 are assumed to be specified. The 𝛼
1−𝑒 −λ+λexp(−βx)
operating procedure of GASP is as follows, 𝐹(𝑥; 𝜃) = ( )
1−𝑒 −λ
 Step 1: Select a random sample of size n from a lot of size -----(2)
N and assign r number of units to each of g groups, so that
n= r*g Where θ (>0) = (α, β, λ), α is the shape parameter, β is
 Step 2: Fix the acceptance number c and the experiment the scale parameter of the Exponential distribution and λ is
time t0. the Poisson parameter. When α = 1, Generalized
 Step 3: Perform the experiment for the g groups Exponential Poisson reduces to Exponential Poisson
simultaneously and record the number of failures for each distribution. When α = 1 and λ→ 0, Exponential Poisson
group till the specified time t0 𝑡
reduces Exponential distribution with parameter β. Let x =β2
 Step 4: Accept the lot if the number of failures from all the
groups together is smaller than or equal to c. , Then consider the CDF of the mean life product quality of
GEP distribution becomes,
 Step 5: Reject the lot whenever number of failures more
than c as well as terminate the test before time t0. 𝑡
−λ+λexp(− )
𝛼
1−𝑒 β

The quality of the product is tested with GASP on the 𝐹(𝑥; 𝜃) = ( 1−𝑒 −λ
)
basis of the above procedure when few items are taken from t, λ,α, β > 0 -----(3)
an infinite lot is tested. Here, Group Acceptance Sampling
Plan (GASP) is studied under the proposed probability IV. TWO POINT ON THE OPERATING
distribution on the truncated life test under percentile as a CHARACTERISTIC CURVE
quality parameter when the life time of a product assumed to
follow the Generalized Exponential-Poisson distribution. The two important risks involved in the acceptance
sampling procedure is well known as producer’s risk and the
III. GENERALIZED EXPONENTIAL-POISSON consumer’s risk. The risk happening in the inspection
DISTRIBUTION procedures which exclusively depends with making of
Most of the probabilistic models are studied to describe wrong decision such as rejecting the good lot and accepting
the life time of data follows a certain life time distribution. the bad lot. Hence rejecting the good lot due to inherent
Here the failure time of an inspecting product may follows a nature of random sampling is the producer’s risk and
life time distribution is modelled using a statistical accepting the bad quality lot due to inherent nature of the
distribution. Kus(2007) introduced a two parameter random sample is known as consumer’s risk. Both the risk
distribution called Exponential-Poisson distribution. Later, have to be kept minimum for producing the reliable product.
Wagner Barreto-Souza and Francisco Cribari-Neto (2009) Hence it is considering the two levels Acceptable Reliability
derived a new distribution with three parameters known as Level (ARL) and Limiting Reliability Level (LRL) to
Generalized Exponential-Poisson (GEP) Distribution. This minimize the risks, which are obtained through Producer’
new distribution is a compounding of an exponential and a confidence level (1-α) and the consumer’s level β. The
Poisson distribution. In reality the failure item of a reliability sampling plan is an efficient one when both the
manufacturing product may not follow a particular risks are under control. Here, α ≤ 0.05 and β ≤ 0.10. Thus
distribution which may vary on the design parameters the probability of acceptance can be obtained for the
regardless on the underlying statistical distribution. The incoming quality using the following inequality,
failure rate of the distribution can be decreasing or 𝐿(𝑝1 ) ≥ 1 − 𝛼and𝐿(𝑝2 ) ≤ 𝛽

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
distribution function of GEP in terms of incoming quality of
Where 𝑝1 is the ARL and 𝑝2 is the LRL. The value of 𝑡⁄ and𝛽⁄ Such that
𝑝1 and 𝑝2 obtained through 𝑝 = 𝐹 (𝑡⁄𝛽 ∗ 1⁄𝑑 ) When 𝛽0 𝛽0
0
𝛽 𝛽 𝛽
𝑑1 = ⁄𝛽 >1 and𝑑2 = ⁄𝛽 =1 respectively. When the 𝑝 = 𝐹 (𝑡⁄𝛽 ∗ 1⁄𝑑 ) Where 𝑑= ⁄𝛽
0 0 0 0
actual mean lifetime of the product is similar to the specified ……………(6)
mean lifetime, i.e., the lot quality is good enough to accept
𝛽 Probability of rejecting a lot even if the lot quality is
at ⁄𝛽 = 1 there is no chance of arising the risk. The
0 good ie.,𝛽≥ 𝛽0 , the actual mean lifetime is greater than the
proposed approach of finding the design parameters is to specified mean lifetime is mentioned as producer’s risk.
satisfy the above two inequalities for the operating Hence to reduce the producer’s risk, one must be interested
characteristic function L (p)simultaneously. 𝛽
in finding the value of ⁄𝛽 in designing the GASP (rg,
0
V. DESIGNING OPTIMAL PLAN PARAMETERS c,𝑡⁄𝛽 )corresponding to P*. This smallest value of the ratio
0
The sampling plan of Group Acceptance Sampling 𝛽
⁄𝛽 can be determined under the condition that producer’s
Plan is exemplified by (rg, c, 𝑡⁄𝛽 ).For the practical use of 0
risk which is kept under 0.05. Thus the proposed life testing
0
the sampling plancan be obtaining with the smallest positive sampling plan is studied under
integer n =(r*g). The group acceptance sampling plan is
reduced to single sampling plan when the group size r = 1. L(p) ≥ 1-α ----------(7)
The designing plan parameters of the proposed sampling
𝛽
plan, minimum number of groups are determined with the Therefore the minimum mean ratio ⁄𝛽 of truncated
0
assumption that the lot size is large enough to use the life test plan can be evaluated by satisfying the following
binomial distribution. The quality of the item is usually inequality,
represented by its true life time such as mean life, median 𝑐
life and percentile life. It is obtained for the given values of 𝑟𝑔 𝑖
∑( ) 𝑝 (1 − 𝑝)𝑟𝑔−𝑖
test termination ratio 𝑡⁄𝛽 andthe acceptance number c at the 𝑖=0
𝑖
0
specified consumer’s confidence level by using the ≥ 0.95 … … … … … … (8)
following non-linear constraint under the percentile life is
𝛽0
studied, wherep = F (𝑡⁄𝛽 . ⁄𝛽 )
0
𝑟𝑔
𝐿(𝑝1 ) = ∑𝑐𝑖=0 ( ) 𝑝1𝑖 (1 − 𝑝1 )𝑟𝑔−𝑖 ≤ 1 − VI. DESCRIPTION OF TABLE VALUES
𝑖
𝑃∗ … … … … . (4)
 Step 1: Fix the parameters of GEP distribution α = 2, λ=2
Where 𝑝1 = 𝐹(𝑥; 𝜃) is the and the test termination ratio
𝑡⁄ = 0.5, 0.6, 0.7, 0.8, 0.9,1.0
𝑡 𝛼 𝛽 0
−λ+λexp(− )
𝐹(𝑥; 𝜃) = (
1−𝑒 β
) t, λ,α, β > 0  Step 2: Obtain 𝑝values in terms of the given
1−𝑒 −λ 𝑡⁄ mentioned in (3)
𝛽 0
 Step 3: Determine the smallest positive integer g by
Where𝑝1 is the probability of failure of an item at time
applying the condition that
t.𝑝1 depends only on𝑡⁄𝛽 Therefore the minimum group size 𝑐
0 𝑟𝑔
determined using the search procedure for the various given 𝐿(𝑝) = ∑ ( ) 𝑝1𝑖 (1 − 𝑝1 )𝑟𝑔−𝑖 ≤ 1 − 𝑃∗
𝑖
values of 𝑃∗ , c and 𝑡⁄𝛽 and tabulated. The minimum 𝑖=0
0
group size is determined while satisfying both the consumer Specify the appropriate consumer’s confidence levels
and the producer by fixing the risk at certain level such as 0.75, 0.90, 0.95, 0.99 and the acceptance number 0 to 4.
𝑃∗ = 0.75, 0.90, 0.95, 0.99. With the assumption of lot size is large enough to the need
of binomial distribution in finding the success or failure item
𝐿(𝑝) in the truncated life test plan and using the search procedure,
𝑐
𝑟𝑔 the minimum group size is obtained for r =2 and exhibited in
= ∑ ( ) 𝑝𝑖 (1 the Table-1
𝑖
𝑖=0
 Step 4: The OC values for the given incoming product
− 𝑝)𝑟𝑔−𝑖 … … … … (5) quality d is evaluated as
𝑐
The probability of acceptance of the GASP can be 𝑟𝑔
found out using (5) only when both the consumer’s and the 𝐿(𝑝) = ∑ ( ) 𝑝𝑖 (1 − 𝑝)𝑟𝑔−𝑖
𝑖
𝑖=0
producer’ risk are used in simulation process. The two
points on the operating characteristic curve are the deciding Where 𝑝 is the cumulative distribution function in
factors in sentencing the lot to meet the necessity of both the 𝛽
producer and the consumer. Where𝑝 is the cumulative terms of incoming quality of 𝑡⁄𝛽 and ⁄𝛽 Such that
0 0

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
𝛽 confidence levels 0.75, 0.90, 0.95, 0.99 and exhibited in the
o 𝑝 = 𝐹 (𝑡⁄𝛽 ∗ 1⁄𝑑) Where 𝑑 = ⁄𝛽
0 0 Table-3.
 Step 5: Fix the ratio 𝑡⁄𝛽 = 0.5, 0.6, 0.7, 0.8, 0.9, 1 and
0
𝛽 VII. OC CURVE
⁄𝛽 = 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 and 4.5 substitute in
0
For the specified test termination ratio t/t 0with q = 0.8
(6) and find 𝑝 values. Through the value of incoming
and the acceptance number c =0 for the consumer’s
quality 𝑝, the probability of acceptance for each 𝑝 value
confidence level 0.99, the percentile lifetime plan is
can be obtained from (5) and presented in the Table-2
obtained from the Table-1, the minimum number of groups
 Step 6: The minimum ratio is obtained by using the
𝛽 g = 3. Hence the plan is executed as (3, 0 and 0.8) with the
inequality (7). For the given values of 𝑡⁄𝛽 , ⁄𝛽 , n = r * minimum percentile ratio is 7.3340 from Table-3. From this
0 0
g also the acceptance number c. obtained plan parameters one can arrive at the conclusion
that the product will have the percentile life of 7 times of the
Here one can obtain the minimum mean ratio which specified percentile life of 1000 hours with the lot
can assures that the producer’s risk will not be more than acceptance 0.99.The OC curve of the proposed plan (n= 4*3
0.05 for the proposed truncated life test plan. The minimum = 12, c= 0and 𝒕⁄𝜷 = 0.8)is shown in the following figure.
𝟎
mean ratio is obtained for the specified consumer’s

OC curve for GASP

1
0.9
0.8
0.7
0.6
L(p)

0.5
0.4
0.3
0.2
0.1
0
1 1.5 2 2.5 3 3.5 4 4.5 5
dq

Fig. 1: OC curve of the (n= 4*3 = 12, c= 0and 𝒕⁄𝜷 = 0.8)

𝟎

The probability of acceptance can be regarded as a function of the deviation for the specified values are given to test the
percentile life. The function is called the Operating Characteristics curve of the proposed sampling plan is given. From this one
can obtain the minimum sample size and interested to find the probability of lot acceptance when the quality of the item is
sufficiently good under the study.

VIII. EXAMPLE

Consider an electronic toys manufacturing company Thus the proposed plan is performed as the testing with
wants to adopt the proposed sampling plan for life testing 6 tester (group) with 2 items in each group simultaneously at
the electronic toys. Suppose that the quality testing engineer the exact consumer’s risk 𝛽 = 0.0096. Accept the lot if no
wants to study the lifetime of a product which may follows more than 1 failure in each of all the groups occur or else
the Generalized Exponential-Poisson distribution, it is reject the lot. For this proposed electronic toy testing a
desired to design the GASP to test the actual lifetime is sample size of 12 items are tested with g=6 and r=2 (2*6, 1,
greater than 1000 hours when the test terminated at 800 0.8) with 12 items are tested and one may interested in
hours and 2 items on each tester with allowed number of finding the probability of acceptance for the method from
failures for each group is 2. It leads the ratio 𝑡⁄𝛽 = 0.8 with the Table-4 when the true lifetime of the product is greater
0 𝛽
c=1. From the Table-1theminimum number of groups for the than the specified mean lifetime 𝛽 ≥ β0 𝑜𝑟 β can be
0
consumer’s risk 0.01 is obtained. obtained.

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
β/β0 1 1.5 2 2.5 3 3.5 4 4.5
L(p) 0.1847 0.3435 0.7221 0.8493 0.9165 0.9522 0.9717 0.9826

Table 4: OC values of (n= 2*6 = 12, c= 1and 𝒕⁄𝜷 = 0.8)under GEP for p*=0.99
𝟎

The minimum mean ratio for this proposed plan efficient plan for studying the percentile life as a quality
referred from the Table-3 is 5.3226 reveals that the product parameter over the other sampling plans. Here the quality
will have an average life of 5 times of the specified average engineer can adopt the proposed sampling plan in the
life of 1000 hours with acceptable probability 0.99. manufacturing sector to reach a decision regarding either to
accept or not to accept the incoming / outgoing quality lots.
IX. CONCLUSIONS To ensure the life quality of the products the pattern of
failure can be occurred using the sampling distribution
This article provides a new statistical probability which protects both the producer and the consumer with
distribution named as Generalized Exponential-Poisson more precision than the specified average life. Suitable
distribution to test the quality of products when acceptance illustrations under electronic toy manufacturing are given
sampling for life test is studied. Numerical table are for ready made reference for the industrial shop floor
developed to obtain the minimum sample size, OC values conditions which provides better discrimination of accepting
and the minimum ratio values are given when producer’s good lots among minimum number of groups.
risk is fixed. The proposed plan was found to be a more

p* c r 𝑡⁄
𝛽0
0.5 0.6 0.7 0.8 0.9 1
0.75 0 2 2 2 1 1 1 1
0.75 1 2 3 3 2 2 2 1
0.75 2 2 5 4 4 3 3 2
0.75 3 2 6 6 5 4 4 3
0.75 4 2 8 7 5 5 5 4

0.90 0 2 3 3 2 2 2 1
0.90 1 2 4 4 3 3 3 2
0.90 2 2 6 5 4 4 4 3
0.90 3 2 8 6 5 5 4 4
0.90 4 2 9 8 7 6 5 5

0.95 0 2 3 3 2 2 2 2
0.95 1 2 5 4 4 3 3 3
0.95 2 2 7 6 5 4 4 4
0.95 3 2 9 7 6 6 5 5
0.95 4 2 11 9 8 7 6 6

0.99 0 2 5 4 3 3 2 2
0.99 1 2 7 6 5 4 4 4
0.99 2 2 9 8 6 6 6 5
0.99 3 2 11 9 8 7 7 6
0.99 4 2 13 11 9 8 7 7
Table 1: minimum number of groups (g) for mean life under GEP Distribution for GASP

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
𝛽
⁄𝛽
𝑡⁄ 0
p* 𝛽0 g 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0.75 0.5 5 0.6878 0.896 0.9619 0.9844 0.9929 0.9965 0.9982 0.999
0.75 0.6 4 0.7275 0.8424 0.9649 0.9852 0.9931 0.9965 0.9981 0.9989
0.75 0.7 4 0.6273 0.7672 0.9396 0.9729 0.9868 0.9931 0.9962 0.9978
0.75 0.8 3 0.7882 0.8749 0.9696 0.9865 0.9935 0.9966 0.9981 0.9989
0.75 0.9 3 0.7308 0.8329 0.9550 0.9791 0.9895 0.9944 0.9968 0.9981
0.75 1 2 * * * * * * *

0.9 0.5 6 0.5507 0.8298 0.9335 0.9717 0.9868 0.9934 0.9965 0.998
0.9 0.6 5 0.5513 0.7154 0.9265 0.9675 0.9844 0.992 0.9956 0.9975
0.9 0.7 4 0.6273 0.7672 0.9396 0.9729 0.9868 0.9931 0.9962 0.9978
0.9 0.8 4 0.5316 0.6873 0.9071 0.9558 0.9775 0.9879 0.9931 0.9959
0.9 0.9 4 0.4446 0.6077 0.8682 0.9337 0.965 0.9805 0.9887 0.9931
0.9 1 3 0.6734 0.7882 0.9374 0.9697 0.9843 0.9914 0.995 0.997

0.95 0.5 7 0.4266 0.7554 0.8981 0.9549 0.9786 0.9891 0.9941 0.9966
0.95 0.6 6 0.3965 0.5844 0.8766 0.9427 0.9717 0.9851 0.9918 0.9952
0.95 0.7 5 0.4277 0.6051 0.878 0.9423 0.9709 0.9844 0.9912 0.9948
0.95 0.8 4 0.5316 0.6873 0.9071 0.9558 0.9775 0.9879 0.9931 0.9959
0.95 0.9 4 0.4446 0.6077 0.8682 0.9337 0.965 0.9805 0.9887 0.9931
0.95 1 4 0.3684 0.5316 0.8243 0.9071 0.949 0.9708 0.9826 0.9892

0.99 0.5 9 0.2376 0.5994 0.8115 0.9104 0.9554 0.9765 0.987 0.9925
0.99 0.6 8 0.1835 0.3571 0.7540 0.8749 0.9344 0.9642 0.9795 0.9879
0.99 0.7 6 0.2743 0.4548 0.8043 0.9015 0.9484 0.9717 0.9838 0.9903
0.99 0.8 6 0.1847 0.3435 0.7221 0.8493 0.9165 0.9522 0.9717 0.9826
0.99 0.9 6 0.1221 0.2539 0.6359 0.7885 0.8766 0.9265 0.9554 0.9717
0.99 1 5 0.1784 0.3242 0.6878 0.821 0.8969 0.9386 0.9625 0.9761
Table 2: OC values for mean life under GEP distribution when c = 2 and r=2 for GASP

p* c 0.5 0.6 0.7 0.8 0.9 1

0.75 0 9.4413 9.6929 9.0878 10.318 11.678 12.936
0.75 1 3.8297 4.0666 4.0701 4.6574 5.248 4.6967
0.75 2 3.1326 3.2184 3.4026 3.4534 3.3427 2.356
0.75 3 2.5081 2.8247 3.0599 2.9279 2.9306 2.7986
0.75 4 2.2781 2.4534 2.3022 2.6307 2.6887 2.6636
0.90 0 11.743 12.738 13.169 15.136 16.944 12.946
0.90 1 4.5896 5.0762 5.3648 5.4389 6.124 5.8175
0.90 2 3.5241 3.7584 3.7553 3.891 4.3589 4.3077
0.90 3 2.9306 3.0048 3.059 3.228 3.2957 3.6514
0.90 4 2.5983 2.7364 3.0256 2.8573 2.9604 2.9891
0.95 0 11.73 12.813 13.259 12.852 17.039 16.226
0.95 1 4.9347 5.4847 5.9173 6.1259 6.1173 6.8047
0.95 2 3.8861 4.0066 4.3795 4.2895 4.3758 4.8652
0.95 3 3.3158 3.3596 3.5127 3.7602 3.9303 4.0357
0.95 4 2.8943 2.9972 3.1883 3.2664 3.4422 3.5721
0.99 0 14.517 16.415 16.457 17.055 17.037 18.834
0.99 1 6.3684 6.6767 6.9081 7.334 7.5843 8.4529
0.99 2 4.5596 5.0792 4.9443 5.3236 6.0006 5.8261
0.99 3 3.7727 3.9763 4.105 4.245 4.7809 4.7092
Table 3: Minimum mean ratio values for the producer’s risk 0.05 under GEP distribution for GASP

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Volume 7, Issue 4, April – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
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