 Open Access
 Total Downloads : 72
 Authors : Dr. D Senthilkumar , A Prakash , Dr. B Esha Raffie
 Paper ID : IJERTV6IS100152
 Volume & Issue : Volume 06, Issue 10 (October 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS100152
 Published (First Online): 28102017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Repetitive Deferred Variables Sampling Plan Indexed By Six Sigma Quality Levels
D. Senthilkumar*, A. Prakash and B. Esha Raffie
Department of Statistics, PSG College of Arts & Science, Coimbatore614014, TN, India.
Abstract This article proposes a repetitive deferred variable sampling plan (RDVSP) indexed by six sigma quality levels for the inspection of normally distributed quality characteristics. In this plan, the acceptance or rejection of a lot in the deferred state is dependent on the inspection results of the preceding or succeeding lots under repetitive group sampling (RGS) inspection is designing plan indexed by Six Sigma AQL (SSAQL, 1) and Six Sigma LQL (SSLQL, ) is indicated. Sampling plan tables are constructed for the selection of parameters indexed by SSAQL and SSLQL in the case of known and unknown standard deviation and sigma values.
Keywords – Acceptable quality level, sampling plan, consumers risk, limiting quality level, producers risk. Repetitive group sampling, Deferred sampling, variables sampling plan, Six Sigma AQL and Six Sigma LQL.
Acceptance sampling was mainly designed to decide whether to accept or reject a lot on the basis of information provided by the sample taken from the particular lot. Acceptance sampling plan may be classified by attributes and variables. Acceptance sampling plan for attributes means that items will be judged as defective/bad or nondefective/well. Further, a sampling plan may be either type are Acceptance Rejection type or Acceptance Rectification type. In an acceptancerejection sampling inspection plan, lots are either accepted or rejected by the sample. In an acceptance rectification sampling plan if we do not accept on the basis of the sample, we take recourse to 100% inspection and in either case replace all defectives by nondefectives.
The RDS plan has been developed by Sankar and Mahopatra (1991) and this plan is essentially an extension of the Multiple deferred sampling plan MDS(c1, c2) which was proposed by Rambert and Vaerst (1981). In this plan, the acceptance or rejection of a lot in deferred state is dependent on the inspection results of the preceding or succeeding lots under repetitive group sampling (RGS) inspection. RGS is the particular case of RDS plan. Wortham and Baker (1976) have developed multiple deferred state sampling (MDS) plans and also provided tables for construction of plans. Suresh (1992) has proposed procedures to select deferred state sampling plan indexed through AQL and LQL. Suresh (1993) has proposed procedures to select Multiple Deferred State Plan of type MDS and MDS1 indexed through producer and consumer quality levels
considering filter and incentive effects. Senthulkumar et al

Production is steady so that results on current preceding and succeeding lots are broadly indicative of a continuing process.

Lots are submitted substantially in the order of production.

Normally lots are expected to be essentially of the same quality.

Inspection is by variables with quality defined as the fraction non – conforming.
Basic Assumptions

The quality characteristic is represented by a random variable X measurable on a continuous scale.

Distribution of X is normal with mean and standard deviation

An upper limit U has been specified and a product is qualified as defective when X>U.
[When the lower limit L is specified, the product is a defective one if X < L] 
The purpose of inspection is to control the fraction defective p in the lot inspected.
When the conditions listed above are satisfied the fraction defective in a lot will be defined by
P=1F (v) with v = (UÂµ) / and
2
F(y) = y 1 exp(z2/ 2)dz (1)
Where Z N(0,1). It is to be recalled, here, that the criterion for the method variable plan is to accept the lot if X + k1 U or X k1 L, when the upper specification limit, U or the lower specification limit, L is specified.
Operating Procedure
Step 1: From each submitted lot take a random sample of size n
n
U X X
(2015) have studied Repetitive Deferred Variables Sampling (RDVS) plan. The resulting plan would be designated as RDVSP and would be applied under the following conditions.
(x1,x2,x3) say and Compute v =
o Where, X = i=1 i
n
11 21 11 21 11 11
Step 2: Accept the lot of v k1
and reject the lot if v < k2
P ( p )
(w ) 1(w ) (w )i (w ) (w ) (w )i
1
7
21 11
a 1 1(w ) (w )i
(w ) 1(w ) (w )i (w ) (w ) (w )i
Step 3: If k2 v < k1 accept the lot provided i proceeding or Pa( p )
2
succeeding lots are accepted under RGS inspection plan.
12
22 12 22 12
22 12
1(w ) (w )i
12
8
Otherwise reject the lot.
Thus, the RDVS plan has the parameters of the sample size n and the acceptable criterion k1 and k2. The RDS plan for variables is simply designated as RDVSP (n; k1, k2).
Operating Characteristic Function
According to Sankar and Mohoputra (1991) the OC function of RDS is given
Pa(1Pc)i+ PcPi
Here w11 is the value of w1 at p=p1, w21 is the value of w2 at p=p1, w12 is the value of w1 at p=p2 and w22 is the value of w2 at p=p2, That is,
w11 = ( Zp1 k1 ) , w 21 = ( Zp2 k2 ) , w12 = ( Zp1 k1 ) , w22 = ( Zp2 k2 )
And Zp is the standard normal variate having upper tail probability of p. By fixing the probability of acceptance of the
Pa(p) ==
a
(1Pc)i
(2)
lot, Pa(p) as 99.99% with normal distribution, where the value of v1 at SSAQL and the value of v2 at SSLQL. For example, if
Under the assumption of normal approximation to the non
central t distributes the values of Pa and Pc are respectively given by,
p1 and p2 are prescribed, then the corresponding value of v1 and v2 will be fixed and if Pa(p1) and Pa(p2) are fixed at 99.99966% and 0.000068% respectively, then we have
(w ) 1(w ) (w )i (w ) (w ) (w )i
P ( p )
11
21 11
21 11
11
0.9999966
9
a 1 1(w ) (w )i
P = (w ) = P [ v k
/ p ] (3)
21 11
a 1 r 1
and
Pc = [(w2) – (w1) ] = Pr [ k2 v < k1 / p] (4)
(w ) 1(w ) (w )i (w ) (w ) (w )i
P ( p )
12
22 12 22 12
12
0.0000068
10
Where, P
= P [ v k
a 2
] is the probability of
1(w ) (w )i
a r 1
22 12
accepting a lot based on under VRGS plan with parameters ( n , k1) and Pc = Pr [ k2 < v < k1a / p ] is the probability of repeating the sample a lot based on under VRGS plan with parameters ( n, k1 , k2, i).
When the expression of Pa and Pc are substituted in equation (2), the OC function of known RDVS ( n; k1 , k2 ) would become
P {v k / p}1 P {k v k / p}i P {k v k / p}P {v k / pi
For given SSAQL and SSLQL, the parametric values of the RDVS plan namely k1, k2 and the sample size n are determined by using a computer search.
Selection of known RDVS Plan Indexed by SSAQL and SSLQL Example
Table 1 can be used to determine RDVS (n; k1, k2, i) for specified values of SSAQL and SSLQL. For example, if it is desired to have a RDVS (n; k1, k2, i for given p1=0.00005
p2=0.00006 and i=1, =0.00034%, =0.00068%, Table 1 given
( p) r
1
r 2
1
r 2
1 r
1
(5)
r 2 1
Pa 1 P {k v k / p}i
Where the first term in the right hand side represents the probability of accepting a lot based on a RGS and the second term is the probability of accepting a lot based on the states of the preceding lots. The probability of acceptance of the lot can be written as
n=417, k1=4.156, k2=4.150 as desired plan parameters with sigma level is 3.8. For the above example, the plan is operated as follows. Take a random sample of size 417 and compute, v
= U X/. Accept the lot if v4.153 and reject the lot if v<4.150. If 4.150v<4.156 accept the lot provided i proceeding or succeeding lots are accepted under RGS inspection plan.
( ) 1( ) ( )
w
w w i
( ) ( )
( )
w w
w i
where
Explanation
( p) 1
2 1
2 1 1
(6)
In screw manufacturing company if the manufacturer
2 1
Pa 1(w ) (w )i
w1 = (U – k1Âµ) / = (v k1)
w2 = (U k2Âµ) / = (v k2)
and v = ( U – Âµ) /
If SSAQL, SSLQL, the producers risk () and the consumers risk () are prescribed then we have
fixes the incoming quality p1=0.00005 and p2=0.00006 (5 to 6 defects out of one lack). Then take a sample of size 417 screw from a given lot. Then the lot has accepted if v4.156 and reject the lot if v<4.150. If 4.150v<4.156 accept the lot provided i proceeding or succeeding lots are accepted under RGS inspection plan.
RDVS with unknown variables plan as the reference plan
If the population standard deviation is unknown, then it is estimated from the sample standard deviation S (n1 as the divisor). If the sample size of the unknown sigma variables
system (Smethod) are ns the acceptance constants are k1s and k2s, then the operating procedure is as follows:
Step 1: From each submitted lot take a random sample of size
The design parameters of the unknown sigma variables RDS plan, namely n, i, k1s, k2s can be determined by solving the following optimization problem when SSAQL and SSLQL are
specified.
n(x1, x2,.xn) say and compute v =
U X
i
Where, = =1
Plotting the OC Curve
Step 2 : Accept the lot if v k1s and reject the lot if v < k2s (K1s>k2s)
Step 3 : If k2s < v < k1s accept the lot provided i proceeding or succeeding lots are accepted under RGS inspection plan. Otherwise reject the lot.
0
1E20
Probability of Acceptance (pa(p))
Thus, the proposed unknown sigma variables RDVS plan is characterized by four parameters, namely, ns, i, k1s, If k1s and k2s. If k1s = k2s then the proposed plan reduces to the RGS variables sampling plan with unknown standard deviation. The determination of parameters of the unknown sigma plan is slightly different from the unknown sigma case. It is known that X+k2sS for a large sample size approximately follows (see Hamaker(1979), Duncan,(1986))
The OC curve for the repetitive deferred variables sampling plan with i=2, n=373, k1=4.367, k2=4.359
1.2
1
0.8
0.6
0.4
0.2
+
~ ( + 2 + 2 2)
2E05
1E05
1E05
1
1
1 2
Fraction Defective (p)
Therefore, the probability of accepting a lot based on a single sample is given approximately by,
P{X U k
 p}
U k1s s
Figure 1: The OC curve of Repetitive deferred (n; k1, k2, i) variables sampling plans where n = 373, k1 = 4.367, k2 = 4.359, i=2.
1s / n
1+ k2 / 2
s 1s
1 2k / 2
p 1s
= z k ns
(11)
Behavior of OC curve
Figure 1 shows that the OC curve of Repetitive Deferred (n; k1, k2, i) variables Sampling plan with i=1,
1s
Analogously to equation (6), the lot acceptance probability for the sigma unknown case is given by
(w ) 1(w ) (w )i (w ) (w ) (w )i
n=373, k1=4.367, k2=4.359.
Figure 2 shows that the comparison of OC curves of the above three nearly equivalent variables RDVS plans having different values of i. It can be seen that the RDVS plan with a
larger value of i seems to be closer to the ideal OC curve in that
( p)
1s
2s 1s 2s
1s
1s
(12)
2s 1s
Pa 1(w ) (w )i
Where,
(w2s) = z k ns
the probability of acceptance at SSAQL, or smaller is increased and the slope at levels between SSAQL and SSLQL becomes sharper although it will require larger sample size. The decision upon choice of the value of i when implementing the plan could be made by considering the sample size and its OC curve.
p
(w1s) = zp
2s
k1s
1 k2 / 2
2s
ns
1s
1 k2 / 2
Here w11s the value of w1s at p=p1, w21s is the value of w2s at p=p1, w12s is the value of w1s at p=p2 and w22s is the value of w2s at p=p2. That is , If (SSAQL, 1) and (SSLQL, ) are prescribed, then we require
(w ) 1(w ) (w )i (w ) (w ) (w )i
and
P ( p )
11
21 11
21 11
11
1
13
21 11
a 1 1(w ) (w )i
(w ) 1(w ) (w )i (w ) (w ) (w )i
P ( p )
12
22 12
22 12
12
14
22 12
a 2 1(w ) (w )i
1.2
1
0.8
0.6
0.4
0.2
1
2
3
0
0
0.00001 0.00002 0.00003
Figure 2: shows the comparison of OC curves of 1) i=1, n=386, k1=4.375, k2 = 4.348;2) i=2, n=373, k1=4.367, k2=4.359; 3) i=3, n=362, k1=4.362, k2=4.354;
Construction of table
The OC function of the variables RDS sampling plan, which gives the proportion of lots are expected to be accepted for a given lot quality p, is obtained by
CONCLUSION
Acceptance sampling is the technique which deals with procedures in which decision to accept or reject lots or process based on the examination of samples. The percent work mainly relates to the construction and selection of tables for Six Sigma Repetitive Deferred Variables Sampling (SSRDVS n, k1, k2,
i) plan through the SSAQL and SSLQL. Tables are provided
here which tailor made, handy and readymade use to the industrial shopfloor condition.
REFERENCES

A.L. Christina, Contribution to the study of Design and Analysis of Suspension System and Some other Sampling Plans, Ph.D. Thesis, Bharathiar University, Tamil Nadu, India, 1995.

A.W. Wortham, and R.C. Baker, Multiple Deferred State Sampling Inspection. Int. J. Prod. Res. 14(6), pp.719731, 1976.

D. Senthilkumar, S.R. Ramya and B. Esha Raffie Construction and Selection of Repetitive Deferred Variables Sampling (RDVS) Plan Indexed by Quality Levels, Journal of Academia and Industrial Research (JAIR), Volume 3, Issue 10, pp.497503. 2015

G. Sankar, and B.N. Mahopatra, GERT analysis of repetitive deferred sampling plans. IAPQR Trans. 16(2): pp. 1725, 1991.

K.K. Suresh, A study on Acceptance Sampling using Acceptable and Limiting Quality Levels, Ph.D. Thesis, Bharathiar University, Tamil Nadu, 1993.

K.K. Suresh, and R. Saminathan, Construction and selection of Repetitive Deferred Sampling plan through AQL and LQL, Int. J. Pure
( p) r 1 r 2 1 r 2 1 r 1
P {v k / p}1 P {k v k / p}i P {k v k / p}P {v k / pi
r 2 1
Pa 1 P {k v k / p}i
(15)
Where
Appl. Math. 65(3): pp.257264, 2010.

R. Vedaldi, A new criterion for the construction of single sampling inspection plans by attributes. Rivista di Statistica Applicata. 19(3), pp.235244. 1986.
the first term in the right hand side represents the probability of
accepting a lot based on a RGS and the second term is the probability of accepting a lot based on the states of the preceding lots. The probability of acceptance of the lot can be written as

Rombert and Vaerst. A procedure to construct Multiple deferred state sampling plan. Meth. Operat. Res. 37: pp. 477485. 1981.

S. Balamurali, and C.H. Jun, Multiple dependent state sampling plans for lot acceptance based on measurement data. Euro. J. Operat. Res. 180: pp.12211230. 2006.

V. Soundararajan, and V. Ramasamy, Procedures and tables for
P (p) =
(1)[1(2)+(1)]+[ (2)(1)][(1)]
a [1(2)+(1)]
(16)
construction and selection of Repetitive Group Sampling (RGS) plans. QR J. 13(13), pp.1421, 1986.
Where w1 = ( U – k1Âµ ) / = ( v k1)
w2 = ( U k2Âµ ) / = ( v k2)
and v = ( U – Âµ) /
If SSAQL, SSLQL, the producers risk () and the consumers risk () are prescribed then we have
P (p )=(w11)[1(w21)+(w11)]i+[ (w21)(w11)][(w11)]i=1 (17)
a 1 [1(w21)+(w12)]i
P (p ) = (w12)[1(w22)+(w12)]i+[ (w22)(w12)][(w12)]i = (18)
a 2 [1(w22)+(w12)]i
For given SSAQL and SSLQL, the design parameters of the variables MDS plan, namely n, m, ka and kr may be determined by satisfying the required producer and consumer conditions in equations (9) and (10). Optimization problem to determine the parameters is formulated as follows:
Values of the parameters (n, k1, and k2) when i=1 and when sigma is known and unknown are tabulated in Table
1. Also i=2 and i=3, the value of the parameters are tabulated in Table 2 and Table 3
Table 1: Variables RDS sapling plans for i=1 indexed by SSAQL and SSLQL
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00001 
0.00002 
386 
4.375 
4.348 
3.8 
4057 
4.375 
4.348 
4.6 
0.00003 
303 
4.275 
4.248 
3.7 
3054 
4.275 
4.248 
4.5 

0.00004 
230 
4.300 
4.273 
3.6 
2343 
4.300 
4.273 
4.4 

0.00005 
203 
4.200 
4.173 
3.5 
1982 
4.201 
4.174 
4.4 

0.00006 
178 
4.175 
4.148 
3.5 
1719 
4.176 
4.149 
4.3 

0.00007 
164 
4.174 
4.147 
3.5 
1583 
4.175 
4.148 
4.3 

0.00008 
121 
4.173 
4.146 
3.3 
1168 
4.174 
4.147 
4.2 

0.00009 
105 
4.165 
4.138 
3.3 
1010 
4.166 
4.139 
4.1 

0.0001 
85 
4.162 
4.135 
3.2 
816 
4.163 
4.136 
4.1 

0.00002 
0.00003 
408 
4.270 
4.223 
3.8 
4090 
4.270 
4.223 
4.6 
0.00004 
310 
4.295 
4.248 
3.7 
3137 
4.295 
4.248 
4.5 

0.00005 
274 
4.195 
4.148 
3.7 
2654 
4.195 
4.148 
4.5 

0.00006 
240 
4.170 
4.123 
3.6 
2302 
4.170 
4.123 
4.4 

0.00007 
221 
4.169 
4.122 
3.6 
2120 
4.169 
4.122 
4.4 

0.00008 
163 
4.168 
4.121 
3.5 
1563 
4.169 
4.122 
4.3 

0.00009 
141 
4.160 
4.113 
3.4 
1352 
4.161 
4.114 
4.2 

0.0001 
115 
4.157 
4.110 
3.3 
1093 
4.158 
4.111 
4.2 

0.00003 
0.00004 
403 
4.293 
4.223 
3.8 
4055 
4.293 
4.223 
4.6 
0.00005 
356 
4.193 
4.123 
3.8 
3429 
4.193 
4.123 
4.5 

0.00006 
312 
4.168 
4.098 
3.7 
2975 
4.168 
4.098 
4.5 

0.00007 
287 
4.167 
4.097 
3.7 
2739 
4.167 
4.097 
4.5 

0.00008 
212 
4.166 
4.096 
3.6 
2020 
4.166 
4.097 
4.4 

0.00009 
184 
4.158 
4.088 
3.5 
1747 
4.158 
4.089 
4.3 

0.0001 
115 
4.155 
4.085 
3.3 
1092 
4.155 
4.086 
4.2 

0.00004 
0.00005 
462 
4.190 
4.098 
3.9 
4432 
4.190 
4.098 
4.6 
0.00006 
405 
4.165 
4.073 
3.8 
3844 
4.165 
4.073 
4.6 

0.00007 
373 
4.164 
4.072 
3.8 
3540 
4.164 
4.072 
4.5 

0.00008 
276 
4.163 
4.071 
3.7 
2611 
4.163 
4.071 
4.5 

0.00009 
239 
4.155 
4.063 
3.6 
2258 
4.155 
4.063 
4.4 

0.0001 
118 
4.152 
<>4.060 
3.3 
1113 
4.153 
4.061 
4.2 
Table 1 (continued )
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00005 
0.00006 
417 
4.156 
4.150 
3.8 
4010 
4.156 
4.150 
4.6 
0.00007 
384 
4.155 
4.149 
3.8 
3693 
4.155 
4.149 
4.6 

0.00008 
283 
4.154 
4.148 
3.7 
2724 
4.154 
4.148 
4.5 

0.00009 
246 
4.146 
4.140 
3.6 
2355 
4.146 
4.140 
4.4 

0.0001 
121 
4.143 
4.137 
3.3 
1161 
4.144 
4.138 
4.2 

0.00006 
0.00007 
386 
4.153 
4.145 
3.8 
3711 
4.153 
4.145 
4.6 
0.00008 
285 
4.152 
4.144 
3.7 
2737 
4.152 
4.144 
4.5 

0.00009 
247 
4.144 
4.136 
3.6 
2366 
4.144 
4.136 
4.4 

0.0001 
122 
4.141 
4.133 
3.3 
1166 
4.142 
4.134 
4.2 

0.00007 
0.00008 
288 
4.148 
4.140 
3.7 
2756 
4.148 
4.140 
4.5 
0.00009 
250 
4.147 
4.139 
3.6 
2391 
4.147 
4.139 
4.4 

0.0001 
123 
4.139 
4.131 
3.3 
1176 
4.140 
4.132 
4.2 

0.00008 
0.00009 
269 
4.145 
4.136 
3.7 
2579 
4.145 
4.136 
4.4 
0.0001 
133 
4.137 
4.128 
3.4 
1268 
4.138 
4.129 
4.2 

0.00009 
0.0001 
134 
4.134 
4.125 
3.4 
1273 
4.135 
4.126 
4.2 
Table 2: Variables RDS sapling plans for i=2 indexed by SSAQL and SSLQL
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00001 
0.00002 
373 
4.367 
4.359 
3.8 
3923 
4.367 
4.359 
4.6 
0.00003 
291 
4.267 
4.259 
3.7 
2935 
4.267 
4.259 
4.5 

0.00004 
219 
4.292 
4.284 
3.6 
2232 
4.292 
4.284 
4.4 

0.00005 
193 
4.192 
4.184 
3.5 
1886 
4.193 
4.185 
4.3 

0.00006 
169 
4.167 
4.159 
3.5 
1633 
4.168 
4.160 
4.3 

0.00007 
157 
4.166 
4.158 
3.4 
1517 
4.167 
4.159 
4.3 

0.00008 
113 
4.165 
4.157 
3.3 
1091 
4.166 
4.158 
4.2 

0.00009 
96 
4.157 
4.149 
3.2 
924 
4.158 
4.150 
4.1 

0.0001 
77 
4.154 
4.146 
3.1 
740 
4.155 
4.147 
4.0 

0.00002 
0.00003 
395 
4.262 
4.254 
3.8 
3979 
4.262 
4.254 
4.6 
0.00004 
297 
4.287 
4.279 
3.7 
3020 
4.287 
4.279 
4.5 

0.00005 
261 
4.187 
4.179 
3.6 
2540 
4.187 
4.179 
4.4 

0.00006 
227 
4.162 
4.154 
3.6 
2188 
4.162 
4.154 
4.4 

0.00007 
208 
4.161 
4.153 
3.6 
2005 
4.162 
4.154 
4.4 

0.00008 
150 
4.16 
4.152 
3.4 
1446 
4.161 
4.153 
4.3 

0.00009 
128 
4.152 
4.144 
3.3 
1234 
4.153 
4.145 
4.2 

0.0001 
102 
4.149 
4.141 
3.2 
974 
4.150 
4.142 
4.1 

0.00003 
0.00004 
390 
4.2845 
4.2765 
3.8 
3962 
4.285 
4.277 
4.6 
0.00005 
343 
4.1845 
4.1765 
3.8 
3336 
4.185 
4.177 
4.5 

0.00006 
299 
4.1595 
4.1515 
3.7 
2879 
4.160 
4.152 
4.5 

0.00007 
274 
4.1585 
4.1505 
3.7 
2641 
4.159 
4.151 
4.5 

0.00008 
199 
4.1575 
4.1495 
3.5 
1915 
4.158 
4.150 
4.4 

0.00009 
171 
4.1415 
3.5 
1640 
4.150 
4.142 
4.3 

0.0001 
102 
4.1465 
4.1385 
3.2 
978 
4.148 
4.140 
4.1 

0.00004 
0.00005 
449 
4.182 
4.174 
3.9 
4371 
4.182 
4.174 
4.6 
0.00006 
392 
4.157 
4.149 
3.8 
3776 
4.157 
4.149 
4.6 

0.00007 
360 
4.156 
4.148 
3.8 
3468 
4.156 
4.148 
4.5 

0.00008 
263 
4.155 
4.147 
3.6 
2525 
4.155 
4.147 
4.4 

0.00009 
226 
4.147 
4.139 
3.6 
2167 
4.147 
4.139 
4.4 

0.0001 
105 
4.144 
4.136 
3.3 
1005 
4.145 
4.137 
4.1 
Table 2 (continued )
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00005 
0.00006 
404 
4.148 
4.14 
3.8 
3870 
4.148 
4.140 
4.6 
0.00007 
371 
4.147 
4.139 
3.8 
3554 
4.147 
4.139 
4.5 

0.00008 
270 
4.146 
4.138 
3.7 
2589 
4.146 
4.138 
4.4 

0.00009 
233 
4.138 
4.13 
3.6 
2222 
4.138 
4.130 
4.4 

0.0001 
108 
4.135 
4.127 
3.3 
1032 
4.136 
4.128 
4.2 

0.00006 
0.00007 
373 
4.145 
4.137 
3.8 
3573 
4.145 
4.137 
4.5 
0.00008 
272 
4.144 
4.136 
3.7 
2603 
4.144 
4.136 
4.4 

0.00009 
234 
4.136 
4.128 
3.6 
2234 
4.136 
4.128 
4.4 

0.0001 
109 
4.133 
4.125 
3.3 
1038 
4.134 
4.126 
4.2 

0.00007 
0.00008 
275 
4.14 
4.132 
3.7 
2623 
4.140 
4.132 
4.5 
0.00009 
237 
4.139 
4.131 
3.6 
2258 
4.139 
4.131 
4.4 

0.0001 
110 
4.131 
4.123 
3.3 
1048 
4.132 
4.124 
4.2 

0.00008 
0.00009 
256 
4.137 
4.129 
3.6 
2447 
4.137 
4.129 
4.4 
0.0001 
120 
4.129 
4.121 
3.3 
1141 
4.130 
4.122 
4.2 

0.00009 
0.0001 
121 
4.126 
4.118 
3.3 
1146 
4.127 
4.119 
4.2 
Table 3: Variables RDS sampling plans for i=3 indexed by SSAQL and SSLQL
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00001 
0.00002 
362 
4.362 
4.354 
3.8 
3797 
4.362 
4.354 
4.5 
0.00003 
276 
4.262 
4.254 
3.7 
2776 
4.262 
4.254 
4.5 

0.00004 
207 
4.287 
4.279 
3.5 
2103 
4.288 
4.280 
4.4 

0.00005 
181 
4.187 
4.179 
3.5 
1762 
4.188 
4.180 
4.3 

0.00006 
158 
4.162 
4.154 
3.4 
1521 
4.163 
4.155 
4.3 

0.00007 
148 
4.161 
4.153 
3.4 
1424 
4.162 
4.154 
4.3 

0.00008 
105 
4.16 
4.152 
3.3 
1009 
4.161 
4.153 
4.1 

0.00009 
87 
4.152 
4.144 
3.2 
833 
4.153 
4.145 
4.1 

0.0001 
68 
4.149 
4.141 
3.0 
650 
4.151 
4.143 
4.0 

0.00002 
0.00003 
287 
4.19 
4.183 
3.7 
2802 
4.190 
4.183 
4.5 
0.00004 
299 
4.215 
4.207 
3.7 
2949 
4.215 
4.207 
4.5 

0.00005 
164 
4.115 
4.107 
3.5 
1546 
4.116 
4.108 
4.3 

0.00006 
231 
4.09 
4.082 
3.6 
2158 
4.090 
4.082 
4.4 

0.00007 
213 
4.089 
4.081 
3.6 
1990 
4.090 
4.082 
4.4 

0.00008 
153 
4.088 
4.08 
3.4 
1429 
4.089 
4.081 
4.3 

0.00009 
132 
4.08 
4.072 
3.4 
1233 
4.081 
4.073 
4.2 

0.0001 
104 
4.077 
4.069 
3.3 
962 
4.078 
4.070 
4.1 

0.00003 
0.00004 
392 
4.2125 
4.2045 
3.8 
3862 
4.213 
4.205 
4.6 
0.00005 
344 
4.1125 
4.1045 
3.8 
3244 
4.113 
4.105 
4.5 

0.00006 
301 
4.0875 
4.0795 
3.7 
2809 
4.088 
4.080 
4.5 

0.00007 
275 
4.0865 
4.0785 
3.7 
2569 
4.087 
4.079 
4.4 

0.00008 
201 
4.0855 
4.0775 
3.5 
1875 
4.086 
4.078 
4.4 

0.00009 
173 
4.0775 
4.0695 
3.5 
1608 
4.078 
4.070 
4.3 

0.0001 
106 
4.0745 
4.0665 
3.3 
985 
4.076 
4.068 
4.1 

0.00004 
0.00005 
436 
4.11 
4.102 
3.8 
4114 
4.110 
4.102 
4.6 
0.00006 
393 
4.085 
4.077 
3.8 
3669 
4.085 
4.077 
4.6 

0.00007 
362 
4.084 
4.076 
3.8 
3379 
4.084 
4.076 
4.5 

0.00008 
266 
4.083 
4.075 
3.7 
2475 
4.083 
4.075 
4.4 

0.00009 
230 
4.075 
4.067 
3.6 
2137 
4.075 
4.067 
4.4 

0.0001 
110 
4.072 
4.064 
3.3 
1020 
4.073 
4.065 
4.2 
Table 3 (continued )
p1 
p2 
n 
k1 
k2 
o – Level 
ns 
k1s 
k2s 
o – Level 
0.00005 
0.00006 
404 
4.076 
4.068 
3.8 
3751 
4.076 
4.068 
4.6 
0.00007 
373 
4.075 
4.067 
3.8 
3463 
4.075 
4.067 
4.5 

0.00008 
274 
4.074 
4.066 
3.7 
2546 
4.074 
4.066 
4.4 

0.00009 
238 
4.066 
4.058 
3.6 
2200 
4.066 
4.058 
4.4 

0.0001 
113 
4.063 
4.055 
3.3 
1047 
4.064 
4.056 
4.2 

0.00006 
0.00007 
374 
4.073 
4.065 
3.8 
3472 
4.073 
4.065 
4.5 
0.00008 
274 
4.072 
4.064 
3.7 
2541 
4.072 
4.064 
4.4 

0.00009 
235 
4.064 
4.056 
3.6 
2174 
4.064 
4.056 
4.4 

0.0001 
112 
4.061 
4.053 
3.3 
1034 
4.062 
4.054 
4.2 

0.00007 
0.00008 
277 
4.068 
4.06 
3.7 
2560 
4.068 
4.060 
4.5 
0.00009 
238 
4.067 
4.059 
3.6 
2198 
4.067 
4.059 
4.4 

0.0001 
112 
4.059 
4.051 
3.3 
1034 
4.060 
4.052 
4.2 

0.00008 
0.00009 
259 
4.065 
4.057 
3.7 
2399 
4.065 
4.057 
4.4 
0.0001 
123 
4.057 
4.049 
3.3 
1133 
4.058 
4.050 
4.2 

0.00009 
0.0001 
126 
4.054 
4.046 
3.3 
1156 
4.055 
4.047 
4.2 