FIGURE 2.10: Comparison of Normal, Tightened, and Scheme OC Curves
SI/ASQ Z1.4 Standard. The rules for switching between Normal, tightened, and reduced sampling using ANSI/ASQ Z1.4 standard are shown in Figure 2.11. Utilizing the plans and switching rules will result in an OC curve closer to the ideal, and will motivate the suppliers to provide lots with the proportion nonconforming at or below the agreed upon AQL.
FIGURE 2.11: Switching rules for ANSI/ASQ Z1.4 (Reproduced from Schilling and Neubauer[84])
The international standard, ISO 2859-1, incorporates modifications to the original MIL-STD-105 concepts to reflect changes in the state of the art, and it is recommended for use in international trade. Again, proper use of the plans requires adherence to the switching rules which are shown in Figure 2.12. When this is done, the producer receives protection against having lots rejected when the percent nonconforming is less than the stated AQL. The customer is also protected against accepting lots with a percent nonconform- ing higher than the AQL. When the rules are not followed, these benefits are lost. The benefit of smaller sample sizes afforded to the customer by the re- duced plan, when quality is good, is also lost when the switching rules are not followed.
FIGURE 2.12: Switching rules for ISO 2859-1(Reproduced from Schilling and Neubauer[84])
The calculation of the switching score inFigure 2.12is initiated at the start of normal inspection unless otherwise specified by a responsible authority.
The switching score is set to zero at the start and is updated following the inspection of each subsequent lot on original normal inspection.
a) Single sampling plans:
1. When the acceptance number is 2 or more, add 3 to the switching score if the lot would have been accepted if the AQL had been one step higher;
otherwise reset the switching score to zero.
2. When the acceptance number is 0 or 1, add 2 to the switching score if the lot is accepted; otherwise reset the switching score to zero.
b) Double or multiple sampling plans:
1. When a double sampling plan is used, add 3 to the switching score if the lot is accepted after the first sample; otherwise reset the switching score to 0.
2. when a multiple sampling plan is used, add 3 to the switching score if the lot is accepted by the third sample; otherwise reset the switching score to zero.
To use the tables from ANSI/ASQ Z1.4 or ISO 2859-1, a code letter is determined from a table, based on the lot size and inspection level. Next, a decision is made whether to use single, double, or multiple sampling, and whether to use normal, tightened, or reduced inspection. Finally, the sam- ple size(s) and acceptance-rejection number(s) are obtained from the tables.
The online NIST Engineering Statistics Handbook (NIST/SEMATECH e- Handbook of Statistical Methods-http://www.itl.nist.gov/div898/handbook/
Section 6.2.3.1) shows an example of how this is done using the MIL-STD 105E-ANSI/ASQ Z1.4 tables for normal inspection.
The section of R code below shows how a single sampling plan from AN- SI/ASQ Z1.4 or ISO 2859-1 can be retrieved using theAASingle() function in the R packageAQLSchemes. The function callAASingle(’Normal’)shown below specifies that the normal sampling plan is desired. When this function call is executed, the function interactively queries the user to determine the inspection level, the lot size, and the AQL. In this example the inspection level is II, the lot size is 1500, and the AQL is 1.5%. The result is a sampling plan with n=125, with an acceptance number c=5, and a rejection number r=6 as shown in the section of code below.
R>library(AQLSchemes) R>planS<-AASingle(’Normal’) MIL-STD-105E ANSI/ASQ Z1.4
If the sample size exceeds the lot size carry out 100% inspection
What is the Inspection Level?
1: S-1 2: S-2 3: S-3 4: S-4 5: I 6: II 7: III Selection: 6
What is the Lot Size?
1: 2-8 2: 9-15
3: 16-25 4: 26-50
5: 51-90 6: 91-150
7: 151-280 8: 281-500
9: 501-1200 10: 1201-3200 11: 3201-10,000 12: 10,001-35,000 13: 35,001-150,000 14: 150,001-500,000 15: 500,001 and over
Selection: 10
What is the AQL in percent nonconforming per 100 items?
1: 0.010 2: 0.015 3: 0.025 4: 0.040 5: 0.065 6: 0.10 7: 0.15 8: 0.25 9: 0.40 10: 0.65 11: 1.0 12: 1.5 13: 2.5 14: 4.0 15: 6.5 16: 10
17: 15 18: 25 19: 40 20: 65
21: 100 22: 150 23: 250 24: 400 25: 650 26: 1000
Selection: 12 R>planS
n c r 1 125 5 6
Executing the function call again with the option tightened (i.e., AASingle(’Tightened’) and answering the queries the same as above re- sults in the tightened plan withn=125,c=3, andr=4. The reduced sampling plan is obtained by executing the function AASingle(’Reduced’) and an- swering the queries the same way. This results in a plan with less sampling required (i.e.,n=50,c=2, andr=5). However, there is a gap between the ac- ceptance number and the rejection number. Whenever the acceptance number is exceeded in a ANSI/ASQ Z1.4 plan for reduced inspection, but rejection number has not been reached (for example if the number of nonconformities in a sample of 50 were 4 in the last example) then the lot should be accepted, but normal inspection should be reinstated.
One of the modifications incorporated when developing the ISO 2859-1 international derivative of MIL-STD 105E was the elimination of gaps between the acceptance and rejection numbers. the ISO 2859-1 single sampling plan, for the lot size AQL and inspection level in the example above, are the same for the normal and tightened plans, but the reduced plan is n=50, c=3, and r=4 with no gap between the acceptance and rejection numbers.
To create an ANSI/ASQ Z1.4 double sampling plan for the same re- quirements as the example above using the AQLSchemes package, use the AADouble()function as shown in the example below.
R>library(AQLSchemes) R>planD<-AADouble(’Normal’) MIL-STD-105E ANSI/ASQ Z1.4 What is the Inspection Level?
1: S-1 2: S-2 3: S-3 4: S-4 5: I
6: II