TPZero User Manual
Tool for Ac=0 Acceptance Sampling Plans
This software tool calculates the sample size for Ac=0 acceptance sampling plans. The user specifies the sampling requirement by entering a Consumer's Point of the oc curve that the sampling plan should have. That is the only input required.
These zero acceptance number plans are usually called C=0 plans when used for manufacturing and quality control applications, and to "Discovery Sampling" plans when used for auditing financial records.
Example Input: a Consumer's Point:
RQL = 0.10 fraction defective, Beta = 0.05
Example Output: a Decision Rule:
n = 28, Ac = 0
Example Output: of Probability Statement describing the Consumer's Point:
If the true lot fraction defective is 0.10 or more, then the probability that a sample of n =28 will contain 0 defectives is 0.05 or less.
TPZero is a simple tool with only three main menus.
The File menu will print a copy of the report on the default printer, copy it to the Windows clipboard, or exit the program.
The Design menu has only one option -- to design a C=0 sampling plan.
The Help menu provides help in using TPZero.
Entering the Consumer's Point, RQL & Beta
You start this form from the Design Menu. [Design][Ac=0].
To calculate the sample size required, you only need to enter two values, RQL and Beta.
To determine a sample size for your application, change the example values of RQL and Beta to your values. Then push the Calculate Button.
You start this form from the Design Menu. [Design][Ac>0].
As you increase the Acceptance number ( Ac) and do nothing else, the oc curve moves to the right (towards higher fraction defective)
As you move Ac up and RQL down the oc curve becomes steeper, making the plan more discriminating.
When you push the Calculate Button, TPZero tool calculates the sample size required by the consumer's point ( RQL, Beta).
Interpretation of the output:
The Decision Rule
· The sample size, n, is rounded to the nearest whole number. · The exact-n displays the value of n that exactly satisfies your consumer's point
-- before rounding to the whole number, n. (Shown only for sample size less than 1,000.)
· The Ac = 0 decision rule is stated.
Performance of the Sampling Plan
· The exact meaning of your consumer's point is shown as a probability statement. · The producer's point is displayed and interpreted for Alpha = 0.05.
This oc curve describes the performance of the decision rule n=28, Ac=0. This plan was designed by specifying the consumer's point: RQL=0.10, Beta=0.05
Every decision rule ( n , Ac ) has an oc curve, which describes the sampling plans' probability of accepting lots having various fractions defective.
The program TPZero displays two points on the oc curve, the Consumer's Point and the Producer's Point.
Points on the OC Curve
( RQL, Beta) and ( AQL, Alpha) define the consumer's and producer's points on an oc curve. Actually, any point on the oc curve, regardless of what you call it, can be entered for (RQL, Beta). TPZero will calculate the sample size for the one Ac=0 sampling plan that has an oc curve going through that point..
For your information, TPZero shows the producers point, ( AQL and Alpha ) at Alpha = 0.05 for all sampling plans. This second point is not necessary in designing an Ac=0 sampling plan because for a given Ac, you only need to specify one point.
However, knowing the producer's point can be useful if you need to know the lot quality that will have a high probability of acceptance with the plan.
For Alpha = 0.05, Pa = (1-Alpha) = 0.95 (95%)
Possible Fractions Defective
TPZero does not use lot size, so it can not automatically limit RQL to the possible series of values of lot p'. For any lot containing N items, the possible fractions defective are:
p': 0, 1/N, 2/N, 3/N ....
For example, if N=100, the possible numbers of defective items are:
defectives = 0, 1, 2, 3 ...
So the values of p' are limited to:
p' = 0.00, 0.01, 0.02, 0.03 ...
Consequently, the probability statements will be inexact when RQL is smaller than1/N.
Terms and Symbols used by TPZero
SYMBOL NAME Pa probability of acceptance of a lot. p' fraction defective of a lot. AQL Acceptable Quality Level. RQL Rejectable Quality Level. Alpha risk of rejecting a lot if p'=AQL. Beta risk of accepting a lot if p'=RQL. n Sample Size Exact-n Sample Size before rounding to whole number N Lot Size Ac Acceptance Number, Same as C C Acceptance number, same as Ac X The number of defective items in a sample.
Range of Input variables
RQL: 0.000001 to 0.999999 (decimal fractions)
Beta: 0.000001 to 0.999999 (decimal fractions)
For Ac>0 option. Ac: 0 to 700
TPZero calculates the sample size using the binomial distribution. The binomial does not use the lot size in calculating n. As such, the binomial is an approximation to the true distribution, the hypergeometric. It is a very accurate approximation and is commonly used when small samples are taken from large lots. As a Rule of Thumb, the binomial distribution is very accurate when N / n =>10. That is, when the lot is 10 times larger than the sample.
Context sensitive help: help F1
Sampling plan help: www.samplingplans.com
The menu [Help][About] displays the version of TPZero, whether it is registered, and if not, how many days of free usage are left.
You can obtain unlimited use of TPZero. Buy a license (Username and password) from H & H Servicco Corp. and register it.
Apply the username and password with: [Help] [Register]
|PO Box 9340
North St Paul, MN 55109-0340
The Acceptance Number is the maximum allowable number of defective items in the sample and still accept the lot. If the number of defectives in the sample exceeds Ac, then the lot is rejected. The symbols "Ac" and "C" are commonly used to represent the acceptance number.
N: Upper case N is the symbol for the lot size (Number of items in the lot.)
The probability of a type II error:
The probability of a type I error:
The probability of rejecting a lot if it contains AQL fraction defective.
TP105 allows input of BOTH consumer's point and producer's point, or (n, Ac) to calculate the Alpha and Beta risk, or to calculate AQL and RQL.
TP105 also calculates, in addition to the complete oc curve, the AOQ, ARL, ASN, and AFI curves.
TP105 also calculates, for any (n, Ac), the matched sequential sampling plan. Or, from two points on the oc curve, both fixed-n and sequential sampling plans.
The author of TPZeroVisual Basic V6 - Microsoft
Stan Hilliard, H & H Servicco corp.
To design and compile the program code. VB Helpwriter
To design the Help system.
FabLock - Teletech Systems
To design the copy protection system
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