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Acceptance Sampling of Bulk Liquids, Powders, Pellets

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This example shows how to develop sampling plans for the mean and the range of measured properties of bulk liquids, powders, and pellets. Software program TP414 develops the sampling plans.

These acceptance sampling plans for the mean develop sample size(n), and the decision limits (A), for the sample average based your specification of two points on the operating characteristic (OC) curve. These plans have OC-curves which have the lot mean on the horizontal axis and probability of acceptance (Pa) on the vertical axis.

Definition of Terms used on the Output Reports
Alpha Risk: Producers risk of rejecting a "lot" when the true lot mean is equal to X=AQLMU or X=AQLML.
Beta Risk: Consumers risk of accepting a "lot" when the true lot mean is equal to RQLML or RQLMU.

For any oc-curve, TP414 provides three matched decision rules :

Three Matched Decision Rules
Fixed-n The sample size, n, is fixed at a constant value.
SPR sequential n is determined by the data sequentially. Smaller average n per lot (ASN) than the matched fixed-n plan
TSS sequential Similar to SPR sequential. Has advantages over SPR.

To develop a sampling plan for the mean, you must provide a known historical within-lot standard deviation (sigma). In addition to developing an acceptance plan for the mean, TP414 provides a decision rule for testing that the standard deviation of the current sampled lot has not changed significantly. This test is uses the range of the sample.

Table of Contents


  Software Program TP414
  Fixed-n Decision Rule for the Mean
  Decision Rule to Check "known" standard deviation
  Graph of OC-Curve for the Mean
  Table of OC, ASN, and ARL-Curve for the Mean
  SPR Sequential Decision-Rule Diagram
  SPR Sequential Decision-Rule Table
  TSS Sequential Decision-Rule Table
  How to Order the Software

Other Documents Available from H & H Servicco Corp.

TP414 product description (Software details)
Product Acceptance Design Journey (How to apply)
Modern Acceptance Sampling (Two-point methodology)


Sections of the output reports:
(1) A user-controlled title
(2) Description of the statistical type of sampling plan.
(3) Two user-defined points on the oc-curve:
(4) Decision rule
(5) Date and name of program that produced the sampling plan.

Fixed-n Decision Rule for the Mean


Decision Rule to check Known Standard Deviation using the Range


Table of OC-Curve, ASN-Curve and ARL Curve for the Mean


The OC-Curve above shows the probability of accepting(column 2) a lot as a function of the lot mean(Column 1). You use it to determine how well the acceptance plan will discriminate between lots having various true means.

The ASN curve shows the Average Sample Number (ASN) to reach a decision with a sequential plan. The ARL curve shows the number of lot decisions between rejections.


Graph of OC-Curve for the Mean


Sequential Sampling
Sequential sampling is the leading methodology to reduce the cost of inspection through reduced testing. Compared to fixed-n plans, sequentials require fewer sample/tests, on average, than is possible with fixed-n plans having the same risks.

SPR Sequential Decision Rule Table

The acceptance decision is made by considering the sample data sequentially, either one at a time or in groups. After each such increase in n, you compare the sample average to the Ac and Re that apply for that n. This determines whether you accept, reject, or continue to build up the sample.

Interface with Microsoft Office
TP414 will export the decision rule table or an oc-curve table to an ASCII file, making it readable by most commercially available graphics software. The example below -- from a different sampling plan example -- was drawn by this method using Microsoft's Excel.


SPR Sequential Decision Rule Diagram



TSS Sequential Decision-Rule Table


This TSS Sequential decision rule operates the same way as the previous SPR sequential. The sample data is examined sequentially until the its average falls out of the continue zone and falls in either the accept zone or the reject zone.

A special property of the TSS type of sequential sampling plan is that the last line of the decision table, contains the n and ac of the fixed-n plan that it is matched to.

If you simulate the operation of a TSS plan, you will find that its OC-curve matches exactly with that of this matched fixed-n plan.


Summary of TP414 applied to bulk liquids, powders, and pellets:

  1. Require enough testing to discriminate between acceptable and unacceptable levels of the mean - with known probabilities.
  2. Use the smallest sample size possible in order to minimize cost.
  3. Describe the protection offered by the decision rule with its operating characteristic curve.

We have refined this software over many years of use in these areas:

  1. By quality Engineers, Technicians, and Consultants.
  2. In classroom training for product acceptance and process control.

At just $245, TP414 will inexpensively streamline your company's product acceptance methodology.
See additional information on how to order TP414

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