# What is Inspection Theory

Inspection theory is changing nowadays. Inspection used to be a means of weeding out lots that have more than a certain percentage of defects and accepting lots that have less or no defects. It is now becoming the supplier’s responsibility to supply lots that are 100% good, or at most, a couple of parts per thousand (and in many cases a couple of parts per million) defective.

## How to achieve defect-free shipment

The only way defect-free shipments can be achieved is for the supplier to have ongoing in-process controls in place. This means that the supplier is continuously monitoring the process and working toward improvement. Inspection is now becoming more a method of reviewing data provided by the supplier to see that the process is still in control, and confirming visually that the customer has the right part.

Since it’s the supplier’s customer asking for the inspection data, the customer may set the standards for what data is collected, how the report is compiled, and how the report is formatted. As the use of SPC grows, more and more customers are requiring that suppliers meet these standards. For some industries, suppliers are being asked to use automated data collection systems, such as the DataMyte 769 data collector, and supply customers with the standard reports printed from the data collector. In addition to requiring data and reports, customers may also conduct periodic audit inspections.

Chapter 2 covers methods of collecting data. Chapter 9 examines supplier certification further. Now, let’s examine some traditional methods of inspection.

# THEORY OF ACCEPTANCE SAMPLING

Acceptance sampling is the practice of inspecting a small quantity of the parts in a lot for conformance to specification. A decision is then made whether to accept or reject the entire lot based on the findings of the sample. The justification for acceptance sampling is that it provides a cost savings over 100% inspection (see 8.5, Minimizing Total Cost of Inspection and Repair, for Dr. W.E. Deming’s proof to the contrary). The cost savings are the result of less time needed to inspect a sample, and requirements for fewer inspectors. There is the additional expense and overhead required to design and administer the sampling plans, however. Other reasons for sampling include:

- Greater speed — More lots can be evaluated faster, and the good separated from the bad for Material Review Board (MRB) dispositioning.
- Minimized handling — By inspecting only a sample, fewer items are subjected to the possible damage which sometimes occurs in handling or measuring during the inspection process.
- Greater accuracy — The problem of inspector error due to monotony is minimized. With fewer items to inspect, more time can be used to ensure completeness and accuracy.
- Faster corrective action — Lot rejection due to sampling tends to dramatize quality deficiencies and to speed up corrective action over 100% sorting.

## The disadvantages of acceptance sampling

The disadvantages of acceptance sampling are administrative costs, sampling risks, and the fact that decisions have to be made with less information than is provided with 100% inspection or vendor-supplied process control charts.

Acceptance sampling should be used when 100% inspection is causing errors due to monotony, when destructive testing is used, when the cost of inspection is high in relation to the cost resulting from passing a defective, and when a particular parameter is a good indicator of a lot’s overall quality.

## Importance of a Random Sample

A random sample is one in which every item in the population has an equal chance of being chosen. The concept of sampling is based on the idea that a sufficient quantity of items is chosen in a random fashion. The sample must contain all the characteristics of the total population. One statistical tool developed to help select a random sample is a random number table (see Appendix, Table A-10 for an example). Before using the table, it is first necessary to assign a number to each unit in the population. Simply enter any column or line, and select the sequence of numbers as they occur. For example, if we require five samples, and choose to enter the table at line 21, we would get the numbers 26, 20, 46, 66, 36 (Appendix, Table A-10). These are the corresponding numbers you would select from the population. Further information on random number tables can be found in various statistical textbooks.

## Risks Associated with Sampling

In sampling, certain inherent risks are involved which must be addressed and understood. These risks can be broken down into the following two types:

- The Producer’s Risk (also referred to as α Risk) can be understood easiest when thought of as the probability that a good lot will be rejected by the sampling plan. The quantified risk must be defined prior to adopting a given sampling plan. The risk is stated with a numerical definition of good quality such as AQL (acceptable quality level). The sampling plan should have a Producer’s Risk that is equal to or better than the AQL.
- The Consumer’s Risk (also referred to as the β Risk) is the risk that a bad lot will be accepted by the sampling plan. The consumer’s risk is generally stated with a numerical definition of bad quality such as LTPD (lot tolerance percent defective).

## Estimating Sampling Risks

The estimation of the Producer’s Risk of a sampling plan includes the following steps:

- Plot an OC curve for the sampling plan in question. OC curves are described in the following section.
- Find the percent defective in the process when it is running at capability.
- Estimate it, if necessary, but if greater accuracy is desired, a process capability study should be done.
- Find the process capability percentage on the OC curve and follow it up to determine the probability of acceptance.
- Subtract this probability of acceptance from 1.0. This number is the producer’s risk for the sampling plan.

To estimate the Consumer’s Risk, proceed as follows:

- Plot the OC curve for the sampling plan in question.
- Find the percent defective that the consumer wants to reject. This may be understood to be the worst-case quality that the customer will accept.
- Find this value on the horizontal scale of the OC curve. Follow it up to determine the probability of acceptance. This number will be your risk of accepting poor quality material.