Statistical Sampling Methods for Project Quality Control

Statistical sampling is a way of identifying the quality of a service or product when it is impractical or too expensive to examine each item. Effective sampling is based on statistical probability theory which identifies the probability of error for a sample size. Using standard deviation and variance calculations, control charts can be constructed, which accurately predict the likelihood of a sample being representative of a population or lot size.

To be accurate, the sample size must be "representative" and "valid." Representative means that enough good and bad items must be included in the sample, so that it portrays the lot it is drawn from accurately. Validity is the measure, whereby the method of testing and the attributes measured are a true indication of what needs to be measured.

Key issues for ensuring accuracy are the proper determination of the sample size and the rejection level acceptable within the sample. Sampling methods include acceptance sample, attributes sampling, special attributes sampling, and variable sampling.

• acceptance sampling
  Acceptance sampling tests selected items against an agreed upon list of necessary criteria. The inspection can be conducted in a variety of ways including electronic, stress testing, sample destruction, reaction testing, and temperature testing.
  
  It is more convenient to conduct acceptance sampling with lots in a production run. This reduces overall costs by making the sample sizes smaller and more manageable. If a quality problem is discovered, it is easier to track down the lot. It is also cheaper to rework or throw out the lot. Lots are often naturally created by factors such as shift changes, raw material lot sizes, handling or packaging sizes, or shipment sizes. Random selection within the lot is also important to ensure sample validity.
  

• attributes sampling
  After the acceptance sampling method has been chosen, attributes sampling defines what exactly will be measured for quality control. This is often based upon past sample failure experience or customer feedback. The quality inspector merely checks the individual sample against the quality criteria. The attribute is measured by a simple "yes" or "no" that the item is acceptable. This method is often used in inspecting for size, color, finishing, marking, and packing. Data is recorded on a simple checklist sheet.
  
  The use of attributes sampling has some advantages and disadvantages. Attributes testing is simpler and less expensive than inspection by variables. Recordkeeping is simplified by having one quality level for a group of like attributes. However, attributes sampling also requires a large sample size to determine the acceptability of the parent lot, which makes the process time consuming and expensive.
  

• special attributes sampling
  Statisticians have various sampling methods that simplify the inspection process, reduce time and cost, yet still ensure accuracy in the inspection process. These methods are referred to as "special attributes sampling" and include continuous sampling, chain sampling, and skip-lot sampling.
  
  With continuous sampling, inspection occurs throughout production, like on an assembly line. This method is often used when storage facilities are inadequate or it is difficult to accumulate large lots for inspection.
  
  Chain sampling occurs when a product is produced as a lot for inclusion into another product. It is tested throughout the manufacturing process. This method is useful when sample sizes are small, and there is good quality history.
  
  Skip-lot sampling reduces inspection costs by inspecting certain lots. This increases the quality risk, therefore a history of high quality is a key consideration. This type of sampling is used after the maturation of a process.
  

• variable sampling
  Variables sampling collects data on possible variable items. When the error rate exceeds a combined level for several of the variables, the lot is rejected. The sample is rated on a scale against such criteria as time, distance, weight, strength, or purity.
  
  Instead of being tested as "acceptable" or "unacceptable," the sample is compared against historic values to determine problems. Variable sampling is used when the quality characteristic is measurable or quantifiable.
  
  Variables sampling allows a quality control team to accomplish more in its inspection and analysis process. Causal links can be explored as well, helping to determine the root problem in a product, process, or sub-process.
  
  The advantages include more data to compare to quality conformance criteria. It also requires smaller sample sizes, reducing cost while ensuring high quality.
  
  The disadvantages are that the quality inspectors need more training and that more sophisticated analysis is required to determine quality conformance.
  
  Acceptance and attributes testing can be tested separately or together. An item can be tested for one or several attributes and whether it achieves the desired specifications. Variables sampling is a more complex process requiring considerable thought in not only what is measured, but how it will be analyzed.
  

Any of the above sampling techniques can use special attributes testing to reduce the time spent sampling. In practice, many companies use all four sampling techniques together to ensure the highest possible quality control.

No matter what kind of sampling plan you choose, all require a sample of a particular size to ensure confidence in the results. The sample must be cost effective to conduct and accurate according to probability and acceptance theory. Sample sizes can be determined from the operating characteristic curve. The curve represents the historic results for a particular process and operating conditions. The curves change shape depending on the size of the sample. Formulas can be used to represent the diagram.

A major tire manufacturing company installed a new tire molding machine. A trial production run tested if the tires made with the new machinery were as strong as the old ones. In a production run of 10,000 tires, only one failed in a sample installation test of 100 tires. To confirm the accuracy of the test, two more test lots were produced with the same results. Since the old process experienced 1.5 failures per 100, this machine represented an improvement and the sample size continued to be valid.

Sampling techniques help ensure quality while controlling inspection costs. It is key that the proper kind of sampling is carried out to obtain the desired results. This ensures the sample will be accurate and valid. The proper determination of the sample size is also important. Representative is the other key consideration. Proper sampling techniques ensure other analysis methods are reliable indications of reality.