Determining the process for acquiring data is an important part of any measurement process. Whether it’s selecting the number of customers to survey or the process of taking samples from a moving conveyor, the sampling process will depend on the purpose, desired statistical conﬁdence, and economics.
Whether or not sampling is needed is an important determination. Some of the reasons for not using sampling include:
- • The customer’s requirement is for 100 percent inspection of entire shipment.
- • The number of items or services is small enough to inspect the entire quantity produced/delivered.
- • The cost of sampling is too high relative to the advantages gained from sampling.
- • Self-inspection by trained operators is sufficient for the nature of the product produced.
- • The inspection method is built in, or the process is mistake-proofed so that no defectives can be shipped.
- • Product is low cost and/or noncritical (wide or no speciﬁcation range) to customer so that the producer can risk not sampling. (For example, delivering the ﬁll to bring a building lot up to grade level to meet town height requirements.)
Acceptance Sampling MethodsAssuming sampling is needed, the intended purpose helps in deciding whether the sample should be randomly selected or stratiﬁed. Random sample selection is similar to pulling a number out of a hat (although a random sample number generator or table of random numbers is more likely used) and helps ensure that data will not be biased toward one particular portion of the population. It is expected that the sample will truly represent the range and relative distribution of characteristics of the population. In some cases, however, it may be desired that only a particular portion of the population be evaluated, which means that a stratified sample will be set up to create the desired distribution within the sample.
Sample size is dependent on the desired level of statistical conﬁdence and the amount of difference between samples that one is trying to detect. For a given difference (for example, between means of two groups of data), testing at a statistical probability of .01 (a one percent chance the result will be labeled as signiﬁcant when it is not), a larger sample size will be needed than if a probability of .05 is acceptable. The cost of selecting the samples and collecting the information also enters into this decision.
An additional sampling issue, rational subgrouping, must be considered for control charts. A chart meant to detect a shift in the mean will be more sensitive if variability within subgroups is minimized. This means that all samples within a subgroup should consist of parts taken within a relatively short time as compared to the time between subgroups. In addition, a subgroup should consist of a single process stream rather than mixing products from different streams (for example, two cavities in the same mold).
Systematic sampling is where every nth item is selected, for example, every tenth item. Cluster sampling is where a random sample is taken from within a selected subgroup. Best judgment sampling is when an expert’s opinion is used to determine the best location and characteristics of the sample group.
Acceptance sampling is the process of sampling a batch of material to evaluate the level of nonconformance relative to a speciﬁed quality level. It is most frequently applied to decide whether to move material from one process to another or to accept material received from a supplier. Many sampling processes are based on the work of Dodge and Romig and standards such as ANSI/ASQ Z1.4 and ANSI/ASQ Z1.9.
Sampling assumes that nonconformances randomly occur throughout a lot and that a random sample can determine whether a given level of nonconformance is exceeded. Whether sampling is the best technique for assessing a product depends on the lot size, frequency of production/receipt, typical level of nonconformance, and acceptable level of risk. For example, pencils received from an office supply house are normally not sampled because the risk associated with defective pencils is minimal. In contrast, medical devices might be subjected to extensive sampling or even 100 percent inspection because of the consequences of failure.
When properly applied over time, sampling can keep nonconformances below a predetermined level called the average outgoing quality limit (AOQL). Compared with 100 percent inspection, sampling is more economical, requires less handling of the product, and is often more accurate since there is less fatigue. Sampling plans do have drawbacks: they may be used to avoid adequate process control, they are less economical than process control, and they yield less information on the true state of nonconformance than do 100 percent inspection or statistical analysis. No sampling plan yields 100 percent detection of nonconformances. Because of this and possible legal or political issues, some industries do not use sampling. For example, a U.S. population census conducted by sampling might be believed to result in misleading allocation of tax funds.
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