statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, a variables sampling plan is an

acceptance sampling Acceptance sampling uses statistical sampling to determine whether to accept or reject a production lot of material. It has been a common quality control technique used in industry. It is usually done as products leave the factory, or in some ...

technique. Plans for

variables Variable may refer to: Computer science * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed Mathematics * Variable (mathematics), a symbol that represents a quantity in a mathemat ...

are intended for quality characteristics that are measured on a continuous scale. This plan requires the knowledge of the

statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model repre ...

(e.g.

normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...

). The historical

evolution Evolution is the change in the heritable Phenotypic trait, characteristics of biological populations over successive generations. It occurs when evolutionary processes such as natural selection and genetic drift act on genetic variation, re ...

of this technique dates back to the seminal work of W. Allen Wallis (1943). The purpose of a plan for variables is to assess whether the process is operating far enough from the specification limit. Plans for variables may produce a similar OC curve to attribute plans with significantly less sample size. The decision criterion of these plans are :

\bar+ k\sigma \leqslant USL

\bar- k\sigma \geqslant LSL

where

\bar

and

\sigma

are the

sample mean The sample mean (sample average) or empirical mean (empirical average), and the sample covariance or empirical covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or me ...

and the

standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...

respectively,

k

is the critical distance,

USL

and

LSL

are the upper and lower regulatory limits. When the above expression is satisfied the proportion nonconforming is lower than expected and therefore the lot is accepted. A variables sampling plan can be designed so that the OC curve passes through two points (AQL,

\alpha

) and (LQL,

\beta

). AQL and LQL are the Acceptable quality limit and the limiting quality level respectively.

\alpha

and

\beta

are the producer and consumer's risks. The required

sample size Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences abo ...

(

n

) and the critical distance (

k

) can be obtained as :

k = \frac

where

Z

is the

function. When the

dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns * Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variat ...

is known the required sample size (

n

) is obtained from :

n = \left ( \frac\right )^

while for unknown

\sigma

the sample size is approximately :

n = \left ( \frac\right )^\left ( 1+\frac \right )

The MIL-STD-414 provides tables to obtain the required sample size and the critical distance according to the type of inspection.

External links

OC curve

References

* *
Online MIL-STD-414 Calculator (SQC Online)

External links

See also

References

Further reading