statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, 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 c ...

technique. Plans for variables 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 repres ...

(e.g.

normal distribution In 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 e^ The parameter \mu ...

). The historical

evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...

of this technique dates back to the seminal work of

W. Allen Wallis Wilson Allen Wallis (November 5, 1912 – October 12, 1998) was an American economist and statistician who served as president of the University of Rochester. He is best known for the Kruskal–Wallis one-way analysis of variance, which is named ...

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

and the

standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...

respectively,

k

is the

critical distance Critical distance is, in acoustics, the distance at which the sound pressure level of the direct sound D and the reverberant sound R are equal when dealing with a directional source. As the source is directional, the sound pressure as a function of ...

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 The acceptable quality limit (AQL) is the worst tolerable process ''average'' (''mean'') in percentage or ratio that is still considered acceptable; that is, it is at an acceptable quality level.Dodge, Y. (2003) ''The Oxford Dictionary of Statisti ...

and the limiting quality level respectively.

\alpha

and

\beta

are the producer and consumer's risks. The required

sample size Sample size determination is the act of choosing the number of observations or Replication (statistics), 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 stat ...

(

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 variatio ...

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