Interactive Statlets - Sampling

Statgraphics has more than 30 special interactive procedures called Statlets. Statlets are displayed in a special window with a control bar across the top. Changes made to the controls are immediately reflected in the Statlet window. In the case of 3-dimensional displays, scrollbars are included that allow dynamic rotation of the output.

This page displays Statlets that may be used to help determine adequate sample sizes.

Statlet
Capability Control Chart Design
Probabilistic Fractal
Reliability Demonstration Test Plans
Sample Size Determination

Capability Control Chart Design

This Statlet assists analysts in determining how large samples should be when constructing capability control charts. Capability control charts monitor processes which have been shown to be stable and capable of producing results that yield small numbers of nonconformities.

Capability control charts may be constructed for::

  1. The short-term capability index Cp.

  2. The long-term capability index Pp.

  3. The short-term capability index Cpk.

  4. The long-term capability index Ppk.

  5. The proportion of nonconforming items.

  6. The rate of nonconformities.

Reliability Demonstration Test Plans

This procedure creates test plans to demonstrate that a failure time distribution satisfies stated conditions. For example, it may be desired to show with 95% confidence that the reliability of a product equals or exceeds 90% at the end of the warranty period. During the demonstration, n units will be tested for a duration equal to t. The demonstration will be considered successful if no more than f units fail during the test.

The user specifies either the number of units to be tested or the duration of the test. The procedure solves for the other quantity. 

Sample Size Determination

This Statlet determines the sample size needed to estimate or test values of various parameters. The size may be based on either the width of a confidence interval or the power of a hypothesis test.

Parameters for which sample sizes may be determined are:

  1. The mean m of a normal distribution.

  2. The standard deviation s of a normal distribution.

  3. The proportion of successes q in a binomial distribution.

  4. The rate of events l in a Poisson distribution.

  5. The difference between the means of 2 normal distributions.

  6. The ratio of the standard deviations of 2 normal distributions.

  7. The difference between the parameters of 2 binomial distributions.

  8. The difference between the parameters of 2 Poisson distributions.

  9. The maximum difference between the means of 3 or more normal distributions.

  10. The Pearson correlation coefficient.

  11. The capability index Cp.

  12. The capability index Cpk.

  13. The capability index Cpm.



Probabilistic Fractal

This Statlet is designed to illustrate the concepts of randomness and uncertainty. It is based on the famous Snowflake Fractal. To create the fractal, an equilateral triangle is first drawn. A number of iterations are then performed during which a new equilateral triangle is added to the exterior of each side of the current figure, with each side having one-third the length of the side on which it is placed. The Splits field varies the number of iterations from 0 to 5.

To make the fractal probabilistic, you may set a probability p that, when a new triangle is added to the figure, it is oriented inward rather than outward, thus removing part of the figure rather than adding to it. By pressing the Rerandomize button, the fractal may be redrawn using a new set of random numbers. It will be apparent that the amount of "chaos" in the figure is a function of p.