Six Sigma and Beyond: Statistical Process Control, Volume IV

This appendix provides some typical formulas used in the control charting process. The list by no means is an exhaustive one; however, it provides the quality professional with some basic approaches to statistical understanding for the everyday application of some common charts. Specifically, the reader will find some explanation of the "average" calculation, the sequence of calculating control limits of selected variable and attribute charts , hints about using a typical calculator, and a list of the most common formulas used in pursuit of SPC.

 
Control Chart Construction Guide ”Variable Data

Testing for Normality and Exponentiality

Condition

Test for Normality

Test for Exponentiality

Remarks

n ‰ 8 and n ‰ 25

  1. Probability plot/histogram and

  2. Anderson-Darling ( A 2 *) test

    or

  3. Moment tests

  1. Probability plot/histogram and

  2. Shapiro-Wilk W(E)

    or

  3. Anderson-Darling ( B 2 *) test

  1. Anderson-Darling A 2 *

    1. Distance test

    2. A 2 * = A 2 (1 + .75/ n + 2*25/ n 2 )

    3. Useful for very small sample sizes

  2. Moment tests

    1. Based on 3rd + 4th Standardized moments

    2. Become more useful as n increases beyond 15 “20

    3. 3rd moment: Index of skewness

      ³ 1 = ¼ 3 /

    4. 4th moment: Index of kurtosis

      ³ 2 = ¼ 4 / ¼ 2 2 - 3

  3. Shapiro-Wilk W(E)

    1. Useful up to sample sizes of 90 “110

    2. Not desirable as B 2 * for very small samples

    3. W(E) = b 2 /s 2

  4. Anderson-Darling B 2*

    1. Distance test

    2. Requires that origin parameter is known

n > 25 and n < 125

  1. Probability plot/histogram and

  2. Moment tests

  1. Probability plot/histogram and

  2. Shapiro-Wilk W(E)

Chi-Square goodness-of-fit test

  1. Optimum interval/ cell ( k ) count:

    K = 4[0.75( n -1) 2 ] 1/5

  2. Use Cochran's procedure where:

    UCL = ¼ +

    (test of normality)

    or

    and

n ‰ 125

  1. Probability plot/histogram and

  2. Moment tests

  3. Chi-square goodness-of-fit test (Cochran's procedure)

  1. Probability plot/histogram and

  2. Chi-square goodness-of-fit test (Cochran's procedure)

 

Note: Not recommended: (1) Kolmogorow-Smirnov; (2) standard chi-square goodness-of-fit test over pretabulated data.

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