Hypothesis testing for the Cp and Cpk index sampled from a Normal distribution

The BIS.Net Team BIS.Net Team

One option is to calculate a confidence interval using sample information. If the confidence interval covers the reference value, then the null hypothesis is accepted. If it does not include the reference value, the null hypothesis is rejected.

Alternatively, randomly sample n1 items from population and:

  • Calculate the average and standard deviation
  • Specify a level of significance
  • Specify an equality (<. > or <>)
  • Specify a reference value for the difference in the two proportions to test against.
  • Determine the test statistic with the following expression
    • Cp: ((N - 1) * (Reference Value / Cp) ^ 2, N - 1)
    • Cpk: (1 – Reference Value / Cpk) / Sqrt(1 / (9 * N * Cpk ^ 2) + 1 / (2 * (N - 1))))
  • Determine the critical region for the test tatistic. The critical region depends on the equality i.e. < or > or <>.
  • Compare the test statistic with the Critical region and conclude significance if the test statistic falls outside the critical region.

Alternatively, a p-value can be calculated and if the p-value falls below the specified level of significance the Null Hypothesis is rejected, and the Alternative Hypothesis is accepted

The BIS.Net Inferences APP use p-values for hypothesis testing, as these are more flexible than imposing a predefined level of significance on users. To place perspective on the p value a P Curve is provided for the analyst.

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