Cheat Sheet Module 3

Cheat Sheet Module 3#

*** - denotes IMPORTANT

  • Control Limit \(L\)-sigma

    • Simply \(z_{\alpha/2}\) for a two-sided control on a normal statistic (CTQ can be any distribution)

  • Type-I error rate \(\alpha\) is the probability of false alarm in a control chart

  • Samples from the same population are also known as sub-groups

Normal CTQ#

Given \(\mu_0\) and \(\sigma_0\) (or similarly estimated \(\hat{\mu}_0 = \bar{\bar{x}} \) and \(\hat{\sigma}_0 = \frac{\bar{R}}{d_2}\) (R-Chart) or \(\hat{\sigma_0} = \frac{\bar{s}}{c_4}\) (s-chart) )#

  • X-bar Chart

    • Upper Control Limits (UCL) = \(\mu_0 + L\frac{\sigma_0}{\sqrt{n}}\) or \(\hat{\mu}_0 + L\frac{\hat{\sigma}_0}{\sqrt{n}}\)

    • Center Line (CL) = \(\mu_0\) or \(\hat{\mu}_0\)

    • Lower Control Limit (UCL) = \(\mu_0 - L\frac{\sigma_0}{\sqrt{n}}\) or \(\hat{\mu}_0 - L\frac{\hat{\sigma}_0}{\sqrt{n}}\)

  • R-Chart (Subgroup size \(\leq 8\)) (LCL must be zero or positive)

    • Upper Control Limit (UCL) = \(d_2\sigma_0 + Ld_3\sigma_0\) or \(d_2\hat{\sigma_0} + Ld_3\hat{\sigma_0}\)

    • Center Line (CL) = \(d_2\sigma_0\) or \(d_2\hat{\sigma_0}\)

    • Lower Control Limit (UCL) = \(d_2\sigma_0 + Ld_3\sigma_0\) or \(d_2\hat{\sigma_0} - Ld_3\hat{\sigma_0}\)

  • s-Chart (Subgroup size \( > 8\)) (LCL must be zero or positive)

    • Upper Control Limit (UCL) = \(c_4\sigma_0+ L\sqrt{1-c_4^2}\sigma_0\) or \(c_4\hat{\sigma_0}+ L\sqrt{1-c_4^2}\hat{\sigma_0}\)

    • Center Line (CL) = \(c_4\sigma_0\) or \(c_4\hat{\sigma_0}+ L\sqrt{1-c_4^2}\hat{\sigma_0}\)

    • Lower Control Limit (UCL) = \(c_4\sigma_0 - L\sqrt{1-c_4^2}\sigma_0\) or \(c_4\hat{\sigma_0} - L\sqrt{1-c_4^2}\hat{\sigma_0}\)

Bernoulli CTQ - (Yes or No, Defective or Not, Conforms or Not)#

Given \(p_0\) or \(\hat{p_0} = \bar{\bar{x}}\)#

(Typically \(1\) will the defectives and \(0\) will be non-defective)

  • p-Chart (LCL must be zero or positive)

    • Upper Control Limit (UCL) = \(p_0 + L\sqrt{\frac{p_0(1-p_0)}{n}}\) or \(\hat{p}_0 + L\sqrt{\frac{\hat{p}_0(1-\hat{p}_0)}{n}}\)

    • Center Line (CL) = \(p_0\) or \(\hat{p}_0\)

    • Lower Control Limit (UCL) = \(p_0 - L\sqrt{\frac{p_0(1-p_0)}{n}}\) or \(\hat{p}_0 - L\sqrt{\frac{\hat{p}_0(1-\hat{p}_0)}{n}}\)

Poisson CTQ (Defect Rate)#

Given \(\lambda_0\) or \(\hat{\lambda}_0 = \bar{\bar{x}}\)#

  • u-Chart (LCL must be zero or positive)

    • Upper Control Limit (UCL) = \(\lambda_0 + L\sqrt{\frac{\lambda_0}{n}}\) or \(\hat{\lambda}_0 + L\sqrt{\frac{\hat{\lambda}_0}{n}}\)

    • Center Line (CL) = \(\lambda_0\) or \(\hat{\lambda}_0\)

    • Lower Control Limit (UCL) = \(\lambda_0 - L\sqrt{\frac{\lambda_0}{n}}\) or \(\hat{\lambda}_0 - L\sqrt{\frac{\hat{\lambda}_0}{n}}\)

Excel Commands#

  • AVERAGE

  • VARIANCE.S

  • MAX, MIN

  • STDEV.S

  • COUNT

  • SQRT

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