Key Equations

(15-1)

Upper control limit (UCL) = \bar{\bar{x}} + z σ_{\bar{x}}

$Upper control limit (UCL) = \bar{\bar{x}} + z σ_{\bar{x}}$

Upper limit for an $\bar{x}$ $\bar{x}$ -chart using standard deviations.

(15-2)

Lower control limit (LCL) = \bar{\bar{x}} - z σ_{\bar{x}}

$Lower control limit (LCL) = \bar{\bar{x}} - z σ_{\bar{x}}$

Lower control limit for an $\bar{x}$ $\bar{x}$ -chart using standard deviations.

(15-3)

{UCL}_{\bar{x}} = \bar{\bar{x}} + A_{2} \bar{R}

${UCL}_{\bar{x}} = \bar{\bar{x}} + A_{2} \bar{R}$

Upper control limit for an $\bar{x}$ $\bar{x}$ -chart using tabled values and ranges.

(15-4)

{LCL}_{\bar{x}} = \bar{\bar{x}} - A_{2} \bar{R}

${LCL}_{\bar{x}} = \bar{\bar{x}} - A_{2} \bar{R}$

Lower control limit for an $\bar{x}$ $\bar{x}$ -chart using tabled values and ranges.

(15-5)

{UCL}_{R} = D_{4} \bar{R}

${UCL}_{R} = D_{4} \bar{R}$

Upper control limit for a range chart.

(15-6)

{LCL}_{R} = D_{3} \bar{R}

${LCL}_{R} = D_{3} \bar{R}$

Lower control limit for a range chart.

(15-7)

{UCL}_{p} = \bar{p} + z σ_{p}

${UCL}_{p} = \bar{p} + z σ_{p}$

Upper control limit for a p-chart.

(15-8)

{LCL}_{p} = \bar{p} - z σ_{p}

${LCL}_{p} = \bar{p} - z σ_{p}$

Lower control limit for a p-chart.

(15-9)

σ_{p} = \sqrt{\frac{\bar{p} (1 - \bar{p})}{n}}

$σ_{p} = \sqrt{\frac{\bar{p} (1 - \bar{p})}{n}}$

Estimated standard deviation of a binomial distribution.

(15-10)

\bar{c} \pm 3 \sqrt{\bar{c}}

$\bar{c} \pm 3 \sqrt{\bar{c}}$

Upper and lower limits for a c-chart.

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Table of Contents for Key Equations