Quantitative Analysis for Management, 13/e

Key Equations

(15-1)

$$\text{Upper control limit }\left(\text{UCL}\right)=\overline{\overline{x}}+z{\sigma }_{\overline{x}}$$

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

(15-2)

$$\text{Lower control limit }\left(\text{LCL}\right)=\overline{\overline{x}}-z{\sigma }_{\overline{x}}$$

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

(15-3)

$${\text{UCL}}_{\overline{x}}=\overline{\overline{x}}+A_2\overline{R}$$

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

(15-4)

$${\text{LCL}}_{\overline{x}}=\overline{\overline{x}}-A_2\overline{R}$$

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

(15-5)

$${\text{UCL}}_R=D_4\overline{R}$$

Upper control limit for a range chart.

(15-6)

$${\text{LCL}}_R=D_3\overline{R}$$

Lower control limit for a range chart.

(15-7)

$${\text{UCL}}_p=\overline{p}+z{\sigma }_p$$

Upper control limit for a p-chart.

(15-8)

$${\text{LCL}}_p=\overline{p}-z{\sigma }_p$$

Lower control limit for a p-chart.

(15-9)

$${\sigma }_p=\sqrt{\frac{\overline{p}\left(1-\overline{p}\right)}{n}}$$

Estimated standard deviation of a binomial distribution.

(15-10)

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

Upper and lower limits for a c-chart. ...