Question

Consider the p chart below. Note that LCL 0, CLp0.01667, and UCL 0.04802 Does the process appear to be in a state of statistical control? a. P Chartof Nonconforming Units 0.05 UaL-0.04802 b. What sample size is needed in order to have a positive lower 0.04 control limit? E 0.03 0.02 ?-0.0 1667 0.01 0.00 1 3 5 79111315 17 19

Answer 1

a.

As, all data points in the p-chart lies between LCL and UCL, the process appear to be in a state of statistical control.

b.

LCL =

a. As, all data points in the p-chart lies between LCL and UCL, the process appear to be in a state of statistical control. b. LCL = p^- - m squareroot p^- (1 - p^-)/n where m is a multiplier (usually set to 3) For a positive control limit, LCL = p^- - m squareroot p^- (1 - p^-)/n > 0 Rightarrow p > m squareroot p^- (1 - p^-)/n Rightarrow p^-^2 > m^2 p^- (1 - p^-)/n n > m^2 (1 - p^-)/p^- Rightarrow n > 3^2 (1 - 0.01667)/0.01667 Rightarrow n > 530.892 The sample size needed for a positive control limit is 531.

where m is a multiplier (usually set to 3)

For a positive control limit,

LCL = > 0

a. As, all data points in the p-chart lies between LCL and UCL, the process appear to be in a state of statistical control. b. LCL = p^- - m squareroot p^- (1 - p^-)/n where m is a multiplier (usually set to 3) For a positive control limit, LCL = p^- - m squareroot p^- (1 - p^-)/n > 0 Rightarrow p > m squareroot p^- (1 - p^-)/n Rightarrow p^-^2 > m^2 p^- (1 - p^-)/n n > m^2 (1 - p^-)/p^- Rightarrow n > 3^2 (1 - 0.01667)/0.01667 Rightarrow n > 530.892 The sample size needed for a positive control limit is 531.

$\Rightarrow \bar{p}^2 > m^2 \bar{p}(1-\bar{p})/n$

The sample size needed for a positive control limit is 531.