Question

XYZ corporation uses statistical quality control to monitor the quality of their product. They have determined the process average, representing the population proportion defective, is 0.02, and size of the samples is 100 units. (3 pts each)

a). In constructing a p-chart using 3-sigma limits, what is the UCL?

b). In constructing a p-chart using 3-sigma limits, what is the LCL?

c). Discuss what would happen if one of the sample values is 0.085.

Answer 1

P charts are charts used in statistical quality control and to monitor the proportion of non confirming parts in a sample.

Population proportion defective is 0.02

Size of Sample units is 100

Part A

The Upper Control Limit for the p charts is given as

where

  is average proportion defective i.e. 0.02

n is the sample size

so the UCL is calculated as below

Part B

The Lower Control Limit for the p charts is given as

where

  is average proportion defective i.e. 0.02

n is the sample size

so the LCL is calculated as below

Part C

If one of sample values are 0.085 then it means the sample falls out side the Control limits (on the higher side)

Thus it means that the process is out of control in the case of this sample.