Question

A p-chart has been prepared. Computations show that the average proportion of defective is 0.032, while the standard deviation is 0.0176. From this data, what are the 3-sigma control limits for this chart?
1. LCL =.032 UCL =.085
2. LCL =.053 UCL =.032
3. LCL = 0 UCL =.085
4. not enough information to determine the control limits:

Answer 1

Correct Answer - Option 4 : not enough information to determine the control limits:

Concept:

\(̅ P = \frac{{Total\;number\;of\;defective}}{{Total\;number\;of\;observation}}\)

\({\rm{UCL}} = ̅ P + {\rm{z}} \times \sqrt {\frac{{̅ P\left( {1 - ̅ P} \right)}}{n}}\)

\({\rm{LCL}} = ̅ P -{\rm{z}} \times \sqrt {\frac{{̅ P\left( {1 - ̅ P} \right)}}{n}}\)

where P̅ = average proportion of defective, z = standard deviation, n = sample size

Calculation:

Given:

P̅ = 0.032, z = 0.0176

As sample size is not given in the Qs, therefore the data is not enough to compute limits