You want to determine the lower control line for a p-chart for quality control purposes. You take several samples of a size of 50 items in your production process. From the samples, you determine the fraction defective is 0.006 and the standard deviation is 0.001. If the desired confidence level is 99.7 percent, which of the following is the resulting LCL value for the line?
A) 0.0
B) 0.002
C) 0.003
D) 0.004
E) None of these choices are correct.

Question

Quizplus · Accepted Answer

The formula to calculate the lower control limit (LCL) for a p-chart is:

LCL = p̂ - 3√((p̂(1-p̂))/n)

where p̂ is the proportion defective in the sample, n is the sample size, and 3 represents the number of standard deviations from the mean for a 99.7% confidence level (which corresponds to a z-score of 3).

Substituting the given values into the formula, we get:

LCL = 0.006 - 3√((0.006(1-0.006))/50)
LCL = 0.006 - 3(0.0356)
LCL = 0.006 - 0.107
LCL = 0.003

Therefore, the resulting LCL value for the line is 0.003, which is choice C.

You Want to Determine the Lower Control Line for a P-Chart