Problem 6S21 Suppose that you collect data for 14 samples of

Problem 6S-21 Suppose that you collect data for 14 samples of 55 units each, and find that on average, 4.0 percent of the products are defective. What are the UCL and LCL for this process? (Leave no cells blank-be certain to enter \"O\" wherever required. Do not round intermediate calculations. Round up negative LCL values to zero. Round your answers to 3 decimal places.) Answer is complete but not entirely correct. UCL LCL 0.066 0.000

Solution

We have following information

Total number of average defects from all samples = 4% or 0.04

Number of samples = 14

Sample size n = 55

The fraction defective, p-bar = Total number of defects from all samples/Number of samples * Sample size = percent of products that are defective

P-bar = 0.04

Standard deviation p = p-bar*(1-p-bar)/n

Where p-bar = 0.04 and n is the sample size =55

Therefore

p = 0.04*(1-0.04)/55 = 0.02642313

Now to calculate the upper control limit for a p chart, let’s assume that it has 3 limits therefore z=3

Upper control limit (UCL) = p + z * p

UCL = 0.04 +3 *0.02642313 = 0.119

Lower control limit (LCL) = p - z * p

LCL = 0.04 - 3 *0.02642313 = - 0.039 or 0 (if the value of LCL is negative then it is used as 0)