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Q. Make a control chart for the proportion of defective light bulbs coming off a certain production line.
Source: Technical Mathematics with Calculus, 3e. Calter & Calter.
Note that categorical variable charts, as opposed to continuous variable, are used in pass / fail scenarios.
Step 1: Choose a sample size n and the testing frequency.
Use the sample size of 1000 bulbs, checked daily for 21 days.
Step 2: Collect the data.
Count the number d of defectives in each sample of 1000.
Obtain: p (the porportion defective)=d∕n
Step 3: Start the control chart by plotting p versus time.
Step 4: Compute the average proportion defective, p ̅.
Step 5: Compute the standard error, SEp.
Standard error of a proportion: (SE_p=√(p(1−p)/n))
Step 6: Choose a confidence interval.
Step 7: Draw a horizontal at p, and upper and lower control limits at p±3SEp.
Relationship between the normal curve and the control chart. Note that the upper and lower limits are placed at three standard errors from the mean so that there is a 99.7% chance that a sample will fall between those limits.
Video “📚 How to make a process control chart (Question 1 – Categorical Variable)” Author: Study Force