šŸ“š How to make a process control chart (Question 1 – Categorical Variable)

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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)=dāˆ•n

Step 3: Start the control chart by plotting p versus time.

Step 4: Compute the average proportion defective, pĀ Ģ….

Step 5: Compute the standard error, SEp.

Standard error of a proportion: (SE_p=āˆš(p(1āˆ’p)/n))

Step 6: Choose a confidence interval.

Step 7: Draw a horizontal at p, and upper and lower control limits at pĀ±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.

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