InfinityQS Real-time SPC Software: Where's My Target?

Where's My Target?

This quiz will test how much you remember from your college statistics 101 and SPC 202 classes. The questions are simple, but deriving the right answers will require reliance on several basic statistical principles.

Given
There is a certain bottle filling operation. The label's stated weight on the bottle is 750ml. The bottle can physically hold 760ml. Any fill less than 750ml is an under fill. Any fills over 760ml will run down the side of the bottle and make a sticky mess. The goal is to set the fill head so that the rate of under fill is 13 bottles per 10,000. Note: The fill head can be

reliably adjusted in increments of 0.1 mil.

The range chart (n=5) is always in-control with an R-bar = 3.9542ml. However, due to excessive operator tampering, predictive statistics from the X-bar chart are not reliable. The bottle can physically hold up to 760ml. Any fills over 760ml will not allow the top enough room to be properly installed.

Question 1: Where should the fill target be set to the level where no more than 13 bottles per 10,000 are under filled?

Question 2: With the fill target optimized, will you expect any of the bottles to be over filled beyond 760ml?

Question 3: If the answer to question 2 is yes, about how many bottles per 10,000 will be over filled?