Please help me to get these answers. I still don’t understand on interpreting s and x bar control chart. I only know that standard deviation is used to know the variation within a sample and mean to know the variation sample to sample. Please help me. I am still new to SPC.

24.14 Dyeing yarn. The unique colors of the cashmere sweaters your firm makes result from heating undyed yarn in a kettle with a dye liquor. The pH(acidity) of the liquor is critical for regulating dye uptake and hence the final color. There are 5 kettles, all of which receive dye liquor from a common source. Twice each day, the pH of the liquor in each kettle is measured, giving samples of size 5. the process has been operating in control with mean=4.22 and std deviation=0.127

The process described in exercise 24.14 goes out of control. Investigation finds that a new type of yarn was recently introduced. The pH in the kettles is influenced by both the dye liquor and the yarn. Moreover, on a few occasions a faulty valve on one of the kettles had allowed water to enter that kettle, as a result, the yarn in that kettle had to be discarded.

Which of these special causes appears on the s chart and which on the x bar chart? Explain your answer.

Please help me to get these answers. I still don’t understand on interpreting s and x bar control chart. The process described in exercise 24.14 goes out of control. Investigation finds that a new type of yarn was recently introduced. The pH in the kettles is influenced by both the dye liquor and the yarn. Moreover, on a few occasions a faulty valve on one of the kettles had allowed water to enter that kettle, as a result, the yarn in that kettle had to be discarded.Which of these special causes appears on the s chart and which on the x bar chart? Explain your answer.

I would expect the yard would probably show up on the X-bar chart and the valve to show up on the s chart.

However, it's unclear to me that the sample of 5 is a rational subgroup. Subgroups are typically time-oriented, rather than mixing data from multiple streams.

If you add the new type of yarn to ALL the kettles then this will shift the average value of the pH up or down but not affect the std dev.
If one of the kettles has a faulty valve then this will have minimal affect on the mean but most likely increase the std dev.

Just for my own curiosity, is this an assignment or test you are looking for answers for?

that was my first reaction as well.

Yep, looks like a homework problem.

If we do accept the setup of the five kettles, and treating each of the kettles as an item into a subgroup of 5, then the reasons "why" for the answers are:

The stuck valve only affected one kettle. The other four are going to keep going as they were. The four inputs averaged in with the fifth input likely won't change the xbar much, so it will not be detected or less readily so (as compared to the s chart).

The s chart is looking for the variation between the 5 kettles. The standard deviation (s) will increase very quickly as the one kettle diverges from the other four. Remember, s is based upon the squared difference of the reading and the average, so the s will increase rapidly.

The change in the yarn affects all 5 kettles simultaneously. We'd expect the variation between the kettles to remain about the same, so the s chart likely won't show an effect. But, the average of the 5 kettles will shift as the yarn shifts the ph in all 5 kettles, and we should detect the signal on the xbar chart.

Not a bad little problem, and glad to see the use of the s chart. Even if it not a "rational subgrouping", with 2 charts I can monitor for shifts in 5 different components.