## Statistical Process Control | Chart for Means (x-bar chart)

Welcome to this statistical process control

tutorial on Control chart for x-bar. We will be constructing an x-bar chart from

process data, and then determine if the process is in statistical control. If you’ve seen the first video in this series

on R-chart, you know that a control chart comprises of a centerline, a lower control

limit, and an upper control limit. Well, the centerline of the x-bar chart is

x-double bar. That is, the mean of the sample means. Now if standard deviation of the process is

known, this formula is used to calculate the control limits.

However, we will be using the range in this video. In our case, the upper control limit, UCL,

is x-double bar plus A2 R-bar. And the lower control limit, LCL, is x-double

bar minus A2 R-bar. R-bar is the average of the sample ranges,

and A2 is found on the control chart factors table. We will be using this process data, consisting

of samples of size 5, collected every day for 10 days. Our objective is to determine if the process

mean is in statistical control. As required in the control limit formulas,

we will first obtain the sample ranges and means. The range is largest minus smallest, so for

the first day or first sample, the range is 509 minus 496 which gives 13.

We do the same for the rest of the samples. The mean for the first sample can also be

obtained by adding up the values and dividing by 5. And that gives 502.

We do the same for the rest of the samples. Next we calculate R-bar and x double bar.

The sum of these ranges is 231. So R-bar, is 231/10 which gives 23.1.

The sample means add up to 4,978 so their mean, x-double bar, is 497.8 Looking again at the formulas for the control

limit here, we have everything but A2. To find A2, we simply go to the control limit

factors table and check under sample size 5. The corresponding A2 value is 0.577. Now we have A2, x-double bar, and R bar. So UCL equals 497.8 + 0.577(23.1) which gives

511.1. And for LCL, we have 497.8 – 0.577(23.1) which

gives 484.5. For the chart let’s first draw the sample

points for the data. And then draw the control limits. And finally, draw out the run chart. The x-bar-chart is now complete.

We can see that the sample mean for day 5 is clearly below the lower control limit. Therefore, the process mean is not in statistical

control, or is out of control. As a result we could recommend that the activities

of day 5 be investigated to determine the special cause of variation and to take necessary

corrective actions. And that’s x-bar chart. Thanks for watching.

Thank you so much, you're awesome

Thank you for this brief and clear video

nice and crisp video sir

thank you so much!!

awesome explanation.

best video on X-bar chart

the best. saved my life

Brilliant! Thank you!

Great job!!!

2 days of searching and watching long videos that did not clear anything up. and here are your videos, 4 minutes long with everything you need to know. great job, thank you very much.

Hands down the easiest to follow video I have seen. THANK YOU!

make it simple reduce the numbers 😣

ok but what if I don't have that A2 table?

thanks…

One of the best explanation videos I've come across. Thank you so much for your clear and easy to follow video!

You are a genius

why did we took the value under 5 for A2?

one of the best video i found on you tube……………thanks for your effort

Thank you for being so clear.

X BAR AND R VALUES FOR THE 10 SAMPLES OF TEA CONTAINING 30 PACKETS

X Bar 320 310 330 360 290 280 340 320 360 300

R 12 16 14 18 22 23 10 13 27 25

Jhilimil Tea company has a packaging machine which pack tea in plastic packets, to ensure consistent quantity in each packet a sample of 30 packets were taken per hour in a day and its mean and range is recorded. Around 10 such sample were taken per day. from the following data answer the following questions.

Answer Section

Q.No 1: omment on the type of data being collected, which control chart is appropriate for the data and why.

File Name :

Q.No 2: what are the values for Central Line, Upper control limit and lower control limit, also show the entire calculations for the response

Can you plz provide the solution of this problem….and x bar r chart to be used or x bar s chart to be used and observations is 30 i guess.

Best vid, thanks!

if the points you plotted were the same in the video, but the one out of control we within the UCL and LCL, would that mean it is in or out of control even if the majority of points is skewed upwards

Solid explanation

Excellent video!

Thank you very much 😊😊 this saved my life👍👍

thanks it help me a lot 🙂

Lovely explanation.

very helpful. thanks

If I am taking the daily 5 samples reading means, my LSL and USL will fluctuate. Then how to plot the values in daily basis(if am plotting daily avg values manually)

Thankyou So muchh 😀

Thank you ,easy simple explained

Thank you!!!

Brilliant video joshua. You explained this very clearly and concisely 🙂

same data,range chart says process statistical in control, but mean chart says not..i am not clear…please explain sir

Awwwwwwwwwwwwwwesssssssssssssome man

Clear story. Thanks!

But how to maintain its on shopfoor. How to operator filled this limit

Thank you so much sir…

Very Helpful video, Thankssss

Super bro

and when is A3 used?

Thank you – clear and easy to follow!

Thnkyuuuu soo mucchhh sirr

Can we either choose to solve the UCL and LCL by using the mean or range or should go hand in hand because it may display different results in term variability, right ? Meaning variations that can be seen using the range cannot be seen using the mean

The best video I've seen on this topic to date.

Wow so simple and clear. Thanks very much 💕👌🏽🙏🏽👏

thank you so much, really save my life!