Sqc - X Bar & R Chart

8/25/2010

Statistical Quality Control (JQB 20503)

Chapter 3: Process Control Chart for Variables 5th July 2010 By Fairul Anwar Abu Bakar

Recap Past Lesson Sources of Variation: 1.Normal causes – within process control (to be expected) 2.Assignable causes – can control i.e. machine, man, material, method

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Ice-Breaking Exercise A worker makes 12 trips to load a truck. The time of each trip, in minutes is; 12.6 , 13.7 , 18.2 , 8.3 , 8.1 , 10.0 , 11.9 , 14.0 , 12.6 , 12.6 , 9.7 , 14.5. Calculate the mean and range of these data. Answer: Mean = 12.2 , Range = 10.1 (Any comment / observation?)

Process Control Chart • Variables – can be measured e.g. weight, height, temperature, volume etc. (x-bar & R chart) • Attributes – have discrete values e.g. yes @ no, good @ bad etc. (p & c chart)

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Today’s Learning Outcomes • Calculate on development of center line (CL), upper (UCL) and lower control limit (LCL) of xbar chart by using related formula. • Construct the x-bar process control chart with reflect to all solution provided.

Develop Mean (x-bar) Chart • • •

monitor central tendency of data monitor changes in the mean of a process Center line:

• •

Upper control limit (UCL): Lower control limit (UCL):

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Exercise - Mean (x-bar) Chart • A quality control inspector at the F&F soft drink company has taken twenty-five samples with four observations each of the volume of bottles filled. The data and the computed means are shown in the table. If the standard deviation of the bottling operation is 0.14 ounces, use this information to develop control limits of three standard deviations for the bottling operation.

Exercise - Mean (x-bar) Chart (cont’d)

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Exercise - Mean (x-bar) Chart (cont’d) Solution Given:• Z=3 • σ = 0.14 • n=4

Exercise - Mean (x-bar) Chart (cont’d)

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Exercise - Mean (x-bar) Chart (cont’d)

Group Exercise • A quality control inspector at the Crunchy Potato Chip Company has taken 10 samples with 4 observations each of the volume of bags filled. The data and the computed means are shown in the following table (next slide). • If the standard deviation of the bagging operation is 0.2 ounces, use the information in the table to develop control limits of 3 standard deviations for the bottling operation.

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Group Exercise

Solution

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Recap - Today’s Learning Outcomes • Calculate on development of center line (CL), upper (UCL) and lower control limit (LCL) of xbar chart by using related formula. • Construct the x-bar process control chart with reflect to all solution provided.

Next Class Review • Developing Range (R) chart • Expected to do more x-bar & R chart exercises in class. • Please bring along your graph paper!

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8/25/2010

Today’s Learning Outcomes • Calculate on development of center line (CL), upper (UCL) and lower control limit (LCL) of xbar chart by using related formula. • Construct the x-bar & R process control chart with reflect to all solution provided.

Another Formula for x-bar Chart

Notice that A2 is a factor that includes three standard deviations of ranges and is dependent on the sample size (n) being considered. Using sample range as an estimate of variability.

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Exercise (x-bar Chart) • Use last x-bar chart data to construct CL, UCL & LCL by using 2nd formula.

R Chart • Monitor the dispersion or variability of the process • The method for developing and using R-charts is the same as that for x-bar charts.

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R Chart Formula

Exercise (R Chart) • Use x-bar chart data exercise 1.

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Exercise (R Chart) - Solution

Next Class Review • Developing x-bar & Range (R) chart using computer software – Microsoft Office Excel • Please bring along your own laptop!

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