Its a Mintab Tutorial 5 for Control Chart and Variables of BITS Pilani

1. MINITAB Tutorial 5
Control Charts for Variables
Department of Mechanical Engineering
BITSPilani, Hyderabad

2. Introduction
• Quality Characteristic : Variable or attribute
• Variable: average length, average diameter, average tensile strength, average service time etc.,
• Attributes: Proportion of non- conforming items, no. of non- conformities in a unit, no. of demerits
per unit etc.,
• Causes of variation –
• Common causes (Improvement of the process)
• Special causes (control of the process)
• A process operating under a stable system of common causes – Statistical control.
Control charts are very simple graphical tools which show us if measurements/results are stable over time. They
look at the mean and variation of the data and check to see whether the observed data shows any patterns that
would not be expected to occur if the data was purely random. They monitor the activity of the ongoing process.

3. Typical control chart

4. Patterns to look for in a control chart
• Individual Outliers – special cause
• Increasing or decreasing trends – process may be drifting
• Jumps in the level around which the observations may vary – process mean might
have shifted
• “Hugging the control limits” – mixed data sets
• “Hugging the center line” – less variability; good process; desirable

5. Rules to identify an Out- of – control process
1. If a single point lies outside the control limits
2. If two out of three consecutive points fall outside 2σ warning limits on the same side of the
center line.
3. If 4 out of 5 consecutive points fall beyond the 1σ limit on the same side of the center line.
4. If 9 or more consecutive points fall to one side of the center line.
5. If there is a run of 6 or more consecutive points steadily increasing or decreasing.

6. Problem 1: Mean and Range Charts
Consider a process by which coils are manufactured.
Samples of size 5 are randomly selected from the
process, and the resistance values (in ohms) of the coils
are measured. The data values are given in the following
table.

7. Step1: Input the data in the worksheet

8. Step 2: Select the ത
𝑋-R chart from the STAT tab

9. Step 3: Select the column containing the data

10. Step 4: Output
Delete the data
points for sample
3,22,23 which are
outlier and plot the
revised control chart
Screenshot 1

11. Step 5: Revised Output Graph
Screenshot 2

13. Step 5: Interpret the result
• It can be observed that there are 3 outliers in the ത
𝑋-R charts.
• Sample 3 is an outlier in range charts and sample 22,23 are outliers in mean chart.
• Special causes identified – Quality of raw materials, high oven temperature, wrong die
used etc.,
• The revised control charts can be made by removing the observations of the outliers.
• Note that sample 15 falls slightly above the upper control limit on the X-chart.
• On further investigation, no special causes could be identified for this sample. So, the
revised limits will be used for future observations until a subsequent revision takes
place.

14. If standard data is given
• Refer to the coil resistance data in previous problem. Let's suppose that the target values for the
average resistance and standard deviation are 21.0 and 1.0 , respectively. The sample size is 5.

15. Problem 2: Individuals - Moving Range Chart
The table shows the Brinell hardness numbers of
20 individual steel fasteners and the moving ranges. The
testing process dents the parts so that they cannot be
used for their intended purpose. Construct the I-MR chart
based on two successive observations.
Sample Brinell Hardness
1 36.3
2 28.6
3 32.5
4 38.7
5 35.4
6 27.3
7 37.2
8 36.4
9 38.3
10 30.5
11 29.4
12 35.2
13 37.7
14 27.5
15 28.4
16 33.6
17 28.5
18 36.2
19 32.7

16. Step 1: Input the data in the worksheet

17. Step 2: Select the I-MR option from the STAT tab

18. Step 3: Assign the columns containing the data

19. Step 4: Output

20. Step 5: Interpret the result
• It can be observed there are no outliers in the individual and moving range chart.
• Thus the observed non-conformance rate is zero and the process is capable.

21. Problem 3: Z-MR Chart
Data on short production runs on the diameters of four parts (A,B,C and D) are given in the table below. It is
believed that the processes for manufacturing the four parts have different variabilities. Since parts are
manufactured on demand, they are not necessarily produced in the same run. Construct an appropriate control
chart and comment on the process.
𝑍 =
𝑖𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑒𝑎𝑛
𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

22. Input data
Run Part Number Quality
Characteristic
5 B 44
B 41
B 45
6 D 35
D 32
D 33
7 B 43
B 45
B 40
B 42
Run Part Number Quality
Characteristic
1 A 30
A 25
A 28
2 B 42
B 40
3 A 31
A 29
4 C 54
C 56
C 53

23. Step 1: Input the data in the worksheet

24. Step 2: Select the Z-MR chart option from the STAT tab

25. Step 3: Assign the column

26. Step 4: Output

27. Step 5: Interpret the result
• All of the points on Z-MR charts are within the control limits with no unusual patterns.
• Note that the upper and lower control limits on the Z-chart are at 3σ and —3 σ, respectively, with the
center line at 0.

28. Thank You!