This document presents a case study analyzing control charts for a CNC manufacturing process. Control charts were created for the weight of shaft tubes being produced, including an X-bar chart to monitor average weight over time and an R chart to monitor the range of weights. Analysis of the control charts found the process to be in statistical control with no special causes of variation. Capability analysis determined the process Cpk value of 1.77 indicates an acceptable level of process capability based on industry standards. In conclusion, the control charts confirmed the process is capable of producing shaft tubes within specifications.

1. TQM ASSIGNMENT 3–CONTROLCHART CASESTUDYREPORT
BIRLAINSTITUTE OF TECHNOLOGYAND SCIENCE, PILANI
I Semester 2023
Date: 10.11.2023
Students Details :
1. Name & ID No.- VigneshwaranV & 2023HT79026

2. Control chart was introduced by Dr. Walter A. Shewhart to control and monitor the
process variation. This chart is also known as the Shewhart chart.
A continuous cnc manufacturing process we want to know whether the process is in
control or not and to know if there is any presence of variation. Variation may be due to
chance or assignable causes.
Control charts help to detect the causes during a process. It prevents us from
manufacturing defective product and further.
Control chart: A control chart is a graph which displays all the process data in order
sequence. It consists of a centre line, the upper limit and lower limit. Centre line of a chart
represents the process average. Control limits (upper & lower) which are in a horizontal
line below and above the centre line depicts whether the process is in control or out of
control. Control limits are based on process variation
INTRODUCTION TO CONTROL CHART

3. TYPES OF CONTROL CHART
Attribute data :When your data is in the form of an attribute or count form of data we
will use control charts like
P chart ,U chart ,C chart
Attribute data are the number of defects, defective units, etc.
Numerical data : When your data is in the form of a continuous type of data we will
use control charts like
X bar chart
R bar chart
S bar chart
Examples like measurement of length, weight, temperature, etc.

4. CONTROL CHART
Use control charts:
• To examine whether the process is stable or not.
• To understand the process variation over time.
• When you need to find out any variation occurs and fixed it instantaneously.
• To find out whether the process is within the statistical control or not (Due to chance or
assignable causes).
• Gives the visual representation of the ongoing in a process.
• Easy to understand and to interpret.
• Helps in decision making for process improvement goals.
• Identification of cause’s type of variation in a process.

5. CONTROL CHART

6. CONTROL CHART
X Bar R Control Chart Definitions
X bar chart: The mean or average change in a process over time from
subgroup values. The control limits on the X bar consider the sample’s mean
and center.
R chart: The range of the process over time from subgroup values. This
monitors the spread of the process over time.

7. CONTROL CHART
Name: V.Vigneshwaran 2023HT79026
Designation: Senior engineer
Department: Machine shop-Manufacturing
Industry: Lakshmi Machine Works Ltd coimbatore
Case study:
Component /part name : Shaft Tube
Size: Weight 500 ± 25 gram
Specification: 525 to 475 gm

8. Case study -CONTROL CHART X and R Calculation
X-Bar R-Chart | Control Chart
PARAM
ETER :
Weight
PART
NAME
Shaft tube
MACHIN
E NO
CNC-01 DATE NOV-02-2023
SIZE
500 ± 25 gram
SPECIFI
CATION
475
TO
525
CHECKE
D BY
VIGNESHWARAN SG = Sub Group
Sam
ple
SG
01
SG
02
SG
03
SG
04
SG
05
SG
06
SG
07
SG
08
SG
09
SG
10
SG
11
SG
12
SG
13
SG
14
SG
15
SG
16
SG
17
SG
18
SG
19
SG
20
n d2 A2 D4
1 504 508 497 504 496 493 494 494 507 499 500 496 494 505 499 498 508 495 493 495 1.00 1.12 2.66 3.27
2 497 505 508 497 498 507 498 502 501 507 504 505 494 495 495 498 506 497 499 497 2.00 1.13 1.88 3.27
3 497 492 496 494 502 496 498 502 497 498 496 493 502 496 496 499 506 492 506 500 3.00 1.69 1.02 2.57
4 497 494 501 498 493 504 506 498 494 498 494 500 503 502 498 507 493 500 504 497 4.00 2.06 0.73 2.29
5 498 492 496 500 494 507 497 502 500 499 500 499 494 502 500 500 503 502 498 492 5.00 2.33 0.58 2.11
SUM
X 9980.60
498
.6
498.
2
499.
6
498.
6
496.
6
501.
4
498.
6
499.
6
499.
8
500.
2
498.
8
498.
6
497.
4
500.
0
497.
6
500.
4
503.
2
497.
2
500.
0
496.
2 X̿
SUM 1+..+
n/n 499.030
R 7.0 16.0 12.0 10.0 9.0 14.0 12.0 8.0 13.0 9.0 10.0 12.0 9.0 10.0 5.0 9.0 15.0 10.0 13.0 8.0
SUM
R1+..+Rn/n 10.550

9. X-Bar-CONTROL CHART (output for ShaftTube)
498.6
498.2
499.6
498.6
496.6
501.4
498.6
499.6 499.8
500.2
498.8 498.6
497.4
500.0
497.6
500.4
503.2
497.2
500.0
496.2
486
488
490
492
494
496
498
500
502
504
506
508
SG 01 SG 02 SG 03 SG 04 SG 05 SG 06 SG 07 SG 08 SG 09 SG 10 SG 11 SG 12 SG 13 SG 14 SG 15 SG 16 SG 17 SG 18 SG 19 SG 20
X - CHART
AVG.
UCL
LCL
X-
DBA
R
SG=SUBGROUP NUMBER

10. R -CHART-CONTROL CHART output for shaft tube
7.0
16.0
12.0
10.0
9.0
14.0
12.0
8.0
13.0
9.0
10.0
12.0
9.0
10.0
5.0
9.0
15.0
10.0
13.0
8.0
0
5
10
15
20
25
SG 01 SG 02 SG 03 SG 04 SG 05 SG 06 SG 07 SG 08 SG 09 SG 10 SG 11 SG 12 SG 13 SG 14 SG 15 SG 16 SG 17 SG 18 SG 19 SG 20
R-CHART
RAN
GE
UCL
LCL
R-
BAR
SG=SUBGROUP NUMBER

11. CONTROL CHART for SHAFT TUBE Result
ANALYSIS OF CONTROL CHART:
X Bar chart:
This is control too since there are neither any points out of control limits,nor eighteen
consecutive points above or below the centre line decreasing or increasing .Based on the
X-bar chart process is in control.
R CHART:
This is control too since there are neither any points out of control limits, nor nineteen
consecutive points above or below the centre line decreasing or increasing .Based on the
R-chart process is in control.

12. Capability Calculations:CONTROL CHART
SIGMA /d2 4.5279
3 SIGMA 3 * /d2 13.5837
6 SIGMA 6 * /d2 27.1674
Cp = USL-LSL/6 SIGMA 1.84
CPU = USL - X̿/ 3 SIGMA 1.91
CPL = X̿- LSL / 3 SIGMA 1.77
Cpk MIN CPU or CPL 1.77
USL 525.000
LSL 475.000

13. CONTROL CHART for SHAFT TUBE Result
Capability analysis Cp:
The capability of this process for Shaft tube will be 1.84
Cpk =1. 77>1.33 which is the acceptable value in our lmw industries, so the
process capability is acceptable

14. CONCLUSIONS
Conclusions:
The target of this assignment is to construct a control chart for a critical dimension in CNC process, and with
the result from this project, we can start to implement control chart at the shop floor. It is confirmed that the
process is still capable and suitable for production.The study here can be expanded for other processes.
Recommendations:
Because of the time study is limited, this only constructs the control chart for one of critical dimension. For
future, we need to develop the control charts for all critical dimensions.
Contribution:
In this assignment also develop an excel template with formulas so that in future use only need to key-in data
to construct x, R− control chart for other critical processes.

15. THANK YOU
Assignment submitted by
v.vigneshwaran
2023HT79026