Objective: To monitor the variation in the bolt weight for consistent quality with the help of SPC, control charts

1. The Bolt Project
(TEAM - METS)
MAMATA SANAGOWDAR
EKTA VASANT
TERESA DOONG
SUNITHA NARENDRA BABU

2. DEFINE
 Objective:
 To monitor the variation in the bolt weight for consistent quality
with the help of control charts.
 Process:
 A special weighing scale is used to measure the weight of the bolt
in milligrams.
 Product
 Flange bolt.

3. • Two inspectors measure the
weight of the bolt by placing it
on the weighing scale.
• The experiment is carried out in
a clean and dry environment.
• The scale is reset every time
before use.
Operating Conditions

4. Choice of m, n & h values.
 Sample size: n=5
 Number of samples: m=20
 USL = 15.56, LSL = 15.52
 Target = 15.54
 Mean = 15.5389
 Spacing between samples: h= 0.1 hours or 6 min
Samples can be taken after every 6 min , in order to detect the shift
in mean quickly.
 Metrics used: Milligrams.
 Measuring Tool: Digital Scale.
 Unit of Focus : Weight of the bolt.

5. K & H values EWMA L & λ
 h=0.1
 k=1, to detect a shift of 1σ
α=0.0027, standard value for 3 sigma
control charts.
H = h*σ, K=k*σ
Unbiased sigma is used the values
are
σ=0.01,K =0.01, H = 0.001.
 L=3 , Usual three sigma
limits.
 λ=0.10, A smaller value of λ
helps to detect smaller shifts.
Cusum & EWMA values.

6. ARL0,ATS0
 Average Run Length (ARL0): Average number of
points that must be plotted before a point indicates an
out-of-control condition.
ARL0 = 1/α=1/0.0027=370 samples
 Average Time to Signal (ATS0):
ATS0 = h*ARL0 = 0.1 *(1/0.0027) = 37 hrs. This
indicates that we will receive a false alarm every 37
hours on average.

7. ARL1,ATS1
 Average Run Length (ARL1): Average run length of the X- bar
chartwhen the process is out of control. ARL1=1/(1-β),
β=Φ(L-k*sqrt(n))-Φ(-L-k*sqrt(n))
β= 0.7764
K=1, L=3 we get
ARL1 = 1/(1-0.7764) = 4.4722 samples.
 Average Time to Signal (ATS1):
Average time to detect shift with time interval of 0.1 hours is
ATS1 = h*ARL1 = 1/(1-β)*h
= 1/(1-0.7764)*0.1
ATS1 =0.4722 Hrs.

8. MEASURE

9. R & R Study Design
 Problem Statement : Determine how much variance is due to
each component, gauge and sample parts. Reproducibility is
associated with the operator while repeatability is associated with
the measuring instrument.
 Goal : The goal of the experiment is to find that all or most of the
variability is due to the samples and that the gauge is capable.
 Gauge Template : It consists of 20 parts 2 operators.

10. Gauge R & R Study
 Two inspectors were selected for the study and asked to measure
the weight of bolts (size m=20, n=5) under the operating
conditions to verify the reproducibility and repeatability.

12. Gage is Capable

13. Gage R&R Report

14. Selection of Charts
Charts Usage Reason
Variables
X-bar Yes
Data is Quantitative; utilizes the sample average
X-Bar to monitor the process mean.
R Yes Data is Quantitative; Control Chart for the Range.
S Yes
Data is Quantitative; Process variability is monitored with
the SD.
MR No Not applicable since n=5
Attribute
C & U No Not measuring non conformities
P Yes Measuring # of defectives using desired specification
Other(s)
CUSUM Yes
Use to detect a small shift; Directly incorporates all the
information in the sequence of sample values
EWMA Yes Effective against small process shifts

15. Phase I

16. Histogram
From the histogram plot we understand that the data is normally
distributed towards the mean.

17. Normality Check
Observation : P Value > 0.05 and hence the plot is normal.

18. X-Bar Chart
UCL CL LCL
15.5627 15.5389 15.5151
There are no out of control points, the process is in control.

19. X Bar - R Chart
No outliers, the process variability is in control and the sample
average is distributed over the mean.
UCL CL LCL
0.0793 0.037 0

20. X Bar - S Chart
No points exceed the control limits hence the process is
in control.
UCL CL LCL
0.034 0.0164 0

21. EWMA Chart
Lambda = 0.1 , L =3, σ = 1

22. CUSU
H = 0.001 , K =0.1
Ci+ and Ci- are within the decision interval H. Hence
the process is in control.
CUSUM Chart
-
0.000
0.000
0.000
0.000
0.001
0.001
0.001
0.001
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
CUSUM
H Ci+ -Ci-

23. P Chart
UCL CL LCL
0.1515 0.0325 0

24. Calculations for Control Limits & Center Line

25. Defects per million opportunities (DPMO) :
DPMO= (13/100) * 1000000
= 130,000 defects per million opportunities.
DPMO
# of defectives = 13
*1,000,000

26. Process Capability

27. Process Capability
Here USL = 15.56, LSL = 15.52
Cp = (USL-LSL)/(6*σ) where [σ = R-bar/d2 ]
= 0.77 < 1.33
Cpu = (USL-μ)/(3* σ)
= 0.82
Cpl = (μ-LSL)/(3* σ)
= 0.72
Cpk = Min (Cpu, Cpl)
= 0.72
=0.768
Since Cp is lesser than 1.33 and Cpk is lesser than unity, the process is
incapable.

28. Confidence Interval on Process Capability
Confidence Interval on Cp:
Cp*sqrt((χ2
1-α/2,n-1)/n-1) ≤ Cp ≤ Cp*sqrt((χ2
α/2,n-1)/n-1)
95% Confidence Interval on Cp is
0.53 ≤ Cp ≤ 1.01
Confidence Interval on Cpk:
Cpk^[ 1-Zα/2*sqrt((1/9ncpk2)+(1/2(n-1))] ≤ Cpk ≤ Cpk^ [ 1-Zα/2*sqrt((1/9ncpk2)+(1/2(n-1))]
95% Confidence Interval on Cpk is
0.45 ≤ Cpk ≤ 0.99

29. Revised ARL1 & ATS1
ARL0 = 1/α
=1/0.0027 = 370 samples
ATSO = h*ARL0
= 0.1*370 = 37 hours
ARL1 = 1/(1- β)
= 1/(1-.79) = 4.76 samples
ATS1 = h*ARL1
= 0.1*4.76 =0.476 hours

30. ANALYZE

31. Zone Rules

32. IMPROVE

33. Phase II
 From the X bar-R, X bar-S chart the process is in control and no
shift has been detected from the EWMA and the CUSUM charts.
Hence no revision is required before proceeding to Phase –II
(Monitoring).

34. Data Collection Phase II

35. Normality Check
Observation : P-Value obtained > 0.05 and hence the data is normal.

36. Histogram
Observation : The data is normally distributed towards the mean.

37. CONTROL

38. X-Bar Chart
UCL CL LCL
15.5647 15.5387 15.5126

39. X Bar - R Chart
Range UCL CL LCL
0.0761 0.036 0

40. X Bar - S Chart
S UCL CL LCL
0.0323 0.0154 0

41. Zone Rules for Control Charts

42. EWMA Chart
Lambda = 0.1 , L =3, σ = 1

43. CUSU
H = 0.001 , K =0.1, σ = 1
-
0.000
0.000
0.000
0.000
0.001
0.001
0.001
0.001
0.001
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
H Ci+ -Ci-
CUSUM Chart

44. P Chart
UCL CL LCL
0.5025 0.2342 0

45. Defect per million opportunities (DPMO) measure
DPMO= (10/100)*1000000
= 100,000 defects per million opportunities.
DPMO
*1,000,000
# of Defectives=10

46. Out of Control Action Plan (OCAP)
Out of Control
points detected in
the X Bar R Chart
Is the
weight
measured
correctly?
Which
test
failed?
No
Yes
Average
Range Report
Supervisor
Is the
weighing
scale
calibrated
?
Stop
Yes
No Calibrate the
weighing scale ,
retest the bolts
and record data.
Check the
procedure and
redo the test.
Adjust
m , n & h
Values.
Update the
comments in
the job
traveller.
Note : The same process is repeated
for the X bar-S Chart

47. QUESTIONS?