The Bolt Project (TEAM - METS) MAMATA SANAGOWDAR EKTA VASANT TERESA DOONG SUNITHA NARENDRA BABU
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The Bolt Project
(TEAM - METS)
MAMATA SANAGOWDAREKTA VASANT
TERESA DOONGSUNITHA NARENDRA BABU
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.
• 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
Choice of m, n & h values.
Sample size: n=5Number of samples: m=20USL = 15.56, LSL = 15.52 Target = 15.54Mean = 15.5389Spacing 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.
K & H values EWMA L & λ
h=0.1k=1, to detect a shift of 1σα=0.0027, standard value for 3 sigma control charts.H = h*σ, K=k*σUnbiased 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.
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.
ARL1,ATS1
Average Run Length (ARL1): Average run length of the X- bar chart when 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.
MEASURE
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.
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.
Gage is Capable
Gage R&R Report
Selection of ChartsCharts Usage Reason
Variable
s
X-bar YesData 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 YesUse to detect a small shift; Directly
incorporates all the information in the sequence of sample values
EWMA Yes Effective against small process shifts
Phase I
Histogram
From the histogram plot we understand that the data is normally distributed towards the mean.
Normality Check
Observation : P Value > 0.05 and hence the plot is normal.
X-Bar Chart
UCL CL LCL15.5627 15.5389 15.5151
There are no out of control points, the process is in control.
X Bar - R Chart
No outliers, the process variability is in control and the sample average is distributed over the mean.
UCL CL LCL0.0793 0.037 0
X Bar - S Chart
No points exceed the control limits hence the process is in control.
UCL CL LCL0.034 0.0164 0
EWMA Chart
191715131197531
15.548
15.546
15.544
15.542
15.540
15.538
15.536
15.534
15.532
15.530
Sample
EWM
A __X=15.5389
UCL=15.54683
LCL=15.53097
EWMA Chart of Xbar
Lambda = 0.1 , L =3, σ = 1
CUSU
H = 0.001 , K =0.1Ci+ and Ci- are within the decision interval H. Hence the process is in
control.
CUSUM Chart
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -
0.001
0.001
H Ci+ -Ci-
CUSU
M
P Chart
UCL CL LCL0.1515 0.0325 0
Calculations for Control Limits & Center Line
Defects per million opportunities (DPMO) :
DPMO= (13/100) * 1000000
= 130,000 defects per million opportunities.
DPMO
# of defectives = 13
*1,000,000
Process Capability
15.5615.5515.5415.5315.52
LSL 15.52Target *USL 15.56Sample Mean 15.5387Sample N 20StDev(Overall) 0.00763027StDev(Within) 0.00867861
Process Data
CPL 0.72CPU 0.82Cpk 0.72CI for Cpk (0.45, 0.99)
Pp 0.87CI for Pp (0.60, 1.15)PPL 0.82PPU 0.93Ppk 0.82CI for Ppk (0.52, 1.11)Cpm *
Cp 0.77CI for Cp (0.53, 1.01)
Potential (Within) Capability
Overall Capability
PPM < LSL 0.00 7127.66 15591.77PPM > USL 0.00 2623.12 7057.77PPM Total 0.00 9750.78 22649.54
Observed Expected Overall Expected WithinPerformance
LSL USLOverallWithin
Process Capability(using 95.0% confidence)
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.
Confidence Interval on Process Capability
Confidence Interval on Cp:
Cp*sqrt((χ21-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
Revised ARL1 & ATS1
ARL0 = 1/α =1/0.0027 = 370 samplesATSO = h*ARL0 = 0.1*370 = 37 hours ARL1 = 1/(1- β) = 1/(1-.79) = 4.76 samplesATS1 = h*ARL1 = 0.1*4.76 =0.476 hours
ANALYZE
Zone Rules
IMPROVE
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).
Data Collection Phase II
Normality Check
Observation : P-Value obtained > 0.05 and hence the data is normal.
Histogram
Observation : The data is normally distributed towards the mean.
CONTROL
X-Bar Chart
UCL CL LCL15.5647 15.5387 15.5126
X Bar - R Chart
Range UCL CL LCL0.0761 0.036 0
X Bar - S Chart
S UCL CL LCL0.0323 0.0154 0
Zone Rules for Control Charts
EWMA Chart
Lambda = 0.1 , L =3, σ = 1
191715131197531
15.548
15.546
15.544
15.542
15.540
15.538
15.536
15.534
15.532
15.530
Sample
EWM
A __X=15.5387
UCL=15.54738
LCL=15.53002
EWMA Chart of Xbar
CUSU
H = 0.001 , K =0.1, σ = 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 -
0.001
0.001
H Ci+ -Ci-
CUSUM Chart
P Chart
UCL CL LCL0.5025 0.2342 0
Defect per million opportunities (DPMO) measure
DPMO= (10/100)*1000000
= 100,000 defects per million opportunities.
DPMO
*1,000,000
# of Defectives=10
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 Superviso
r
Is the weighing scale
calibrated ?
StopYes
NoCalibrate the
weighing scale ,
retest the bolts and
record data.
Check the procedure
and redo the test.
Adjust m , n &
hValues.
Update the comments in
the job traveller.
Note : The same process is repeated for the X bar-S Chart
QUESTIONS?
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