Process Capability Analysis with Two Datasets

This assignment examines process capability using two separate datasets. The analysis involves calculating key statistical parameters like A2, Rbar, Sigma (SD), and Process Capability Index (Cp). The impact of sample size on Cp is explored, highlighting how the smaller sample size in the second dataset influences the results despite a reduced standard deviation. Additionally, the assignment delves into the cyclic patterns observed within the second dataset and their implications for process control.

Running head: SUPPLY CHAIN OPERATIONS MANAGEMENT
Supply Chain Operations Management
Name of the Student
Name of the University
Author’s Note

1SUPPLY CHAIN OPERATIONS MANAGEMENT
Table of Contents
Answer 1: ZenoFex Case Study......................................................................................................2
Answer 2: FORTech Inc. Case Study..............................................................................................6
2.1 Conclusion to the first process..............................................................................................6
2.2 Observations in the second process.....................................................................................10
2.3 Computation of the potential process capability using the second data set........................10
2.4 Revealing of the small samples...........................................................................................14
References......................................................................................................................................15

2SUPPLY CHAIN OPERATIONS MANAGEMENT
Answer 1: ZenoFex Case Study
Period
Semiconducto
r
1 40
2 39
3 55
4 88
5 51
6 54
7 66
8 63
9 57
10 68
11 77
Trend Analysis
Perio
d
Semiconduct
or
Foreca
st Error
ABS(erro
r)
Square
d Error
Perce
nt
Error
1 40 47.45 -7.45 7.45 55.57 0.19
2 39 49.93 -10.93 10.93 119.41 0.28
3 55 52.40 2.60 2.60 6.76 0.05
4 88 54.87 33.13 33.13 1097.42 0.38
5 51 57.35 -6.35 6.35 40.26 0.12
6 54 59.82 -5.82 5.82 33.85 0.11
7 66 62.29 3.71 3.71 13.76 0.06
8 63 64.76 -1.76 1.76 3.11 0.03
9 57 67.24 -10.24 10.24 104.78 0.18
10 68 69.71 -1.71 1.71 2.92 0.03
11 77 72.18 4.82 4.82 23.21 0.06
0 8.05 136.46 0.13
BIAS MAD MSE
MAP
E
Method 1: Using Excel's
function
a=
44.9818
2
b=
2.47272
7

3SUPPLY CHAIN OPERATIONS MANAGEMENT
1 2 3 4 5 6 7 8 9 10 11
0
20
40
60
Forecast vs. Actual
Semiconductor
Forecast
Time
Semiconductor
Figure 1: Trend Comparison
(Source: As Created by the author)
0 2 4 6 8 10 12
0
2
4
6
8
10
12
f(x) = NaN x + NaN
Time
Semiconductor
Figure 2: Scatter Diagram of the Trend
(Source: As Created by the author)

4SUPPLY CHAIN OPERATIONS MANAGEMENT
Moving Average Model
Moving Average
Model
(1) Simple MA models
perio
d
Semiconducto
r
3-
month
MA
forecas
t error
ABS(erro
r)
1 40 - - -
2 39 - - -
3 55 - - -
4 88 44.67 43.33 43.33
5 51 60.67 -9.67 9.67
6 54 64.67 -10.67 10.67
7 66 64.33 1.67 1.67
8 63 57.00 6.00 6.00
9 57 61.00 -4.00 4.00
10 68 62.00 6.00 6.00
11 77 62.67 14.33 14.33
5.88 11.96 297.65
BIAS MAD MSE
1 2 3 4 5 6 7
0
20
40
60
80
100
Forecast vs. Actual
Semiconductor
3-month MA forecast
Time
Sales

5SUPPLY CHAIN OPERATIONS MANAGEMENT
Figure 1: Moving Average Comparison
(Source: As Created by the author)
Exponential Smoothening Model
Alpha = 0.4
Period
Semiconduct
or
forecas
t error
ABS(erro
r)
1 40 40.00 - -
2 39 40.00 -1.00 1.00
3 55 39.60 15.40 15.40
4 88 45.76 42.24 42.24
5 51 62.66 -11.66 11.66
6 54 57.99 -3.99 3.99
7 66 56.40 9.60 9.60
8 63 60.24 2.76 2.76
9 57 61.34 -4.34 4.34
10 68 59.61 8.39 8.39
11 77 62.96 14.04 14.04
7.14 11.34 256.04
BIAS MAD MSE
1 2 3 4 5 6 7 8 9 10 11
0
10
20
30
40
50
60
70
80
90
100
Forecast vs. Actual
Semiconductor
Fcst (alpha=0.4)
Time
Sales

6SUPPLY CHAIN OPERATIONS MANAGEMENT
Figure 2: Exponential Smoothing Comparison
(Source: As Created by the author)
Comparison of the Models
Model Comparison and Selection
Models
BIA
S
MA
D MSE MAPE
Trend 0.00 8.05 136.46 0.13
Moving Avg 5.88 11.96 297.65 0.00
(best weighted
moving average
with n=3)
Exponential Smoothing 7.14 11.34 256.04 0.00
(using Solver to find
the best alpha=0.599
which minimizes
MAD)
Rationale for selection of Exponential Smoothing
The main considerations for the exponential smoothing have been interpreted as per
MSE. MSE value is interpreted as per the difference between the estimator and the total
estimated value. The main rationale for the selection of the exponential is due to a lower MSE
and the consideration of exponential smoothing is done with alpha = 0.4. The MSE value for the
moving average is 297.65 while exponential smoothing is seen as 256.04. The mead average
deviation of the MAD is lower for exponential smoothing making it the most appropriate method
of forecasting.

7SUPPLY CHAIN OPERATIONS MANAGEMENT
Answer 2: FORTech Inc. Case Study
2.1 Conclusion to the first process
The main interpretation has further shown that the mean is 10.49 and range is 0.88. The
upper control limit has been discerned as 10.663, while the lower control limit is 10.32 for the X
Bar control chart. The UCL and the LCL for the R bar control chart has been further discerned as
0.34 and 1.42.
Sampl
e Mean Range
1 10.565 0.850
2 10.523 0.749
3 10.487 0.962
4 10.439 0.946
5 10.516 0.842
6 10.492 0.900
7 10.429 0.949
8 10.453 0.818
9 10.512 0.927
10 10.523 0.945
11 10.467 0.905
12 10.502 0.713
13 10.521 0.942
14 10.456 0.960
15 10.493 0.869
16 10.492 0.927
17 10.555 0.826
18 10.418 0.861
Mean
10.4913
9
0.88284
6
X Bar Chart
LCL CL UCL
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663

8SUPPLY CHAIN OPERATIONS MANAGEMENT
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
10.320 10.491 10.663
R Bar Chart
LCL CL UCL
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420
0.3452 0.883 1.420

9SUPPLY CHAIN OPERATIONS MANAGEMENT
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
10.100
10.200
10.300
10.400
10.500
10.600
10.700
X Bar Control Chart
Mean
LCL
CL
UCL
Figure 3: Line diagram for X Bar Control Chart
(Source: As Created by the author)

10SUPPLY CHAIN OPERATIONS MANAGEMENT
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
R Bar Control Chart
Range
LCL
CL
UCL
Figure 3: Line diagram for R Bar Control Chart
(Source: As Created by the author)
Data
Specification
Width
Number of
observations
Number
of
Samples A2 D3 D4 Rbar
Sigma
(SD)
Process
Capability
Index
1st
Data
Set 1.44 17 18 0.194 0.391 1.608
0.8828
5 0.2354 1.020
The main depiction made in the computation has revealed that the Process capability
Index is measured at 1.020. This has been further seen to be less than 1.33, which is not
considered as a recommended process.

11SUPPLY CHAIN OPERATIONS MANAGEMENT
2.2 Observations in the second process
The initial results have not seen to be up to the mark for taking fewer samples. Jane is
expecting recover the lost cluster and the capital freeze value of $ 10k. The consideration from
the second sample has depicted with better accuracy and the range of data. The important
applicability of the second process needs to increase the clarity of the data.
2.3 Computation of the potential process capability using the second data set
The important depiction form the second process has shown a mean 10.51 and range of
0.58. The UCL and the LCL for the X bar has been depicted as 10.17 and 10.85. It has been
further discerned that the UCL and the LCL for the R Bar has been discerned as 0.34 and 0.43.
Sampl
e Mean Range
1 10.324 0.364
2 10.281 0.530
3 10.471 0.620
4 10.462 0.399
5 10.732 0.446
6 10.685 0.276
7 10.241 0.517
8 10.614 0.992
9 10.611 0.839
10 10.521 0.644
11 10.665 0.532
12 10.289 0.449
13 10.493 0.853
14 10.653 0.402
15 10.659 0.570
16 10.655 0.468
17 10.196 0.602
18 10.465 0.760
19 10.460 0.613
20 10.245 0.348
21 10.605 0.745
22 10.738 0.391
23 10.498 0.558
24 10.471 0.540

12SUPPLY CHAIN OPERATIONS MANAGEMENT
25 10.718 0.388
26 10.490 0.941
27 10.488 0.951
Mean 10.50843 0.582877
X Bar Chart R Bar Chart
LCL CL UCL LCL CL UCL
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313
10.170 10.508 10.846 0.3381 0.583 0.4313

13SUPPLY CHAIN OPERATIONS MANAGEMENT
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
9.800
10.000
10.200
10.400
10.600
10.800
11.000
X Bar Control Chart
Mean
LCL
CL
UCL
Figure 4: X Bar control chart for the second process
(Source: As Created by the author)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
0.000
0.200
0.400
0.600
0.800
1.000
1.200
R Bar Control Chart
Range
LCL
CL
UCL
Figure 5: R Bar control chart for the second process
(Source: As Created by the author)

14SUPPLY CHAIN OPERATIONS MANAGEMENT
Dat
a
Specificatio
n Width
Number of
observation
s
Numbe
r of
Sample
s A2 D3 Rbar
Sigm
a
(SD)
Process
Capabilit
y Index
2nd
Data
Set 1.44 4 27
0.5
8
0.7
4
0.5828
8
0.225
4 1.065
Comparison of the result
Dat
a
Specificatio
n Width
Number of
observation
s
Numbe
r of
Sample
s A2 Rbar
Sigm
a
(SD)
Process
Capabilit
y Index
1st
Data
Set 1.44 17 18
0.19
4
0.8828460
1 0.235 1.020
2nd
Data
Set 1.44 4 27 0.58 0.5828765 0.225 1.065
The process capability of the second process is considered as 1.065, this slightly more
than the 1st data, hence it should be accepted.
2.4 Revealing of the small samples
The important considerations of the study have been further seen to be discerned as per
the various types of the cyclic pattern of the data, which was not present during the first data set.
The standard deviation from the distribution of the samples in the second data set has been able
to reduce the SD from 0.235 to 0.225. However, the Cp criterion is not met even after
considering more samples.
The smaller size of the sample is ideal for representing the adequate population. The
larger sample size is the result of the findings based on the population size. A better idea has
been depicted in terms of the recall in process, quality inspection and trade process. The

15SUPPLY CHAIN OPERATIONS MANAGEMENT
computations and the application of the statistical concepts has been able to improve the
Capability index.

16SUPPLY CHAIN OPERATIONS MANAGEMENT
References
Aly, A.A., Saleh, N.A., Mahmoud, M.A. and Woodall, W.H., 2015. A reevaluation of the
adaptive exponentially weighted moving average control chart when parameters are
estimated. Quality and Reliability Engineering International, 31(8), pp.1611-1622.
Azam, M., Aslam, M. and Jun, C.H., 2015. Designing of a hybrid exponentially weighted
moving average control chart using repetitive sampling. The International Journal of Advanced
Manufacturing Technology, 77(9-12), pp.1927-1933.
Şentürk, S., Erginel, N., Kaya, İ. and Kahraman, C., 2014. Fuzzy exponentially weighted moving
average control chart for univariate data with a real case application. Applied Soft
Computing, 22, pp.1-10.
Zhang, J., Li, Z., Chen, B. and Wang, Z., 2014. A new exponentially weighted moving average
control chart for monitoring the coefficient of variation. Computers & Industrial
Engineering, 78, pp.205-212.