Statistical Process Control and Kanban Card Calculations Report

This report presents a statistical analysis of a company's operational processes across four branches, utilizing X-Bar and R-Bar charts to assess consistency and identify areas for improvement. The analysis covers 27 randomly selected dates, examining data averages and ranges to determine if processes stay within control limits. The X-Bar chart helps in assessing the average performance, while the R-Bar chart highlights the range of variation, with a focus on fluctuations and potential inefficiencies. The report also includes calculations for Kanban cards, a lean production tool, to optimize inventory management. The findings suggest that while most processes are manageable, fluctuations in certain branches and instances beyond control limits necessitate management attention to ensure efficiency, consistency, and optimal performance. The report emphasizes the importance of statistical analysis in making informed decisions and initiating corrective measures to avoid delays and losses. This comprehensive analysis provides valuable insights into process control and optimization within the organization.

Name of student
Professor
Date

a.
processes in the four branches were varied throughout the 27 randomly selected dates. However,
the data range in each process in all the four branches did not go beyond the control limits. This
made it possible for the processes to be manageable. In the R-Bar however, the processes went
under the lower control limit in two occasions, a signal that calls for management to ensure
efficiency and optimum performances to be achieved.
However, the fluctuation shown in branch three is massive and there is need for the management
of the firm to reduce the fluctuation margin to ensure consistency of the process. control limits
indicate the extreme limits the processes can be allowed to go beyond which, control
mechanisms are put in place for control measures. This is in the case as indicated the R-Bar, the
lower control limit of the processes being set at zero, the two scenarios which went beyond the
control limit indicated the possibility of the company doing detrimental processes which are
using the resources in the firm with no tangible benefits realized in the company.
Analyzing the statistical data using the X-Bar and R-bar is essential since it establishes how the
processes carried in various branches are consistent with the operation process set in the
organization. This makes it possible for the management to efficiently manage the processes and
initiate the corrective measures when it is necessary to avoid delays which may lead to losses in
the company. The outcome from the analyzed data is useful to manager to make objective
decision on the overall performance of the firm.
The data for the firm is statistically analyzed using the X-Bar and R-Bar in the charts shown
bellow
data average and data range

Day Branch1 Branch2 Branch3 Branch4
avg. (X-
Bar) Range
1 15 11 26 22 18.5 12
2 13 13 23 17 16.5 10
3 23 17 23 11 18.5 20
4 20 14 31 9 18.5 17
5 11 14 26 15 16.5 18
6 24 10 29 12 18.75 15
7 13 19 25 11 17 30
8 9 25 41 24 24.75 24
9 22 13 33 21 22.25 12
10 22 6 25 9 15.5 22
11 16 8 28 22 18.5 20
12 23 22 28 25 24.5 -1
13 12 12 21 20 16.25 14
14 8 19 26 14 16.75 22
15 11 7 30 23 17.75 18
16 25 9 16 25 18.75 15
17 19 11 20 24 18.5 21
18 4 18 32 8 15.5 20
19 7 11 24 8 12.5 30
20 27 21 37 13 24.5 8
21 24 12 16 21 18.25 21
22 11 9 33 18 17.75 15
23 20 11 19 24 18.5 24
24 19 21 35 21 24 26
25 7 10 45 6 17 6.5
26 24 5 9 12 12.5 11
27 15 16 10 7 12 -7
X-BAR
Day
avg. (X-
Bar) X-DBAR UCL ( LCL
1 18.5
18.1574
1
21.5902
4
14.7245
7
2 16.5 18.1574 18.1574 18.1574

1 1 1
3 18.5
18.1574
1
18.1574
1
18.1574
1
4 18.5
18.1574
1
18.1574
1
18.1574
1
5 16.5
18.1574
1
18.1574
1
18.1574
1
6 18.75
18.1574
1
18.1574
1
18.1574
1
7 17
18.1574
1
18.1574
1
18.1574
1
8 24.75
18.1574
1
18.1574
1
18.1574
1
9 22.25
18.1574
1
18.1574
1
18.1574
1
10 15.5
18.1574
1
18.1574
1
18.1574
1
11 18.5
18.1574
1
18.1574
1
18.1574
1
12 24.5
18.1574
1
18.1574
1
18.1574
1
13 16.25
18.1574
1
18.1574
1
18.1574
1
14 16.75
18.1574
1
18.1574
1
18.1574
1
15 17.75
18.1574
1
18.1574
1
18.1574
1
16 18.75
18.1574
1
18.1574
1
18.1574
1
17 18.5
18.1574
1
18.1574
1
18.1574
1
18 15.5
18.1574
1
18.1574
1
18.1574
1
19 12.5
18.1574
1
18.1574
1
18.1574
1
20 24.5
18.1574
1
18.1574
1
18.1574
1
21 18.25
18.1574
1
18.1574
1
18.1574
1
22 17.75
18.1574
1
18.1574
1
18.1574
1
23 18.5
18.1574
1
18.1574
1
18.1574
1
24 24
18.1574
1
18.1574
1
18.1574
1
25 17
18.1574
1
18.1574
1
18.1574
1
26 12.5 18.1574 18.1574 18.1574

1 1 1
27 12
18.1574
1
18.1574
1
18.1574
1
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
14.72
16.72
18.72
20.72
22.72
24.72
26.72
X- BAR
avg. (X- Bar) X-DBAR UCL ( LCL
R-BAR
Day Range r-bar Ucl Lcl
1 12
16.4259
3
33.0161
1 0
2 10
16.4259
3
33.0161
1 0
3 20
16.4259
3
33.0161
1 0
4 17
16.4259
3
33.0161
1 0
5 18
16.4259
3
33.0161
1 0
6 15
16.4259
3
33.0161
1 0
7 30
16.4259
3
33.0161
1 0
8 24
16.4259
3
33.0161
1 0

9 12
16.4259
3
33.0161
1 0
10 22
16.4259
3
33.0161
1 0
11 20
16.4259
3
33.0161
1 0
12 -1
16.4259
3
33.0161
1 0
13 14
16.4259
3
33.0161
1 0
14 22
16.4259
3
33.0161
1 0
15 18
16.4259
3
33.0161
1 0
16 15
16.4259
3
33.0161
1 0
17 21
16.4259
3
33.0161
1 0
18 20
16.4259
3
33.0161
1 0
19 30
16.4259
3
33.0161
1 0
20 8
16.4259
3
33.0161
1 0
21 21
16.4259
3
33.0161
1 0
22 15
16.4259
3
33.0161
1 0
23 24
16.4259
3
33.0161
1 0
24 26
16.4259
3
33.0161
1 0
25 6.5
16.4259
3
33.0161
1 0
26 11
16.4259
3
33.0161
1 0
27 -7
16.4259
3
33.0161
1 0

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
-10
-5
0
5
10
15
20
25
30
35
40
R-BAR
Range r-bar ucl lcl
Statistical analysis
b.
kanban cards calculations
no. of Kanban cards = {average demand(waiting time+process time)(1+safety
factor)}/{container quantity}
{500(0.26+0.64)(1+10)}/50
= 99 kanban cards