Submit your statistical analysis report and recommendations

Submit your statistical analysis report and recommendations to management. It should be a complete, polished artifact containing all of the critical elements of the final product. It should reflect the incorporation of feedback gained throughout the course.

Note that you will need to refer to the scenario in the article “A-Cat Corp.: Forecasting.”

A-CAT Corp., a company that produces appliances in a poor region of India is price sensitive mainly rural market. In recent months, there has been an alarming drop in sales of its main product, a voltage regulator which is used for various purposes, but more often as a protective device for refrigerators and televisions, to protect the latter against the risks of fluctuations in load and / or frequent power cuts, which are a very common phenomenon in the region. At the same time, the production department has complained about the shortage of spare parts and components. Place orders above a certain limit for critical transformers used in most products has also extended the system – while the company had prior access to four suppliers of transformers, is now alone. The Vice President asked the Director of Operations leaders to address the problem. COO trace the process of production planning and its dependence on accurate forecasts. The director’s job is to collect data, analyze data patterns, the use of prediction methods, perform back-testing and make recommendations to management to solve the problem.

Vice-president Arun Mittra speculates:

We have always estimated how many transformers will be needed to meet demand. The usual method is to look at the sales figures of the last two to three months and also the sales figures of the last two years in the same month. Next make a guess as to how many transformers will be needed. Either we have too many transformers in stock, or there are times when there are not enough to meet our normal production levels. It is a classic case of both understocking and overstocking.

Ratnaparkhi, operations head, has been given two charges by Mittra. First, to develop an analysis of the data and present a report with recommendations. Second, “to come up with a report that even a lower grade clerk in stores should be able to fathom and follow.”

In an effort to develop a report that is understood by all, Ratnaparkhi decides to provide incremental amounts of information to his operations manager, who is assigned the task of developing the complete analyses.

A-Cat Corporation is committed to the pursuit of a robust statistical process control (quality control) program to monitor the quality of its transformers. Ratnaparkhi, aware that the construction of quality control charts depends on means and ranges, provides the following descriptive statistics for 2006 (from Exhibit 1). 2006

Mean

801.1667

Standard Error

24.18766

Median

793

Mode

708

Standard Deviation

83.78851

Sample Variance

7020.515

Kurtosis

-1.62662

Skewness

0.122258

Range

221

Minimum

695

Maximum

916

Sum

9614

Count

A-Cat’s president asks Mittra, his vice-president of operations, to provide the sales department with an estimate of the mean number of transformers that are required to produce voltage regulators. Mittra, recalling the product data from 2006, which was the last year he supervised the production line, speculates that the mean number of transformers that are needed is less than 745 transformers. His analysis reveals the following:

t = 2.32

p = .9798

This suggests that the mean number of transformers needed is not less than 745 but at least 745 transformers. Given that Mittra uses older (2006) data, his operations manager knows that he substantially underestimates current transformers requirements. She believes that the mean number of transformers required exceeds 1000 transformers and decides to test this using the most recent (2010) data.

Initially, the operations manager possessed only data for years 2006 to 2008. However, she strongly believes that the mean number of transformers needed to produce voltage regulators has increased over the three-year period. She performs a one-way analysis of variance (ANOVA) analysis that follows

2006

2007

2008

779

845

857

802

739

881

818

871

937

888

927

1159

898

1133

1072

902

1124

1246

916

1056

1198

708

889

922

695

857

798

708

772

879

716

751

945

784

820

990

SUMMARY

Groups

Count

Sum

Average

Variance

2006

9614

801.1667

7020.515

2007

10784

898.6667

18750.06

2008

11884

990.3333

21117.88

ANOVA

Source of Variation

P-value

F crit

Between Groups

214772.2

107386.1

6.870739

0.003202

3.284918

Within Groups

515773

15629.48

Total

730545.2

The results (F = 6.871 and p = 0.003202) suggest that indeed the mean number of transformers has changed over the period 2006–2008. Mittra has now provided her with the remaining two years of data (2009 and 2010) and would like to know if the mean number of transformers required has changed over the period 2006–2010.

Finally, the operations manager is tasked with developing a model for forecasting transformer requirements based on sales of refrigerators. The table below summarizes sales of refrigerators and transformer requirements by quarter for the period 2006–2010, which are extracted from Exhibits 2 and 1 respectively.

Sales of Refrigerators

Transformer Requirements

3832

2399

5032

2688

3947

2319

3291

2208

4007

2455

5903

3184

4274

2802

3692

2343

4826

2675

6492

3477

4765

2918

4972

2814

5411

2874

7678

3774

5774

3247

6007

3107

6290

2776

8332

3571

6107

3354

6792

3513

A-Cat Corporation is committed to the pursuit of a robust statistical process control (quality control) program to monitor the quality of its transformers. Ratnaparkhi, aware that the construction of quality control charts depends on means and ranges, provides the following descriptive statistics for 2006 (from Exhibit 1). 2006
Mean	801.1667
Standard Error	24.18766
Median	793
Mode	708
Standard Deviation	83.78851
Sample Variance	7020.515
Kurtosis	-1.62662
Skewness	0.122258
Range	221
Minimum	695
Maximum	916
Sum	9614
Count	12

All the work is done in the question except last question and in the last we have to calculate forecast for the next years.

The operations manager is tasked with developing a model for forecasting transformer requirements based on sales of refrigerators. The table below summarizes sales of refrigerators and transformer requirements by quarter for the period 2006–2010, which are extracted from Exhibits 2 and 1 respectively

This we can dine by using MINITAB:

steps :

STAT --> Time series --> Trend analysis --> variable : requirement --> Model type : linear --> generate forecasts --> number of forecasts = 3 --> Storage : second and third option --> results : third option --> ok

This will gives us following output.

Trend Analysis for requirement

Data requirement
Length 20
NMissing 0

Fitted Trend Equation

Yt = 2327.21 + 56.9233*t

Accuracy Measures

MAPE 8.3
MAD 241.6
MSD 95515.7

Time requirement Trend Detrend
1 2399 2384.13 14.871
2 2688 2441.05 246.948
3 2319 2497.98 -178.975
4 2208 2554.90 -346.898
5 2455 2611.82 -156.822
6 3184 2668.75 515.255
7 2802 2725.67 76.332
8 2343 2782.59 -439.592
9 2675 2839.52 -164.515
10 3477 2896.44 580.562
11 2918 2953.36 -35.362
12 2814 3010.28 -196.285
13 2874 3067.21 -193.208
14 3774 3124.13 649.868
15 3247 3181.05 65.945
16 3107 3237.98 -130.978
17 2776 3294.90 -518.902
18 3571 3351.82 219.175
19 3354 3408.75 -54.748
20 3513 3465.67 47.329