Viadromes Case Study: Descriptive Statistics Analysis (Case Study Sample)

Viadrome Case Study
Name
Institution
Viadrome Case Study
The manufacturing process involves the use of various machines. As such, the failure of one machine may hamper the whole process. Therefore, efficient facility managers regularly conduct quality control analysis, in order to monitor the performance of their machines. This analysis presents a case of a facility manager in Michigan at the Viadrome Plant, who was concerned about the quality of measurements during the manufacturing process. The data utilized in the study was sourced from a measurement process, during which 150 upper tracks were measured by two operators, A and B. Several statistical tests are conducted in order to examine the variation in measurements between the two operators. The excel spreadsheet program is used for conducting various tests.
Statistical Analysis
Descriptive Statistics
The following tables show the output summaries for all variables as generated by excel
OA

 

OB

 

OAR

 







Mean

0.264667

Mean

0.5852

Mean

0.3598

Standard Error

0.035302

Standard Error

0.041087

Standard Error

0.038052

Median

0.27

Median

0.585

Median

0.35

Mode

0.1

Mode

0.71

Mode

0.25

Standard Deviation

0.43236

Standard Deviation

0.503209

Standard Deviation

0.466044

Sample Variance

0.186935

Sample Variance

0.25322

Sample Variance

0.217197

Kurtosis

-0.06798

Kurtosis

0.629609

Kurtosis

-0.02203

Skewness

-0.02741

Skewness

-0.10351

Skewness

0.074945

Range

2.52

Range

3.23

Range

2.31

Minimum

-1.04

Minimum

-1.14

Minimum

-0.71

Maximum

1.48

Maximum

2.09

Maximum

1.6

Sum

39.7

Sum

87.78

Sum

53.97

Count

150

Count

150

Count

150

OA_OB_DIFF

 

OA_OAR_DIFF

 





Mean

-0.321533333

Mean

-0.0956

Standard Error

0.026262781

Standard Error

0.020158

Median

-0.31

Median

-0.1

Mode

-0.31

Mode

-0.16

Standard Deviation

0.321652062

Standard Deviation

0.246885

Sample Variance

0.103460049

Sample Variance

0.060952

Kurtosis

-0.132351701

Kurtosis

0.299276

Skewness

-0.004367437

Skewness

-0.02964

Range

1.68

Range

1.31

Minimum

-1.13

Minimum

-0.75

Maximum

0.55

Maximum

0.56

Sum

-48.23

Sum

-14.34

Count

150

Count

150

According to this output, the mean measurements for OA, OB, OAR, OA OB DIFF, and OA OAR DIFF are 0.26, 0.59, 0.36, 0.32, and -0.09 respectively. The standard deviations and range values are useful in examining the extent of variation in measurement for each operator. A significantly large standard deviation value or range value would depict a considerable variation in the measurement of tracks generated by each operator. The descriptive analysis results above imply that the measurements generated by operator B have a greater variation compared to those generated by operator A; the standard deviation and range values for OB 0.50 and 3.23 are larger than those of both OA and OAR. Nevertheless, it is necessary to conduct further analysis on these measurements in order to generate a more conclusive report about the quality control of the machines.
Z-Test
OA and OB. The Z test is preferred in this case, because the sample size is relatively large. The set of hypotheses generated for the test is as follows
H0: µ1- µ2 = 0
H1: µ1- µ2 ≠ 0
Significance level = 0.05
Decision: To reject the null hypothesis if the P value is less than 0.05
The table below shows the output for this test
 

OA

OB

Mean

0.264667

0.5852

Known Variance

0.18

0.25

Observations

150

150

Hypothesized Mean Difference

0


Z

-5.98666


P(Z<=z) one-tail

1.07E-09


z Critical one-tail

1.644854


P(Z<=z) two-tail

2.14E-09


z Critical two-tail

1.959964

 

Since the P value f...