A Comprehensive Statistical Review of Supplier Delivery Performance

MAIN TASK

Question 1

1. Identify each parameter

• Qualitative parameters are in the form of categories (Job level, Sector, Education, Discipline).
• Quantitative parameter is numeric (Age, Salary, Customer Satisfaction).

2. Create summary table for Job Level.

Tally

Table 1 summary table

Job Level	Count
Junior	83
Manager	295
Senior	304
N=	682

3. Draw Bar graph for Education.

4. Draw pie chart 

                                                                                               Figure 2 pie chart

5. Draw a histogram for salary.

                                                                                   Figure 3 histogram

 6. Descriptive statistics, its normality.

Statistics

Table 2 Statistics

Variable	Mean	StDev	Minimum	Median	Maximum	Mode	N for Mode
Salary	13310.2	7039.15	4830	10471	30534	7350	3

                                                                                 Figure 4 normality

7. Draw box blot for Age 

                                                                                          Figure 5 box blot for Age

8. Draw Pareto chart 

                                                                                                    Figure 6 Pareto chart

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Question 2 

A. The normal distribution 

1. Probability that TV will work < 3,350 hours

Table 3 probability

2. If a TV will work > 3,750 hours

Table 4 probability that TV will work

3. Probability if a TV will work among 3,350 & 3,750 hours

To derive this, take cumulative probability at 3,750 hours minus the cumulative probability at 3,350 hours:

P(3350<X<3750) =P(X≤3750) −P(X≤3350) =0.894350−0.226623

=0.667723

Therefore, it is 66.77% probability that a TV will work in the range of 3.350 to 3.750 hours.

4. TV life that is confident 95%

Normal with mean = 3500 and standard deviation = 200

Table 5 confident at 95%

P( X ≤ x )	x
0.95	3828.97

B. Determine average time needed 

1. What if it will serve 10 customers

Table 6 probability that will serve 10 customers

2. What is probability that will serve more than 15 customers?

Table 7 probability serve > 15 customers

3. The probability if it will serve between 10 & 15 customers

Table 8 Probability of between 10 and 15

Step	Calculation	Result
1. Time to Serve 10 Customers	10×4.78=47.8	47.8 minutes
2. Time to Serve 15 Customers	15×4.78=71.7	71.7 minutes
3. Cumulative Probability for 10 Customers (P(X ≤ 47.8))	Use Normal CDF with μ = 4.78 and σ = 1.32	P(X≤47.8)=0.226627P(X ≤ 47.8) = 0.226627
4. Cumulative Probability for 15 Customers (P(X ≤ 71.7))	Use Normal CDF with μ = 4.78 and σ = 1.32	P(X≤71.7)=0.894350P(X ≤ 71.7) = 0.894350
5. Probability of Serving Between 10 and 15 Customers	P(10≤Customers≤15)=P(X≤71.7)−P(X≤47.8)	0.894350−0.226627=0.667723
6. Final Probability (10 ≤ Customers ≤ 15)	Â	66.77%

4. A number of customers will be with 95% confident

Table 9 number of customers

C. The normal distribution 

1. Probability if it will achieve the contract term

Table 10 achieve the contract terms

2. An orange quantity

Table 11 orange quantity

Question 3 

Using of Delivery Time Data 

Table 12 Delivery Time Data

A. Calculate the capability indices and provide your comments on the results.

Using the Delivery Time data, will find Cp and Cpk indices of capability.

Given Data:

USL (Upper Specification Limit) = 35 days.

LSL (Lower Specification Limit) = 25 days

Mean (μ) = 30.7539 days

Standard Deviation (σ) = 3.27027 days

Table 13 capability indices

Index	Formula	Value
Cp	(USL−LSL)/6σ	(35−25)/(6*2.7027)	0.061666728
Cpk	min(USL−μ)/3σ,μ−LSL/3σ)	MIN(35-30.7539)/(3*3.27027)*(30.7539-25)/(3*3.27027)	0.2538

B. Provide recommendation 

According to Cp and Cpk values, the supplier’s process is unable to consistently process to the required 25 to 35-day window. To improve performance:

• Reduce Process Variability: Pinpoint sources of change in the process of delivering and apply correcting measures, for example, optimize production and transportation.
• Center the Process: Towards aligning process more to the target delivery time, implement better scheduling, allocation of resources and departments communication.
• Continuous Monitoring: Keep an eye on the process with the use of control charts to maintain any improvements (Chalmer, 2020).

Question 4 

A. Transforming of the data using Box-Cox transformation.

Figure 7 Box-Cox transformation

B. Transforming data using Johnson transformation.

Figure 8 Johnson transformation

Question 5 

Use Data to perform

Figure 9 X-bar R chart

A. Provide comments 

From the Xbar-R Chart for the number of cars produced, it can be seen that the sample mean is almost always within the control limits, which means the daily production is quite stable. Despite some small variability, the process appears to be under control. But the range chart shows that there is some change in the daily production hence variability should be tracked to identify unvarying performance (Galetto, 2021).

B. Stability of defective cars.

To check the stability of faulty cars we would have to use control charts for the number of cars repaired in a similar way. When the data points for fixed cars are in control limits and display no major trends and outliers, then there is indication of stable process. Out-of-control points or trends would indicate that the control rate or variation is on the increase or erratic and that improvement should be made in the quality control.

C. Provide comments on stability of car defects. 

The stability of car defects can be studied with the help of control charts for the number of fixed parts. If the plotted points on the control chart are within control limits then it means that resolution of defects process is stable (Okagbue et al., 2021). This will serve to show signs of problem in the defect resolution processes in case of any consistent upward or downward trends in the fixed parts.

Question 6 

A. The comments on sales trend. 

Figure 10 sales trend

B. Comments on the sales seasonality. 

 

Method

Model type	Linear Trend Model
Data	Sales
Length	18
NMissing	0

Figure 11 Trend plot

C. The comments on obtaining of accuracy model.

D. Predict 3 quarter sales.

 

Figure 12 Times series plot

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CONCLUSION 

Concluded that the analysis of the processes of supplier indicated that there is huge variability of delivery time and both the Cp and Cpk indices point to the fact that the process is not capable of sustaining the 25 to 35-day delivery window consistency (Hinton, 2024). To enhance performance, the supplier needs to put more emphasis on lowering variability, keeping the process in line with the target delivery time and continuous monitoring. Such measures will contribute towards delivering a consistent reliable delivery performance.

REFERENCES

Alin, A. (2010). Minitab. Wiley Interdisciplinary Reviews: Computational Statistics, 2(6), pp.723–727. doi: https://doi.org/10.1002/wics.113 

Chalmer, B.J. (2020). Understanding Statistics. CRC Press eBooks. Informa. doi: https://doi.org/10.1201/9780367813161 

Galetto, F. (2021). Minitab T charts and quality decisions. Journal of statistics & management systems/Journal of Statistics & Management Systems, 25(2), pp.315–345. doi: https://doi.org/10.1080/09720510.2021.1873257 

Hinton, P.R. (2024). Statistics Explained. doi: https://doi.org/10.4324/9780429353260 

Okagbue, H.I., Oguntunde, P.E., Obasi, E.C.M. and Akhmetshin, E.M. (2021). Trends and usage pattern of SPSS and Minitab Software in Scientific research. Journal of Physics: Conference Series, 1734(1), p.012017. doi: https://doi.org/10.1088/1742-6596/1734/1/012017 

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