Statistical Analysis Sample on Quality Control

Statistical Quality Control

[Name of Student]

[Name of Professor]

[Date of Submission]

Introduction

            This report sheds light on a well-established pest control company that provides services to the households, businesses and hotels to reduce pest and allow to live a healthy lifestyle. The significance of the Pest control has increased after emergence of the COVDI-19 as the fear among the general population has increased to become more cautious about the unwanted creatives surrounding them (Jiguet, 2020). These unwanted creatures include the cockroaches, bed bugs, poisonous spiders, termites, mice and many others that contaminate food, living area, washrooms and even kitchen. Therefore, the threat to health prevails from these creatures and if they are not eliminated effectively then this could lead to a various health complication that may vary from less serious to life-threatening. Given the complexity and importance of pest control in the United Kingdom, the companies also need to ensure that they use most effective methods of eliminating the pest out of the premises, and meet with the needs of the customers (Baker et al., 2020). Hence, in following report, the analysis is conducted how low service levels could affect the overall customer satisfaction, revenues and company’s reputation in the market. Therefore, reports present technical analysis by using boxplot to determine bad outliers in the data followed by control chart to see if issues with the service prevails in terms of customer’s disagreement. Lastly, empirical analysis is also conducted to test if the service quality really affects the customer satisfaction.

Findings and Results

Descriptive Statistics

            Table 1 provides the descriptive statistics that provides the mean, median, maximum, minimum standard deviation of the data. The observations are collected from National Institute of Standards and Technology (NIST, 2022) The five-number summary is used to present the attributes and characteristics of the data.

Table 1 Descriptive Statistics

            The mean number of the complaints is 16.02 which reveals number of complaints on average company receives 16.02 complaints from the customers those have received. These complaints are related to misbehavior of the staff, ineffective use of methods and material and quality concerns over the pest control. Therefore, it can be determined that on average company receives around 16.03 complaints from the customers but the standard deviation is 5.05 indicating that on number of average complaints could increase or decrease by the value of standard deviation.  In addition to, minimum number of complaints are 10 at least in a one of the month but maximum complaints stand at 31.

Box-plot

            In a large dataset, it is critical to determine if there are outliers in the data or errors that might be human made while creation or compilation of data. Because, presence of outliers in the data could affect overall results and provide misleading insights that may be opposite to the reality (Walker et al., 2018). Therefore, boxplots were used to determine if there are outliers in data that could affect the results.

Figure 1 Boxplot

            From the figure 1 it is evident that there are no outliers in the data and data is free from any outliers that could affect results and data. Hence, it can be said that data is free from any statistical error that could influence the results and the results from the data would be trustworthy and reliable. Therefore, the data containing the number of complaints for 30 months actually is a real data and there is no error or outlier that may be an error or mistake by human.

Control Chart

            Control charts are used to depicts the processes over a period of time and different types of data could be used to see if the processes are under control or not. For instances, a manufacturing company want to see how much variation occurs in the process or how many defective products are produced in each batch of manufacturing. A small number of defects in a manufacturing process are inevitable but when it goes out of control then it can become a problem for the company as the defective products would affect overall company’s reputation in the market and ultimately affect the revenues of the company (Woodall and Faltin, 2019). Because the quality expectations of the customers must be met in order to achieve better position and satisfy the customers. Similarly, referring the case of pest control company, it is evident that number of complaints from the customers is effective to monitor the quality and satisfaction level of the customers with services provided by company.

            The application of the control charts varies industry by industry and is applicable anywhere in the processes of manufacturing or services. Hence, it was used in following case study to see how much complaints company receives every month and if the number of complaints cause of concern for the company of not. See figure 2 control chart

Figure 2 Control Chart for number of complaints per month

            Figure 2 provides control chart for the number of complaints per month, where the gray line presents the upper control limit and yellow line represents the lower control limit that provides a space or corridor under which the number of complaints are acceptable and normal but if the number of complaints outside of the control limits indicates a problem. Similarly, referring to the control chart above, it can be evidently claimed that there have been four instances where number of complaints have exceeded the control limits; point 4, point 15, point 19 and point 24. These are instances at which the number of complaints have exceeded the control limits that indicates serious problem with the services provided by company. This control chart reveals that there are problems and issues with the services provided by the company and need an urgent intervention to control the quality concerns of the customers and ensure a service level quality to the customers.

Customer Satisfaction Survey

            In order to measure the customer satisfaction, company conducts survey from each customer after one week of services, where a 5-point scale is used to measure customer’s satisfaction with the service. Table provides the scale of satisfaction measurement

Table 2 Satisfaction Scale

            Table 2 provides the scale used by the company to measure the satisfaction level; the customers were asked how much are they satisfied with the service of company, where 5 represents the strongly satisfied, 4 represents satisfied, 3 represents neither satisfied nor dissatisfied which is a neutral state, 2 represents the dissatisfied and 1 represents the strongly dissatisfied. Based on each month’s data, following descriptive statistics were calculated as follows

Table 3 Descriptive Statistics of the Customer Satisfaction

            Table 3 presents the descriptive statistics of the customer satisfaction, where it can be determined that mean satisfaction of the customers is 2.88 with standard deviation of 1.182 which reveals that mean satisfaction could increase or decrease by the value of standard deviation. Meanwhile, the minimum satisfaction was 0.41 and maximum level of satisfaction is 4.82 that level of satisfaction. The mean value of customer satisfaction shows that there are issues in the services provided by the company because the average customer satisfaction is 2.88 that is near to neutral state where customer neither is satisfied nor is dissatisfied and this state of customer is also a cause of concern that why customers are not actually satisfied with the service. Because, if the customers are not satisfied with the service then this would affect company market position since customers will not encourage or refer to others to use services of company. Therefore, the company’s word of mouth marketing would be negatively affected. Meanwhile, in order to depict the number of complaints with level of customer satisfaction each, following graph was constructed

Figure 3 Complaints Vs Customer Satisfaction by month

            Figure 3 presents the number of complaints vs customer satisfaction each month, where blue bars represent the number of complaints and orange line represents the customer satisfaction each month. The figure clearly reveals that number of complaints increases the customer dissatisfaction as in month 3, 4 and 5 the level of complaints was higher so the customer dissatisfaction was also high in these months. Similarly, same trend can be observed in month 15, 19, 22 and 24 as well, which reveals that customer satisfaction is associated with lower number of complaints.

Correlation

            In preceding section, the number of complaints were depicted with customer satisfaction level, and it was found that number of complaints associated with high customer dissatisfaction. However, there was no empirical evidence based on which it can be claimed that there is a significant relationship between the number of complaints and customer satisfaction. Therefore, in following section, Pearson’s correlation is used to determine the association between two variables. Number of complaints and customer satisfaction are two quantitative variables, and Pearson’s correlation allow to measure relationship between both variables (Pandey, 2020). The Pearson’s correlation reveals three important characteristics of the relationship between two variables. First characteristic of the relation is either the relation is positive or negative, because a positive relation means change will be in same direction but relation is negative than change will be in opposite direction in variables. The direction of variable is represented by the sign of coefficient positive or negative.

            The second characteristic revealed is strength of the relationship between the variables, where the coefficient represents the strength which if remains below 0.5 then relation is indicated as weak but if coefficient remains above 0.5 then relation is interpreted as strong. Meanwhile, the last characteristic revealed by the Pearson’s correlation is significance of the relation that reveals either relation is statistically significant or not. Because, if the correlation is not significant than it may indicate the relation is influenced by statistical error and result may be misleading. Table 4 provides the results of the Pearson’s correlation

Table 4 Pearson’s Correlation

            Table 4 provides the relation between number of complaints and customer satisfaction relation with each other, where coefficient is -0.739; since the coefficient has negative sign then relation is said to be negative and value of coefficient is also greater than 0.5 that shows relation is strong. Therefore, referring to the results of correlation, it can be determined that there is negative strong correlation between the number of complaints and customer satisfaction. Hence, it can be interpreted that if the number of complaints increases then customer’s satisfaction will decrease as a result. In same case, if the number of complaints declines then customer satisfaction will increase as result. Thus, company must focus on reducing the number of complaints in order to increase the customer satisfaction, sustain reputation and enhance word of mouth.

Regression

            In case study of pest control company, the ordinary least square (OLS) regression has been used to determine extent to which number of complaints affect the customer satisfaction (Gogtay, Deshpande and Thatte, 2017). Table 5 provides the summary output of the regression

Table 5 Summary Output

            The multiple R represents the correlation coefficient between the variables indicating the relation between the independent and dependent variable that there is a strong relation between the variables. Meanwhile, R-square of the regression is 0.547 that shows that 54.7% variance of the customer satisfaction is being predicted by number of complaints in the model (Gogtay, Deshpande and Thatte, 2017). However, other variance could not be accounted for and it remains the residual of the regression model. Furthermore, the table 6 provides the ANOVA

Table 6 ANOVA Table

            The table 6 provide the significance of the model, where significance F value also termed as p-value is 0.00 that is less than significance threshold 0.05. Hence, it can be determined that regression mode is significant and results of the regression can be trusted because mode is not influenced by any statistical error (Gogtay, Deshpande and Thatte, 2017). Since, regression model is significant, hence, results can be used to draw implications. Table 7 provides the coefficient table showing effect of one variable on another

Table 7 Coefficient

            Table 7 reveals that if one complaint increases then it will decrease the customer satisfaction by -0.12; and if the one complain declines then customer satisfaction will improve by 0.12. Since, the p-value of the coefficient is 0.00 that is less than alpha 0.05; thus, it can be asserted that effect of complaints on the customer satisfaction is statistically significant (Gogtay, Deshpande and Thatte, 2017). This implies that for every complaint received by company, it losses 0.12 in customer satisfaction and increases distrust, loss of new customers, loss of word of mouth and ultimately company’s reputation and revenues are affected at the same time.

Conclusion and Recommendations

            The selected case study for the technical study is pest control company in the United Kingdom that provides services to eliminate unwanted creatures that includes bugs, cockroaches, mice and other creatures that contaminate the household items. As it is important to live a healthier life to avoid health complications, hence, pest control plays an important role. Therefore, in order to satisfy customers, the service quality plays an important role in order to sustain market position and achieve greater revenues. Hence, this technical report focuses quality of services and customer satisfaction at pest control company and try to analyze quality issues and customer satisfaction through empirical evidences. In this regards, 30 months’ observations in which number of monthly complaints and customer satisfaction was measured through 5-point scale.

The results of the boxplot revealed that data is clean and there is no error or outliers that could influence the results. The control chart shows four instances in 30 months’ observations where number of complaints were significantly and out of control that needed interventions to reduce the complaints. In addition to, the results of correlation also revealed that there is a strong negative and significant relationship between the number of complaints and customer satisfaction. Regression analysis also provided similar results where it is found that number of complaints have a significant and negative effect on the customer satisfaction. Therefore, if the number of complaints increases then customer dissatisfaction decreases. This emphasize on the company to ensure

·       Staff is friendly with the customers and cater to all their requests while providing services

·       The material and equipment used for the pest control should be upgraded to meet customer demands

·       The company should provide follow-up services twice a month to ensure there are no complaints from the customers

References

E. Baker, S., A. Maw, S., Johnson, P.J. and W. Macdonald, D., 2020. Not in my backyard: Public perceptions of wildlife and ‘pest control’in and around UK homes, and Local Authority ‘pest control’. Animals, 10(2), p.222.

Gogtay, N.J., Deshpande, S.P. and Thatte, U.M., 2017. Principles of regression analysis. Journal of the Association of Physicians of India, 65(48), pp.48-52.

Jiguet, F., 2020. The Fox and the Crow. A need to update pest control strategies. Biological conservation, 248, p.108693.

NIST. 2022. Control Charts. [Online] Available at: https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm (Accessed 6th November 2022)

Pandey, S., 2020. Principles of correlation and regression analysis. Journal of the practice of cardiovascular sciences, 6(1), pp.7-7.

Walker, M.L., Dovoedo, Y.H., Chakraborti, S. and Hilton, C.W., 2018. An improved boxplot for univariate data. The American Statistician, 72(4), pp.348-353.

Woodall, W.H. and Faltin, F.W., 2019. Rethinking control chart design and evaluation. Quality Engineering, 31(4), pp.596-605.