c-chart……………………………………………………………………………..11
Is the process in our control or not?.............................................................................12-13
DISCUSSION & RECOMMENDATION
APPENDIXES
Appendix 1……………………………………………………………………………….17
Appendix 2……………………………………………………………………………….18
Appendix 3……………………………………………………………………………….19
INTRODUCTION & PROBLEM DESCRIPTION
In the recent weeks, we have received high number of customer returns.
The problem is associated with the size, and the surface quality of the steel roots in the hydraulic products, which have caused them to leak.
The resolution of this issue is extremely important for a whole of the organisation, due to high competition from Chinese and India manufactures.
Our aim is to satisfy customer all the time and more effectively, as well as reduce the waste at every level of the organisation. As part of this plan, the company has recently adopted a number of quality management tools associated with the Total Quality Management. One of these tools is Statistical Process Control, which the company wants to use to measure the performance of their manufacturing processes, to ensure that the processes meet the required stand
METHODOLOGY
This denotes the collection of a random daily inspection sample of three steel rods. The selected products are then inspected and two types of data are collected: the diameter of the steel rod and the number of surface errors. The collected data take over a 25 days period. The collected data is summarised as follows:
- The diameter of the selected steel rods was measured and recorded in centimetres over a 25-day period. The results are shown in table 1.
- The number of surface errors in the selected steel rods was calculated and recorded over a 25-day period. The results are shown in table 2.
Table 1: Diameter measurements (cm) Table 2: Number of surface errors
RESULTS
What type of SPC chart(s) should be used to monitor this process and why?
To monitor Statistical Process Control we should use control charts for identifying processes that are out of the control.
For the first type of the data which is the diameter of the steel rods (cm), we are using variable charts, mean (x – chart) and range charts (R – chart).
The reason why is because when using the x–charts and the R–charts observations are variables, which are usually products measured for size or weight.
For the second type of data, which is number of surface errors, we are using
c–chart because this type of chart is used to control the number of defects per unit of output.
What are the 3-sigma control limits for these processes?
VARIABLE DATA
Setting mean chart limits (x-Charts)
Because the process historical data is unavailable and we do not know the standard deviation, we usually calculate 3-sigma control limits based on the average range values. Appendix A provides the necessary conversion for us to do so. The range is defined as a difference between the one largest and the smallest items in sample.
To set 3-sigma (upper, central and lower) control limits for sample mean (x– Chart) we are using equation:
Upper control limit:
UCLx = x + A2 R
Central control limit:
CL= x
Lower control limit:
LCLx = x - A2 R
To set up action and warning limits we are using equation:
Upper action line:
UAL = x + 3 A2 R
Upper warning line:
UWL = x + 2 A2 R
Process or grand mean:
CL = x
Lower warning line:
LWL = x – 2 A2 R
Lower action line:
LAL = x – 3 A2 R
Where:
R = average range of the sample (value found in Appendix 2)
A2 = value found in the Appendix 1
x = mean of the sample means (value found in Appendix 2)
x = ∑(X1…Xn)
n
n is number of sample
SOLUTION
- (X-bar chart) 3 – sigma control limits
x = 10.57547
A2 = looking in the Appendix 1, for a sample size of 3 in the mean factor A2 column, I found the value 1.023.
R = 0.322
Upper control limit:
UCLx = x + A2 R
= 10.57547 + (1.023)(0.322)
= 10.57547 + 0.329406
= 10.90487
Central control limit:
CL = 10.57547
Lower control limit:
LCLx = x – A2 R
= 10.57547 – 0.329406
= 10.24606
Setting range chart limits (R – Charts)
To set 3-sigma (upper, central and lower) control limits for the range chart
(R – Chart) we are using equation:
Upper limit control:
UCLr = D4 R
Central limit control:
CL = R
Lower limit control:
LCLr = D3 R
Where:
D3 and D4 = values from Appendix 1
R = average range of the sample (value found in Appendix 2)
R = ∑ (R1…Rk)
k
k is the number of subgroups
SOLUTION
- (R-bar chart) 3-sigma control limits
D3 = looking in the Appendix 1, for a sample size of 3 in the lower range factor D3 column, I found the value 1.023
D4 = looking in the Appendix 1, for a sample size of 3 in the upper range factor D4 column, I found the value 2.574
R = 0.322
Upper control limit
UCLr = D4 R
= (2.574) (0.322)
= 0.828828
Central control limit:
CL = R
= 0.322
Lower control limit:
LCLr = D3 R
= (0) (0.322)
= 10.57547 – 0.329406
= 0
ATTRIBUTE DATA
Setting the 3-sigma control limits for the c - charts
Upper control limit:
UCLc = c + 3√c
Central control limit:
CL = c
Lower control limit:
LCLc = c - 3√c
Where:
c = the mean of the number of errors per unit
SOLUTION
c = 1.32 (value found in Appendix 4)
Upper control limit:
UCLc = c + 3√c
= 1.32 + 3√1.32
= 1.32 + 3(14.891)
= 1.32 + 3.44674
= 4.76674
Central control limit:
CL = 1.32
Lower control limit:
LCLc = c - 3√c
= 1.32 - 3√1.32
= 1.32 - 3(14.891)
= 1.32 - 3.44674
= 0 ← (sine it cannot be negative)
Are the processes in control according to the control limits?
According to the control limits, what we have set up, the finding are - the first process is out of the control, and the second process is in control.
The reason why we have assumed that the first process is out of the statistical process control is because; as we can see from the graph below the average of the sample falls outside the upper and lower control limits in the range chart.
The next step will be to investigate the process to identify assignable causes and to correct them, thereby bringing the process under control. Because the primary focus of control charts is to bring the process back into control.
The reason why I assumed that the second process is in control is because as we can see from the graph below the average range sample falls within the lower and upper limit.
DISCUSSION AND RECOMMENDATION
Is the problem in the hydraulic production process?
From my findings, there is clear evidence that one of the process might be out of the control. However, there is only one point outside the control limits, which means that we should repeat the control process, because we could have done something wrong when the data was taken.
Normally when there is evidence that process is out of the control we should stop the production, eliminated the causes and start again. However, we have to keep in mind that when we stop the production line it will cost the money. In addition, we need remember that SPC is a new improvement plan in our organisation, and we could have done some mistakes when data was recorded. When SPC is implemented, we must be sure that the data and measurements are recorded precisely. That is why the best option for us to do is to repeat the control process.
CONCLUSION
How might you use the quality tools to determine the source of the defects and where might you start your improvement efforts to eliminate the causes.
The aim of quality control is to ensure each finished product meets the standards set out by the organisation. To achieve this quality standards inspectors check the finished products and reject defective one. This system detects quality problems at the end of the production process before the products are selling to the potential customers. However, we have to remember that inspectors are only human. They become tried and bored in the end of a day; machines itself has variability.
A new approach of improving quality in our organisation is Total Quality Management system. It is the method where everyone in the business has to commits in achieving the quality standards; not only inspectors at the end of the production process. It means those quality standards are check at every stage of the production process. In addition, we have to check the machine regularly, as well as look at measurements methods, communication style among the employees and employers, responsibilities within departments, and to invest more money in training for all employees and employers.
REFERENCES
Heizer, J. H, and Render, B. (2010), Operations management, 10th edition, London: Pearson
APPENDICES
Appendix 1
Tabular values for X-bar and range charts
Appendix 2
Mean and range value for the diameter steel rods
Appendix 3
Total umber of surface errors
