1. QUALITY CONTROL AND QUALITY ASSURANCE (Contd.)
Chapter 28
QUALITY CONTROL AND QUALITY ASSURANCE (Contd.)

2. SPC Errors Type I error Type II error
Concluding a process is not in control when it actually is or concluding that nonrandomness is present when it is only randomness that is present.
Type II error
Concluding a process is in control when it is not that nonrandomness is not present when it is present.

3. Type I Error Figure 10.8 Mean LCL UCL /2
Probability of Type I error

4. Observations from Sample Distribution
Figure 10.9
Sample number
UCL
LCL 1 2 3 4

5. Mean and Range Charts Figure 10.10A Detects shift x-Chart
(process mean is
shifting upward)
Sampling
Distribution
UCL
x-Chart
Detects shift
LCL
UCL
Does not detect shift
R-chart
LCL

6. Mean and Range Charts Figure 10.10B Does not reveal increase x-Chart
Sampling
Distribution
(process variability is increasing)
UCL
Does not reveal increase
x-Chart
LCL
UCL
R-chart
Reveals increase
LCL

7. Control Chart for Attributes
p-Chart - Control chart used to monitor the proportion of defectives in a process.
c-Chart - Control chart used to monitor the number of defects per unit.

8. Use of p-Charts
When the data consists of multiple samples of several observations each

9. Use of c-Charts
Table 10.3
Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.

10. Use of Control Charts What size samples to take.
At what point in the process to use control charts.
What type of control chart to use:
Variables
Attributes

11. Run Tests Run test – a test for randomness.
Any sort of pattern in the data would suggest a non-random process.
All points are within the control limits - the process may not be random.

12. Nonrandom Patterns in Control charts
Trend
Cycles
Bias
Mean shift
Too much dispersion

13. Counting Runs Counting Above/Below Median Runs (7 runs)
B A A B A B B B A A B
Counting Up/Down Runs (8 runs)
U U D U D U D U U D

14. Process Capability Process variability relative to the specifications.
Tolerances or specifications
Range of acceptable values established by engineering, design or customer requirements.
Process variability
Natural variability in a process.
Process capability
Process variability relative to specification.

15. Process Capability Figure 10.15
Lower Specification
Upper Specification
A. Process variability matches specifications
B. Process variability well within specifications
C. Process variability exceeds specifications

16. Process Capability
Case C, A manager in case C can take the following steps:
Redesign the process to obtain the desired output.
Use an alternative process to obtain the desired output.
Retain the current process but attempt to eliminate output using 100 percent inspection.
Examine the specifications to see if they are necessary or can be relaxed.

17. Process Capability
Process Variability is the key factor in Process Capability.
It is measured in terms of process standard deviation.
Process capability is considered to be + 3 Standard Deviations from the process mean.
An insurance company provides a service of registering a new membership ( filling of form) in 10 mins, acceptable range of variation around the time is + 1 minute, the process has a standard deviation of 0.5min.It would not be capable because + 3 SDs would be Mins, exceeding the specification of + 1 minute.

18. Process Capability Ratio
Process capability ratio, Cp =
specification width
process width
Upper specification – lower specification 6
Cp =

19. Improving Process Capability
Simplify
Standardize
Mistake-proof ( Poka Yoke)
Upgrade equipment
Automate

20. Traditional cost function
Taguchi Loss Function
Figure 10.17
Cost
Target
Lower spec
Upper spec
Traditional cost function
Taguchi cost function

21. Limitations of Capability Indexes
Process may not be stable
Process output may not be normally distributed
Process not centered but Cp is used

22. Operations Strategy WRT Q/C
Neither necessary nor desirable to use Control charts for every production process.
Some processes are highly stable and do not require Control Charts.
Use control Charts for new processes till they obtain stable results.
Managers should use Control Charts on processes that go out of control.
Judicious use of SPC will ensure detection of departures from randomness in a process.