1. Statistical Methods for Biotechnology Products
Part I: Biopharmaceutical Product
Statistical Quality Control by
Professor, Jen-pei Liu, PhD, Professor
Division of Biometry, Department of Agronomy National Taiwan University, and
Division of Biostatistics and Bioinformatics
National Health Research Institutes
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

2. Statistical Quality Control
1. Introduction
2. Concept
3. Simple Graphical Techniques
4. Control Charts
and R Charts
6. Process Capability
7. P Charts
8. C Charts
9. Six Sigma Concept
10. Summary
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

3. 1 Introduction Total Quality Control (TQC) Malcolm Baldridge Award
Products or service of the highest quality
Avoid defective products
Avoid customer complaints
Malcolm Baldridge Award
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

4. 2 Concepts Single Process Process Output Inputs
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

5. 2 Concepts
Breakdown of a product or service into a series of interrelated subprocesses
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

6. From: Cronin, et al (Clinical Chemistry, 2004)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

7. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

8. 2 Concepts Statistical Process Control (SPC)
The use of statistical quality control techniques is called statistical process control
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

9. 2 Concept Detection Approach to Quality Control
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

10. 2 Concept Prevention Approach to Quality Control
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

11. 2 Concept Costs of Inspection vs Cost of Undetected Defects
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

12. 2 Concepts
The control chart is based on sample information, measurable or qualitative from the process at different point in time
Control charts for variables(measurable quantity)
Control charts for attributes(attribute data)
Costs of Inspection vs cost of undetected defects
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

13. 2 concepts On-line quality control technique - control charts
Off-line quality control technique
- Experimental design
- Taguchi methods for optimizing the
process to set level key process
variables for yielding the highest
possible quality
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

14. 3 Simple Graphical Techniques
Specification Limits : A variable should be if it is to meet function and quality standards
The largest allowable value of a variable is called the upper specification limit(USL)
and the lowest allowable value is the lower specification limit(LSL)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

15. 3 Simple Graphical Techniques
Example: Copper thickness of 50 printed
circuit board
Specification:
0.001~0.003 in.
26/50(52%) not meet specification
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

16. 3 Simple Graphical Techniques
A Pareto chart is a bar chart where each bar is associated with a particular area of concern and the bars are drawn, from left to right, in order of decreasing height
PC Rejection DATA
Type of Defect Number of Rejected Boards
Poor electroless coverage
Lamination problems
Low copper plating
Plating separation
Etching problems
Miscellaneous
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

17. 3 Simple Graphical Techniques
Pareto Chart
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

18. 3 Simple Graphical Techniques
The fishbone diagram is a graphical way of displaying the possible reasons, or causes, of a particular problem
The fishbone diagram is called the cause-and-effect diagram
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

19. 3 Simple Graphical Techniques
Construction of a cause-and-effect diagram
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

20. 3 Simple Graphical Techniques
A cause-and-effect diagram
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

21. 4 Control Charts
To differentiate controlled variable-assignable causes from uncontrolled variables-chance variation
(W.A. Shewhart,1931)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

22. 4 Control Charts
Example of assignable causes: types of raw materials used, differences in workers used, slow wearing down of the machinery, changes in temperature or humidity
Statistical Control:
When all the assignable causes have been found and eliminated,a process is then said to be statistical control
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

23. 4 Control Charts A typical Control Chart
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

24. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

25. 4 Control Charts Centerline:grand average of all the sample statistics
Lower and upper Control Limits:
Determined by the sampling distribution and are positioned 3 standard deviations above and below the centerline
Out of Control: Points outside the control limits
In control: Points within the control limits
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

26. 4 Control Charts Classification of Control Charts
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

27. 4 Control Charts
Difference between Control limits and specification limits
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

28. 5 and R Charts
The Chart monitors the means of small samples taken from a process
The R Chart monitors the range(or variability) of small samples taken from a process
The Control Limits of the Chart are computed by using the centerline of the R chart
The Chart should not be used without constructing the corresponding R Chart
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

29. 5 and R Charts Data Sample Number 1 2 ………. K Sample Size n n ……… n
Sample mean ……
Sample Range R1 R2 ……. Rk
k=20 to 25 , n=3 , 4 or 5
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

30. 5 and R Charts The R Chart Centerline: Upper control limit UCL=D2
Lower control limit LCL=D1
D1and D2 depend on sample size n and can be found in table
If n  6; D1= LCL=0
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

31. 5. and R Charts Product: Precision ball bearings
Characteristic: bearing diameter
Target value: in.
Specification Limits: in.
Data: Hourly measurements of 5 learning diameters (x1000) from the target value
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

32. 5 and R Charts
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

33. 5 and R Charts N=5 K=25 R=6.56 in. D2=2.115 D1=0
UCL=D =(2.115)(6.56)=13.874
LCL=D =(0)(6.56)=0
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

34. 5 and R Charts R Charts for ball bearing diameters
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

35. 5 and R Charts Charts Centerline: Upper Control limit: UCL=
Lower Control limit: LCL=
A: depends upon the sample size and can be found in Table
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

36. 5 and R Charts Example: K=25 n=5 =0.048 =6.56 A1=0.577
UCL=0.048+(0.577)(6.56)=3.83
LCL= (0.577)(6.56)=-3.74
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

37. 5 and R Charts Chart for ball bearing diameters
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

38. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

39. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

40. 1. Most sample means are scattered at random around the central line
2. A few sample means spread out and are close to either the lower or upper control limit.
3. No sample mean is outside the control limits.
4. No recognized pattern of the distribution of sample means is observed.
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

41. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

42. 1. A sample mean is outside the control limits 3
The probability of this event under normality
assumption is about In general, from Chebyshev's inequality, there is a probability of 0.11 that a sample mean is outside the three standard deviation control limits (or action limits).
2. Under normality assumption, the probability of two out of three consecutive means outside two standard deviation warning limits is
3(0.05)2(0.95) =
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

43. 3. Eight consecutive sample means are on the same side of the central line. The probability of this event for any distribution symmetrical about the population mean is
4. Sometimes, it is also worthwhile noticing that four of five successive sample means are outside the one standard deviation limits because that probability of this event under the normality assumption is given by
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

44. 5. In many cases, samples collected from two or
more underlying distributions are combined
together for construction of control chart. An
unnatural pattern of all sample means scattering around the central line with unnaturally small fluctuations will occur. This type of control charts is invalid because samples from different distributions have been combined. This phenomenon is referred to as stratification.
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

45. 6. If half the samples come from one distribution and the other half come from another distribution, the sample means will scatter within the control limits rather than concentrate on the central line. This phenomenon is called mixture.
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

46. 7. The existence of a trend for a manufacturing process can be identified by the following unnatural patterns:
(a) One sample mean outside the control limits on one side is followed by the next consecutive sample mean, which is outside the control limits on the other side. (b) There are at least six consecutive sample means, one of which is greater (or lower) than the previous one.
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

47. 8. The presence of a systematic variable in the process is suggested if at least eight consecutive sample means alternate large, small, large,and small without interruption. This pattern may occur when samples are selected alternately from different operators or machines.
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

48. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

49. 2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

50. 6 Process Capability
Process capability refers to the ability of a process to stay within its specification limits
Actual process spread: Under normal assumption,all measurements generated by the process should be within a range of 6
Allowable process spread: The distance between the specification limits
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

51. 6 Process Capability The process capability index is defined by
Where is the SD of measurements from the process
A cp Continue to maintain
B cp < Improve to A
C cp < Improve at once
D cp < Consider stopping product
E cp < Stop production at once
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

52. 6 Process Capability
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

53. 6 Process Capability
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

54. 6 Process Capability The Cpk Index Min=minimum K-factor :
The relationship between cpand cpk
Cpk=Cp(1-k)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

55. 6 Process Capability Data:Ball bearing diameters
Target value: USL=10 LSL=-10
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

56. Cpk=Cp(1-k)=(1.182)( )=1.176
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

57. 7 The P-Chart
A control chart for controlling the percent of defectives in a sample is called a P chart
Sample Number … k
Sample Size n1 n2 … nk
# of defectives x1 x2 … xk
% of defective
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

58. 7 The P-Chart Centerline : Upper control limits UCL=
Lower control limits LCL=
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

59. 7 The P-Chart # of rejected circuit boards
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

60. 7 The P-Chart
Since =0.054 and =305(given in table 16.11),the average sample size method gives control limits of or or
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

61. 7 The P-Chart Average Sample Size
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

62. 7 The P-Chart Variable Sample Sizes
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

63. 8 The C-Chart
A C-chart is used when the objective is to control the number of defects per unit
A defective item may have more than one defect
A defect is just a flaw or nonconformity
To monitor defects requires determination of the inspection unit
Example:
Accounting records: # of error per 10 records
Sheet metal:surface flaws in 1 square foot
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

64. 8 The C-Chart (Poisson Distribution)
Inspection unit 1 2 …K
#of defects C1 C2…Ck
Centerline:
Upper Control limit UCL=
Lower Control limit LCL=
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

65. 8 The C-Chart The Data of Solder Defects
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

66. 8 The C-Chart
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

67. 8 The C-Chart Solder Defects
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

68. 9 Six Sigma Concept
A management method to pursue excellence in quality
Improvement in manufacturing capability
Eliminate waste in manufacturing process
Improve manufacturing quality
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

69. 9 Six Sigma Concept The usual concept
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

70. 9 Six Sigma Concept The concept 1.5 off the target value
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

71. 9 Six Sigma Concept 製程命中目標與偏離目標1.5 缺點之對照表
製程命中目標與偏離目標1.5 缺點之對照表
PPM : Part per Million; Source: Pan and Lee (2003)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

72. 9 Six Sigma Concept Motorola(1987) started six sigma program
Won the Baldridge award in 2 years
A five-fold growth between 1987 and 1997
A 20% profit increase per year
A reduction of 14 billion USD in cost
Allied Signal(1991)
GE(1995)
Application to all different business
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

73. 9 Six Sigma Concept
Source: Pan and Lee (2003)
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only

74. 10 Summary Graphical Techniques Charts R Charts P Charts C Charts
Process Capability
Six Sigma
2018/11/21
Copyright by Jen-pei Liu, PhD, Products are just for illustrations only