Training Module including 116 slides and 6 exercises covering Introduction to Statistical Process Control, The Histogram, Measure of Location and Variability, Process Control Charts, Process Control Limits, Out-of-Control Criteria, Sample Size and Frequency, and Out-of-Control Action Plan.

1. Operational Excellence – Statistical Process Control Presented by Frank Adler, Ph.D. www.Operational-Excellence-Consulting.com

2. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

3. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

4. The History of Statistical and Process Thinking The quality control methods and techniques used today got their start in the American Civil War, when Eli Whitney tried in year 1789 to produce 10,000 rifles by copying one rifle, part by part. At that time most of the products were hand made by small owner-managed shops and product parts were thus not interchangeable. The result of Whitney’s mass production trail was that the rifles did not work as well as the handmade rifles. In addition, the copied parts did not fit as expected.

5. The History of Statistical and Process Thinking GO - Test NO-GO - Test The first time that one presented machine produced parts was 1851 at the industry exhibition in the Crystal Palace in London. An American gun smith took 10 working guns, took them apart, mixed all the parts in a box and re-assembled them again. This was found a quite surprising “experiment”.

6. The Traditional Production Concept The Detection Control Scheme Process Inspection Good Bad Repair Scrap + Monitor/Adjust

9. Statistical Thinking - A Definition All work is a series of interconnected processes All processes vary Understanding and reducing variation are keys to success ASQ

10. Customer Satisfaction Process/ System M aterial M achines M ethods M en E nvironment The Variation Management Approach

12. The A and O of process control and continuous process improvement is to understand the meaning and causes of variation in the outcome of the process. Variation Management – Continuous Improvement

14. Remarks or Questions ?!?

15. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

23. The Histogram – The Normal Distribution

24. The Histogram – Exercise 1 Distribution of Heights of U.S. Population: Use the plot area below to construct a histogram from the random sample of heights on the right:

25. Remarks or Questions ?!?

26. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

30. Measure of Variability – Sample Variance x 3 x 2 x 1 x 10 x average _

34. Measure of Variability – The Principle of Subgrouping Time t Performance Characteristic Process not in control average Subgroup size n = 5 Number of subgroups N = 7

36. Measure of Variability – Difference between s LT and s ST Long-term standard deviation : Short-term standard deviation : The difference between the standard deviations s LT and s ST gives an indication of how much better one can do when using appropriate production control, like Statistical Process Control (SPC).

37. Measure of Location and Variability – Exercise 2 Distribution of Heights of U.S. Population: Calculate the Mean Value or Average, Median, Range, and long-term Standard Deviation of the sample data. You may copy the data into MS Excel and simplify the calculations. Mean Value = Median = Range = Long-term Standard Deviation =

38. Remarks or Questions ?!?

39. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

40. Process Control Charts – Types of Control Charts Count or classification (attribute data) Measurements (variable data) Count Classification (Yes/No) Incidences or nonconformities Defectives or nonconforming units Fixed oppor- tunity Variable oppor- tunity Fixed subgroup size Variable subgroup size Variable subgroup size Subgroup size of 1 Fixed subgroup size c - chart u - chart np - chart p - chart x chart x-bar R chart x-bar s chart Type of data

41. Process Control Charts – The x - Chart The x - chart is a method of looking at variation in a variable data or measurement. One source is the variation in the individual sample results. This represents “long term” variation in the process. The second source of variation is the variation in the range between successive samples. This represents “short term” variation. Individual or x - charts should be used when there is only one data point to represent a situation at a given time. To use the x - chart, the individual sample results should be sufficient normally distributed. If not, the x - chart will give more false signals.

42. Process Control Charts – x/mR Chart Example

43. Process Control Charts – The Central Limit Theorem Regardless of the shape of the distribution of a population, the distribution of average values, x-bar’s, of subgroups of size n drawn from that population will tend toward a normal distribution as the subgroup size n becomes large. Laplace and Gauss or The standard deviation s x of the distribution of the average values is related to the standard deviation s of the individual values by the following: _

45. Process Control Charts – (x-bar/R) - Chart Example

46. Process Control Charts – The (x-bar/s) - Chart The (x-bar / s) - chart is a method of looking at sources of variation. One chart looks at variation in the subgroup averages x-bar. The other chart examines variation in the subgroups standard deviation s . The (x-bar / s) - chart can be used whenever one can use the (x-bar / R) - chart. The (x-bar / s) - chart should be used instead the (x-bar / R) - chart if the subgroup is larger than 10. In this case, the standard deviation is a better measurement than the range for the variation between individual measurements in a subgroup.

47. Process Control Charts – Exercise 3 Throw the Dice: Step 1: Throw the dice 30 times and record the results in the table on the right. Step 2: Draw a Histogram of the 30 data points in one of the spreadsheets below. Step 3: Calculate the average to 2 consecutive throws and draw the histogram of the resulting 15 data points. What do you see and why?

50. Process Control Charts – The Binomial Distribution Number of defect items 1 0 2 3 4 5 6 7 8 9 Average

51. Process Control Charts – The p - Chart The p - chart is used to look at variation in the yes/no type. It can for example be used to determine the percentage p of defective items in a group of items. The number n of items in each group has not to be constant, but should not vary more than 25 %. Operational definitions must be used to determine what constitutes a defective item. The percentage of defect items is given by

52. Process Control Charts – The p – Chart Example

53. Process Control Charts – The np - Chart The np - chart, like the p - chart, is used to look at variation in yes/no type attributes data. np - charts are used to determine the number np of defective items in a group of items. The p - chart looked at the percentage of defective items in a group of items. Because the np - chart uses the number of defects, it is easier to use. However, the major difference between the np - chart and the p - chart is that the subgroup size has to be constant for the np - chart. This is not necessary for the p - chart.

56. Process Control Charts – The Poisson Distribution Number of defects 1 0 2 3 4 5 6 7 8 9 Average

57. Process Control Charts – The c - Chart The c - chart is used to look at variation in counting-type attributes data. It is used to determine the variation in the number of defects in a constant subgroup size. For example, a c - chart can be used to monitor the number on injuries in a plant. In this case, the plant is the subgroup. To use the c - chart, the opportunities for defects to occur in the subgroup must be very large, but the number that actually occur must be small.

58. Process Control Charts – The u - Chart A u - chart is used to examine the variation in counting-type attributes data. It is used to determine the variation in the number of defects per inspection unit (subgroup). The size of the subgroup does not have to be constant. The subgroup size, n , for a u - chart is expressed in terms of the number of inspection units. The u - chart is very similar to the c - chart. The only difference is that the subgroup size for the c - chart must be constant. This is not necessary for the subgroup size of a u - chart. To use the u - chart, the opportunities for defects to occur in the subgroup must be very large, but the number that actually occur must be small.

59. Process Control Charts – Charts for Attribute Data Defective Items Defects Number (constant subgroup size) Percentage (variable subgroup size) np - chart c - chart u - chart p - chart

60. Process Control Charts – Summary Statistics Mean Value Standard Deviation Normal Poisson Binomial Distribution x 1 , x 2 , ..., x N are the measurements and N is the number of measurements. (np) 1 , (np) 2 , ..., (np) N are the number of defects in the N subgroups and n, n 1 , n 2 , ...,n N are the number of items in each subgroup. (np) 1 , (np) 2 , ..., (np) N are the number of defects at each time and N is the number of measurements/subgroups.

61. Process Control Charts – Exercise 4 Black Beads: Step 1: Take 20 beads out of the bag and record the number of black beads in the sample. Step 2: Repeat Step 1 until you have 25 data points. Step 3: Draw the histogram of the 25 data points in the left spreadsheets below. Step 3: Select the correct process control chart and draw it in the right spreadsheet.

62. Remarks or Questions ?!?

63. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

65. Process Control Limit – Upper & Lower Control Limit Upper Control Limit (UCL) = average + 3*sigma Lower Control Limit (LCL) = average - 3*sigma average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

66. Process Control Limit – Upper & Lower Control Limit Because the variation of a process is not known in before hand, one can not calculate or define the control limits in advance . Control limits are characteristics of a stable process . They bound the variation of the process that is due to common causes . The calculation of the control limits should be based on at least 20 to 25 data points from a process that was in statistical control (stable). The limits should not be recalculated and modified unless there is a reason to do so (e.g. a process change).

67. Process Control Limit – Two Types of Process Variability where the constant d 2 depends on the number of items in each subgroup used to calculate the range. The LT and ST subscripts represent long-term and short-term variability. The difference between s LT and s ST gives an indication of how much better one can do when using SPC.

68. Process Control Limit – The x - Chart Upper control limit = Lower control limit = Upper control limit = Lower control limit = The x- chart The R- chart , where x 1 , x 2 , ..., x N are the measurements, N the number of measurements, , and .

69. Process Control Limit – The x-bar/R - Chart Upper control limit = Lower control limit = The R- chart Upper control limit = Lower control limit = The x-bar - chart where x-bar 1 , x-bar 2 , ..., x-bar N are the averages of each subgroup, n the number of items in a subgroup, N the number of subgroups, . , and

70. Process Control Limit – Factors for x- and x-bar/R - Charts n 2 3 4 5 6 7 8 9 10 A 2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 D 3 0 0 0 0 0 0.076 0.136 0.184 0.223 D 4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 d 2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

71. Process Control Limit – The x-bar/s - Chart Upper control limit = Lower control limit = Upper control limit = Lower control limit = The s- chart The x-bar - chart , and where x-bar 1 , x-bar 2 , ..., x-bar N are the averages of each subgroup, s 1 , s 2 , ..., s N are the standard deviations of each subgroup, n the number of items in a subgroup, N the number of subgroups, .

72. Process Control Limit – Factors for x-bar/s - Charts n 2 3 4 5 6 7 8 9 10 A 3 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 B 3 0 0 0 0 0.030 0.118 0.185 0.239 0.284 B 4 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 c 4 0.7979 0.8862 0.9213 0.9400 0.9515 0.9594 0.9650 0.9693 0.9727

73. Process Control Limit – The np - Chart Lower control limit = Upper control limit = with and where np 1 , np 2 , ..., np N are the number of defect items in each subgroup of constant size n, and N the number of subgroups.

74. Process Control Limit – The p - Chart Lower control limit = Upper control limit = for i = 1, 2, 3,..., N, where (np) 1 , (np) 2 , ..., (np) N are the number of defect items in the subgroups and n 1 , n 2 , ..., n N are the number of items in the N subgroups. Note : The sample sizes should not vary more than 25% around the average sample size when using control limits for the whole chart. with and or or Control limits for whole chart Control limits for each subgroup

75. Process Control Limit – The c - Chart Lower control limit = Upper control limit = with where c 1 , c 2 , ..., c N are the number of defects in each subgroup of constant size and N the number of subgroups.

76. Process Control Limit – The u - Chart Lower control limit = Upper control limit = with and where c 1 , c 2 , ..., c N are the number of defects in the subgroups and n 1 , n 2 , ..., n N are the number of items in each of the N subgroups. Note : The sample sizes should not vary more than 25% around the average sample size.

77. Process Control Charts – Exercise 5 Black Beads: Calculate the average and the upper and lower control limit for the “Bead” exercise.

78. Remarks or Questions ?!?

79. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

80. USL LSL USL LSL large variation  problem exist  root cause analysis  process improvement trend  problem occurs  root cause analysis  corrective and/or preventive action Defect Defect nominal value nominal value Out-of-Control & Process Improvement

81. 50 55 = USL LSL= 45 50 55 45 Sample Sample 50 55 45 50 55 45 Process Tempering & Overcontrol

82. 50 55 45 LSL USL Process tampering may substantially increase the product variability since the process average is shifted each time an adjustment is made. Process Tempering & Overcontrol

83. Out-of-Control Criteria – Two Causes of Variation Common Causes : Causes that are implemented in the process due to the design of the process, and affect all outcomes of the process. Identifying these types of causes requires Design of Experiment (DOE) methods. Special Causes : Causes that are not present in the process all the time and do not affect all outcomes, but arise because of specific circumstances. Special causes can be identified using SPC. Shewhart (1931)

84. Out-of-Control Criteria – Two Types of Processes Unstable Process : A process in which variation is a result of both common and special causes . Stable Process : A process in which variation in outcomes arises only from common causes .

85. Time Target Target Target Target UCL LCL UCL LCL UCL LCL UCL LCL "In-Control" and "Out-of-Control" Processes

86. Target Time Target Target Target UCL LCL UCL LCL UCL LCL UCL LCL "In-Control" and "Out-of-Control" Processes

88. P = 0.0013 (0.13 %) SPC Criteria – 1 Point above or below 3 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

89. P = 0.001 (0.1 %) SPC Criteria – 2 of 3 Points above or below 2 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

90. P = SPC Criteria – 4 of 5 Points above or below 1 Sigma Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

91. P = SPC Criteria – 8 Points on the same Side of the Average Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

92. SPC Criteria – Trend of 7 Points Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

93. P = SPC Criteria – 15 consecutive Points in the 1 Sigma Zone Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

94. *) The number of runs (crossing the average line) should be about one-half of the number of points on the control chart. SPC Criteria – Too few or too many Runs *) Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

95. P = SPC Criteria – 8 Consecutive Points with none in the 1 Sigma Zone Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

96. SPC Criteria – Seasonal Variation Patterns Example: ___________________________________________________ average average + 3*sigma average + 2*sigma average + 1*sigma average - 1*sigma average - 3*sigma average - 2*sigma

97. SPC Out-of-Control Criteria – Summary x x / R x / s c u np p Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Chart - -

98. SPC Out-of-Control Criteria – Exercise 6 Efficiency Out-of-Control Conditions: Determine why the process control chart below indicates that the efficiency of production line H300 is out-of-control. Notes:

99. Remarks or Questions ?!?

100. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

102. If a shift in the process average of “E” units will harm the customer or one of the next process stages, the necessary subgroup sample size (n) can be calculated as: where The next plotted point will with 90% confidence identify a process shift larger than “E” units, that means the next point will be above or below 3 sigma control limits. Sample Size and Frequency – Subgroup Size and Precision

103. avg avg + avg + E E Sample Size and Frequency – Subgroup Size and Sensitivity

105. Remarks or Questions ?!?

106. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan

107. Out-of-Control-Action-Plans (OCAP) Activators (out-of-control decision rules) Checkpoints (list of possible assignable causes) Terminators (corrective actions) An OCAP is a flowchart that guides the operator through a defined and repeatable response to “any” out-of-control situation .

108. Out-of-Control-Action-Plans (OCAP) Start Checkpoints Activators Corrective Actions No No No Yes Yes Yes Yes Yes Yes End No No

109. Out-of-Control-Action-Plans – Activators 1. One point outside the 3-sigma control limits. 2. A run of at least seven or eight consecutive points, where the type of run could be either a run up or down, a run above or below the centre line. 3. Two out of three consecutive points plot beyond from the 2-sigma warning level. 4. Four out of five consecutive points at a distance of 1-sigma or beyond. 5. One or more consecutive points near a 2-sigma warning or 3-sigma control level. etc.

110. Out-of-Control-Action-Plans – Checkpoints The checkpoints instruct the operator to investigate specific items as possible assignable causes for the out-of-control situation. Once a checkpoint has identified a probable assignable cause for the out-of-control situation, the OCAP will flow into a terminator or corrective action.

111. Out-of-Control-Action-Plans – Terminators The terminator contains a detailed description of the corrective action that the operator has to take to resolve the out-of-control situation.

114. Remarks or Questions ?!?

115. Statistical Process Control – Table of Content Section 1: Introduction Section 2: The Histogram Section 3: Measure of Location and Variability Section 4: Process Control Charts Section 5: Process Control Limits Section 6: Out-of-Control Criteria Section 7: Sample Size and Frequency Section 8: Out-of-Control Action Plan