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0135067537_pp7.pdf
Chapter 7
Other Variable Control Charts
Evolution from Inspection to SPC
Customer Supplier 100% Insp.
100% Insp.
SPC.
Customer Supplier 100% Insp.
Sample Insp.
Customer Supplier Sample Insp.
Customer Supplier SPC.
SPC.
So far! Statistical Process Control
Customer Supplier
• Sample output of process and make inferences about its state • Demonstrate that the distribution of process output is known and unchanging • Plot and monitor over time • Use statistical tests to detect shifts and anomalies and react to them quickly • Use statistical evidence to guide and confirm process improvements
Trial control limits and revised control limits for Xbar and R charts
Achieve the Objective
Continuing use of control charts, showing improved quality
Patterns in Control Charts
Some unnatural runs-process out of control
Out-of-Control Patterns
Change or jump in level Trend or steady change in level
Recurring cycles Two populations
Case I: When the process capability is less than the tolerance 6σ<USL-LSL
Process Capability & Tolerance
Case I 6σ<USL-LSL
Case II: When the process capability is less than the tolerance 6σ=USL-LSL
Process Capability & Tolerance
Case II 6σ=USL-LSL
Case III: When the process capability is less than the tolerance 6σ>USL-LSL
Process Capability & Tolerance
Case III 6σ>USL-LSL
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
Cpk Measures
What Now!��� How about the Short Run?
X-bar and R charts track process with long production runs or repeated services
What if the number of sample measurements is insufficient to create either chart?
Would SPC ideas apply to new processes or short runs?
What happens when only one sample is taken from a process?
Let us look at situations when the traditional X- bar, R and S charts cannot be used.
Ø Individual & Moving Range Charts
When ? n data is collected once per period n single value measurement n few units of each product
n Then! n a. Individual Values Chart
n Plot Individual measurements, Xi n X-bar is the average of all Xi
Individual & Moving Range Charts
n b. Moving Range Chart n Calculate Ri, orValue-to-value difference of individual
data n R-bar is the average of all Ri n (m-1) ranges n Plot Individual measurements, Ri starting on the
second observation
Individual & Moving Range Charts ��� Control Limits
Individual Values Chart UCL x = X + 2.66 R LCL x = X - 2.66 R
Moving Range Charts UCL R = 3.27 R LCL R = 0
At least 80 samples Interpret similar to traditional charts
n Charts for individuals and moving range are created when the measurements are single values or when the number of products produced is too small to form traditional X-bar and R charts. σ = R-bar/d2 and n=2.
X i =
∑X i m
R = ∑R i m − 1
UCLX = Xi + 2.66(R) LCLX = Xi − 2.66(R)
UCLR = D4 × R = 3.27 × R
Individual & Moving Range Charts, Again!
Individual & Moving Range Charts
Individual & Moving Range Charts § For reliable charts, number of subgroups > 80. § If control limits are inflated, calculate 3.144 times median moving range. • If it is greater than 2.66, do not recalculate the control limits and center lines. • Otherwise, re-compute all control limits and center lines using new X-bar.
Revised Control Limits: UCLX = X + (3.144) (Median Moving Range) LCLX = X - (3.144) (Median Moving Range) Center line X-Chart = X UCLR = (3.865) (Median Moving Range) LCLR = None Center line R-Chart = Median Moving Range
Ø Moving-Average & Moving-Range Charts
Combine n individual values to form a group
Create average & range per group; Moving: new value in - oldest one out
Find UCL, LCL & Process Capability using the same methods as the traditional control charts (TCC)
Moving-Average & Moving-Range Charts
Moving Average smoothes out short term variation
User can concentrate on trends Mostly used for seasonal products Always lag behind changes in process Best when process changes slowly
n moving-average and moving-range charts to combine n number of individual values to create an average. n Moving averages smooth out short-term variations and
allow users to study the underlying trends in data. n Moving average charts are frequently used for seasonal
products. n Moving averages because of the nature of their construction,
will always lag behind changes in the process, making them less sensitive to such changes,
n The larger the size of the moving average subgroup, the less sensitivity to change.
n To quickly detect process change, use the individual and moving-range combination of charts.
n Moving average charts are best used when the process changes slowly.
Moving-Average & Moving-Range Charts
n Used for continuous process chemical industry: The moving average is particularly appropriate in continuous process chemical manufacture. The smoothing effect of the moving average often has an effect on the figures similar to the effect of the blending and mixing that take place in the remainder of the production process.
Moving-Average & Moving-Range Charts
n moving-average and moving-range charts to combine n number of individual values to create an average. n When a new individual reading is taken, the oldest value
forming the previous average is discarded. The new reading is combined with the remaining values from the previous average and the newest value to form a new average, thus the term “moving average.”
n This average is plotted on the chart and the limits are calculated using the formulas for the X-bar and R charts presented in Chapter 5.
n Capability indices can also be calculated using the methods presented in Chapter 6. The number of individual values grouped together to form a subgroup will be the size of n used to select the A2, D4, and D3.
Moving-Average & Moving-Range Charts
n Interpretation: n – a point outside control limits: interpretation is same as before - process is out of
control n – runs above or below the central line or control
limits: interpretation is not the same as before - the successive points are not independent of one another
Moving-Average & Moving-Range Charts
Moving-Average & Moving-Range Charts
Ø A Chart Plotting Individual Values
Explains concept of variation compared to the average
Picture worth 1000 words
Useful in training staff on interpreting R or S charts
Individual Values Charts
n Individual values chart are mostly used for training people on interpreting values of R or s charts.
n Small marks are used to show individual values, and circles are used to show the subgroup averages.
n Figure 5.5, p. 247, on next slide.
Individual Values Charts
Ø Multi-Vari Chart ��� Chapter 7 n Multi Vari analysis [Multi-Vari Chart]
[Len Seder (1915 – 2004), used by Dorian Shainin (1914-2000) ] is used to clarify and study the spread of individual measurements in a sample and the variability due to three or more factors.
n Used for smaller, point-in-time studies of variation [TCC track variation over time]. n Samples are taken and measured. n The greatest and least sample values are plotted vertically
with subgroup numbers on the X-axis and the values of the sample measures on the Y-axis.
n This results in a stacked set of measures through which a vertical line is drawn (Figure 7.7, p.248).
n Three types of variation [piece-to-piece, between subgroups, and time-to-time] can be detected.
n Specification limits are sometimes placed on the diagram.
Ø Multi-Vari Chart ��� Chapter 7
Ø Multi-Vari Chart ��� Chapter 7
MULTI-VARI ANALYSIS, VARIATION FAMILIES The key is reducing the number of possibilities to a manageable few.... Within Individual Sample (Within Piece) Variation is present upon repeat measurements within the same sample. Piece to Piece Variation is present upon measurements of different samples collected within a short time frame. Time to Time Variation is present upon measurements collected with a significant amount of time between samples.
Ø Multi-Vari Chart ��� Chapter 7
Ø Multi-Vari Chart ��� Chapter 7
Ø Multi-Vari Chart ��� Chapter 7
Ø Median and Range Charts
n Study process variation n Steps:
n record subgroup measurements n rank in decreasing order n find median & range in each subgroup n Median Chart Center = AVG of all medians n Range Chart Center = AVG of all ranges n Determine UCL & LCL for the Median &
Range Charts
Median and Range Charts
Median Charts: UCL Md = XMd + A6 RMd LCL Md = XMd - A6 RMd
Range Charts UCL R = D4 RMd LCL R = D3 RMd
Record Median & Range on chart Interpret Charts similar to TCC
Chapter 7
n Median and range chart n The median of the data is calculated and charted rather than the value for the
average. n To create the median and range chart: 1. Calculate and record the sample measurements. 2. Arrange the sample measurements in each subgroup in order from
highest to lowest. 3. Calculate the median and the range for each subgroup. 4. To find the centerline of the median chart, calculate the average of
the subgroup medians. 5. To find the centerline of the range chart, calculate the average of the
subgroup ranges. 6. The control limits of the median and range charts are determined by
the following formulas and the values shown in Table 7.3, p. 249 [A6] and Appendix 2 [D3 and D4].
Chapter 7
Chapter 7
Median chart formula [Method I]
Or, you can use the formulas on page 251, where medians instead of averages are used. [Method II].
UCLMd = X Md + A6 R Md LCLMd = X Md − A6 R Md UCLR = D4 R Md LCLR = D3R Md
Chapter 7 Median chart formula [Method II]
Chapter 7 Median chart formula [Method II]
Ø Run Charts n Monitor changes in a particular
characteristic over time n Can be used for Variables or Attributes n Data: measurements, counts, subgroup
averages n Easily spot trends, runs and other
patterns
Run Charts: Steps n Identify time increments to study process n Scale the Y axis to reflect values n Collect data n Record data on chart n Interpret the chart (limited to looking for data
patterns) n No out of control points
Chapter 7
n Run charts n Run charts can be used to monitor process changes
associated with a particular characteristic over time. n Run charts are versatile and can be constructed with
data consisting of either variables or attributes. n These data can be gathered in many forms, including
individual measurements, counts, or subgroup averages. n Time is displayed on the x axis of the chart; the value
of the variable or attribute being investigated is recorded on the y axis.
n See an example on p. 253.
Chapter 7
Chapter 7
n Two ways to misinterpret run charts: n You conclude that some trend or cycle exists, when in fact you
are just seeing normal process variation (and every process will show some variation).
n You do not recognize a trend or cycle when it does exist. n Both of these mistakes are common, but people are
generally less aware that they are making the first type, and are tampering with a process which is really behaving normally. To avoid mistakes, use the following rules of thumb for run chart interpretation: n Look at data for a long enough period of time, so that a "usual"
range of variation is evident. n Is the recent data within the usual range of variation? n Is there a daily pattern? Weekly? Monthly? Yearly?
Chapter 7 n Using run charts to detect "special causes" of variation:
n If you have 25 points or more in your data series, you can use run charts to detect special causes - something beyond the usual variability of the process -acting on the process.
n Shifts: If you see eight or more consecutive points on one side of the center line, that indicates that a special cause has influenced the process. Points on the center line don't count; they neither break the string, nor add to it.
n Trends: Six consecutive jumps in the same direction indicate that a special cause is acting on the process to cause a trend. Flat line segments don't count, either to break a trend, or to count towards it.
n Pattern: If you see a pattern that recurs eight or more times in a row, it is a good idea to look for a special cause.
Ø Variable Subgroup Size Charts
Subgroup size, n, Varies
Re-compute Control Limits (CL) for each n
As n increases - CLs get closer to center
Too many calculations
Limit the useful of this chart
Chapter 7: Charts for variable subgroup size��� n Charts for variable subgroup size As the subgroup size changes from 2 to 3 to 4, … the A2, D4, D3, …
values have to be changed and the control limits have to recalculated and will be closer to the center line. And the charts will not be as useful as before. Figure 7.13, p. 255.
Chapter 7: Charts for variable subgroup size���
Ø Precontrol Charts n Compare product made against
specification [tolerance] limits n Assume process is capable of meeting
specifications n Use specifications for limits n More false alarms or missed signals n Simple to setup
Precontrol Charts n Useful for setup operations or short
production runs n Less powerful than TCC n Provide little information about actual
process performance n Cannot be used in problem solving or
calculating process capability
Precontrol Charts • Shainin (1914-2000) recommended using a “Portion of Tolerance Spread (PTS)” to account for difference in spread for individuals and averages
Precontrol Charts n Desired Process Capability (Cp) dictates this
portion: Cp PTS 1.2 (100/1.2) = 83 % 1.1 (100/1.1) = 90 %
Chapter 7
n Precontrol charts study and compare product produced with specification [tolerance] limits.
n Unlike the control charts, these charts cannot be used for problem solving or calculating process capability. They are useful for setup operations to determine if the setup results in producing products within the tolerances [Table 7.7, p. 256]. They are also used to monitor very short production runs [Table 7.8, p. 256].
Chapter 7 n Precontrol charts study and compare product
produced with tolerance limits. Creating a precontrol chart is a three-step process: 1. Create the zones.
Place the upper and lower specification limits on the chart. Determine the center of the specification; this becomes the centerline on the
chart. Create the zones by finding the center of area between the specification limits and the center of the tolerance. To do this, subtract the centerline from the upper specification limit, divide this value in half, and add the result to the centerline. To divide the lower half of the precontrol chart, subtract the lower specification limit from the centerline, divide this value in half, and subtract the result from the centerline.
2. Take measurements and apply setup rules. Figure 7.7, p. 256.
3. Apply the precontrol sampling plan. Figure 7.8, p. 256.
Precontrol Charts: Steps ��� Create the zones for the used PTS
o Place USL, LSL and center (SC) on chart o Divide (USL-SC) in 2 equal zones: green- yellow o Divide (SC-LSL) in 2 equal zones: green- yellow o Green zones (GO SECTION) are next to center o Yellow zones (CAUTION) are next to the limits o Zones above or below yellow area are colored in
RED (UNDESIRABLE)
Precontrol Charts: Steps ��� Create the zones for the used PTS
Precontrol Charts: Steps ��� Take measurements & apply setup rules
Record and plot measurement for first piece If measured piece is
n in green zone-continue running n inside limits but outside green zone [i.e. in yellow zone]-check next
piece n if second piece is in green zone – continue running n if second piece is also outside green zone[i.e. in same yellow zone]-
reset process [adjust process average] n in red zone, stop, adjust process, remove variation.
If 2 successive pieces fall outside green zone[i.e. in yellow zone], one high and the other low, reduce variability
Whenever process is reset, need 5 successive pieces inside the green zone before implementing sampling plans
Precontrol Charts: Steps ��� Apply the precontrol sampling plan
n If 5 pieces in a row fall in the green zone-begin
running the job n Use the run rules, randomly sampling 2 pieces at
intervals to monitor process n For example: Sampling Two PARTS every 15
minutes. n Experts suggest sampling > 25 pairs between
setups n Repeat whenever the process is reset
Precontrol Charts: Steps ��� Apply the precontrol sampling plan
Ø Measure two pieces at intervals n Both in green zone - Continue n One in yellow zone & one in green zone - Continue n Two in same yellow zone - Adjust process average n Two in opposite yellow zones - Stop, Adjust process average and
Remove variation n One point in red zone - Stop, adjust process average, remove
variation, begin precontrol setup rules.
• Problems with Pre-Control: Pre-Control procedures have many serious disadvantages compared to Control Charts. Several are briefly described below:
• Pre-control begins with a set of assumptions (that drive the
probabilities and reaction criteria) that in practice are rarely true: • the process is centered between the specification limits • the individuals are normally distributed • the specification limits happen to fall at a distance of 3 standard
deviations from the process average • Pre-control does not concern itself with understanding or estimating
process characteristics vital to achieving product quality (process average and process standard deviation)
• Because pre-control often does not employ charts, any obvious patterns over time that indicate trends or cycles are not easily detected.
Precontrol- Versus Control- Charts
• Problems with Pre-Control Pre-Control procedures have many serious disadvantages compared to Control Charts. Several are briefly described below:
• Pre-control utilizes individuals values as opposed to statistics like
sample averages. As discussed at length in an earlier, the use of individual values provides little power to detect anything but large process changes. So, while the process may be changing and adding harmful variation, pre-control is powerless to detect it.
• Pre-control is reactionary in nature and does not focus on finding or eliminating the sources of process changes. Rather, it encourages ongoing efforts by operators to make frequent adjustments rather than promoting attempts at eliminating sources of variation.
Precontrol- Versus Control- Charts
• Problems with Pre-Control Pre-Control procedures have many serious disadvantages compared to Control Charts. Several are briefly described below:
• Careful and comprehensive analyses of pre-control practices by
qualified statisticians have concluded that its use will likely lead to unjustified and unnecessary "over-control" of the process, which actually leads to increased variability.
• Pre-control is a poor substitute for statistical process control charts. Rather than enabling manufacturers to conquer and control unpredictable processes (and ultimately improve them), they perpetuate the obsolete mindset of trying to inspect quality into a product. It also relies on unjustifiable assumptions that may lead to ineffective or harmful reactions.
Precontrol- Versus Control- Charts
Precontrol- Versus Control- Charts
Ø Short-Run Charts��� n TCC : effective in long continuous operations
n Real life: need to switch products (FMS) n Use Short-Run charts n Different Methods:
n First and last pieces n 100 % inspection (costly, maybe inaccurate) n TCC for each part # & each different run of
each part # (many charts- little information)
Chapter 7
n Short Run Control Charts n Traditional charts work mostly with long
continuous production runs. n Usually, short-run control charts include multiple
part numbers on the same chart. n The nominal and R short run charts use coded
measurements based on the nominal print dimension. This creates a common distribution and set of control limits.
Ø Nominal X-bar and R Charts���
n Use coded measurements based on nominal dimension.
n Show process centering and spread n Assume similar variations for each of the
part numbers n If variation of a part > 1.3 R-bar, then it must
be plotted on a separate graph
Nominal X-bar and R Charts ��� Steps ��� n Identify parts monitored using same chart
(same operator, machine , material, ...) n Find nominal spec. for each part n Collect data using same subgroup size for all
parts n Coded Xi= measured value - nominal value n Calculate X-bar for each subgroup
Nominal X-bar and R Charts ��� Steps ��� n Plot all X-bars on the chart
n Continue the above for the entire run of this particular part number
n Repeat the above for another part number n If the number of subgroups (from any
combination of parts) > 20, calculate the control limits
Nominal X-bar and R Charts Steps ���
Centerline = Average of all coded X-bars Control limits: Nominal X-bar Chart UCL x = Centerline + A2 R LCL x = Centerline - A2 R
Control limits: Nominal range Charts UCL R = D4 R LCL R = D3 R
Draw center and CL on the chart Interpret the chart
Nominal X-bar and R Charts ���
n Most useful when FOR ALL PARTS n Subgroup size, n, is the same n Nominal is the most appropriate target value
n Control charts should be selected based on: n What aspect of process need to be
monitored. n Identifying the chart that best meet such
need.
Chapter 7 Use the following steps to create a nominal and R chart: 1. Determine which parts will be monitored with the same control chart. Pay
careful attention to select parts made by the same operator using the same machine, methods, materials, and measurement techniques.
2. Determine the nominal specification for each part number. 3. Begin the chart by collecting the data. The subgroup sample size should be
the same for all part numbers. 4. Once the measurements have been taken, subtract the nominal value for the
appropriate part number from the measurements. X-bar is then calculated for each subgroup.
5. Plot the coded average measurements, from step 4 on the chart. The coded values will show the difference between the nominal dimension, represented by a zero on the control chart, and the average measurement.
6. Continue to calculate, code, and plot measurements for the entire run of this particular part number.
7. When another part number is to be run, repeat the above steps and plot the points on the chart.
Chapter 7
8. When 20 subgroups have been plotted from any combination of parts, the control limits can be calculated with a modified version of the traditional variables control chart formulas:
Centerline = ∑ coded X
m UCLX = centerline + A2 R LCLX = centerline − A2 R
R = ∑R i m
UCLR = D4 R LCLR = D3R
9. Draw the centerlines and control limits on the chart. 10. Interpret the chart.
