2. TOOLS FOR PROCESS CONTROL
1. Detection :- A past oriented strategy that attempts to identify unacceptable output after it
has been produced and then separate it from the good output.
2. Prevention :- A future oriented strategy that improves quality and productivity by
directing analysis and action toward correcting the process itself so that unacceptable
parts will not be produced.
TECHNIQUES FOR PROCESS CONTROL
1. Mistake Proofing :- In this technique 100% process control is achieved by
preventing all types of failures by using modern techniques to get defect free
product. Here causes are prevented from making the effect.
2. 100% Inspection : In this technique 100% checking of all the parameters of all
products has been done to get defect free product. Here only defects are
detected.
3. Statistical Process Control : In this Statistical technique such as Control Chart,
Histogram etc. are used so as to analyses the process and achieve and
maintain state of statistical control to get defect free product. Causes are
detected and prompting CA before defect occurs.
WHY S.P.C. IS REQUIRED ?
Effectiveness of any activity in an Organization is measured with respect to time and cost
involved in it.
3. Mistake Proofing 100% Inspection Statistical Process Control
In this method more
advanced and modern
techniques are used
which require
substantial investment
during its installation
and maintenance.
As it is detection type of
technique it can’t avoid
failure but rejects defective
products.
Requires more inspectors,
more inspection times and in
turn more cost.
For this technique investment is very
less and process is controlled on each
workstation therefore defective
components is not forwarded to next
operation. Predictability reduces
frequent adjustments & in turn
increases productivity, reduces
inspection cost at station & at final
inspection
From above we can observe that S.P.C. is the economical way of controlling the process in
comparison with Mistake Proofing and 100% inspection.
WHAT IS S.P.C. ?
1. Statistics :- A value calculated from or based upon sample data (e.g. a subgroup
average or range) used to make inferences about the process that produced the
output from which the sample comes.
2. Statistical Control :- The condition describing a process from which all special
causes of variation have been eliminated and only common causes remain.
3. Statistical Process Control :- The use of Statistical techniques such as control
charts to analyze a process or it’s outputs so as to take appropriate actions to
achieve and maintain a state of statistical control and to improve the process
capability.
4. STATISTICAL PROCESS CONTROL
VARIATION: - The inevitable differences among individual outputs of a process;
the sources of variation can be grouped into two major classes: Common Causes
and Special 0Causes.
Common Causes: - A source of variation that affect all the individual values of the
process output and inherent in the process itself and can not be eliminated
totally.
Special Causes: - A source of variation that is intermittent, unpredictable,
unstable; This causes can be identifiable and can be eliminated permanently.
Random Variation Non-Random Variation
Only common cause are present Common & Assignable cause are present
Common causes are more in nos. Assignable causes are very few in nos.
Common causes are part of process Visitor to the process
Contributes to constant variation Highly fluctuating variation
Predictable Unpredictable
Statistics Apply Statistics shall not apply
Management controllable Operating personnel controllable
5. PROCESS CONTROL :-
A process is said to be operating instate of statistical control when the only source
of variation is common causes.
PROCESS STABILIITY: -
The process is said to be stable when the process is in control and variation is
constant with respect to time i.e. Being in statistical control.
PROCESS CAPABILITY: -
The measure of inherent variation of the process ( i.e Six Sigma (+/- 3 σ) when it is
in stable condition is called as process capability.
OVER ADJUSTMENT: -
It is the practice of adjusting each deviation from the target as if it were due to a
special cause of variation in the process. If stable process is adjusted on the basis
of each measurement made, then adjustment becomes an additional source of
variation and in turn it increases the total variation.
6. METHODOLOGY TO IDENTIFY SPECIAL CAUSES
This write up is for assignment any one identify Assignable causes. As you are aware the
success of any SPC program is not in our ability to collect data, draw charts etc., but in
effectively identifying and eliminating assignable causes. Assignable causes are those
causes that do not allow one to predict the behavior of processes. There is no meaning in
calculating Process Capability without having a predictable process.
Many companies have initiated SPC charts. But the charts do not benefit them. One of the
main reason for this is that they have not stopped the process when an assignable cause is
indicated and eliminated the cause. This is not done because no body is aware on how to do
it. Many experts only say that the cause is to be eliminated but no one is able to assist a
company in doing this. We are sharing with you our approach for doing this cause
elimination.
Before starting the SPC data collection, let us do the following steps:
1. Identify the characteristic for which SPC is to be done.
2. Have a brainstorming to list all the causes that may influence the variation in this
characteristic
3. Prepare a Cause & Effect Diagram
4. Prepare a Master Cause Analysis Table (Annexure 1)
5. Prepare a Why-Why Analysis Table (Annexure 2)
6. Identify factors that may affect Average and those that may affect Range
After completion of the above, plan for data collection, calculation of preliminary limits, etc.
Then use the chart for On -Line control.
When you are routinely using the chart, when ever a point goes beyond the control limits,
using the Master Cause Analysis Table, we can narrow the assignable cause (Based on our
preliminary listing as mentioned in Sl. No.6 above) by verifying the condition of the cause from
the limits specified in the table.
7. ANNEXURE – 1
MASTER CAUSE ANALYSIS TABLE
Sl.
No.
Cause Is there a
specn?
If so, what
is the
specn?
Basis for
the specn.
Is it
checked
and how?
What is
the
actual?
Diff. in
Specfn.
Vs
Actual
Action
plan
8. ANNEXURE – 2
WHY – WHY ANALYSIS TABLE
Sl.
No.
Cause WHY WHY WHY WHY WHY
9. GUIDELINES FOR USING ANNEXURE – 1
1. Enter a serial number
2. Enter the cause from the cause and effect diagram. All the causes from the cause and
effect diagram must be covered
3. For each cause ask the Question: Is there a Specification? Please note that the
specification is for the cause. The answer can be Yes or No.
4. If there is a Specification, write the actual value of the specification. If there is no
specification, Enter in the Action Plan column “Specification is to be established”.
5. Give the basis for the specification mentioned in Column No.4. Sometimes the
Specification may be based on the drawing, machine manufacturer’s catalogue, work
instruction, Past Experience, etc. Do not write your expectations. Only enter what is
actually existing. Remember that there has to be some basis.
6. Is this specification being checked. If yes, write the actual method used for checking. If it
is not being checked, then enter No. It may be possible that there are methods for
checking but not done here, in which case the answer is No. If the answer is No, then
enter in the Action Plan Column “Method of checking is to be established”.
7. Enter here the actual value of the cause by using the method of checking. Sometimes it
may be the range of variation (Ex: Input material condition) or it may be One Value (Ex:
Taper in the fixture). This is the actual value and not a guess. Time may be required to
complete this column.
8. If there is a difference between the actual value and the specification, then examine how
important based on technical knowledge. If the difference is not major, then mention No.
Otherwise mention Yes. If the answer is Yes, then enter in the Action Plan Column that
further analysis is needed like Why-Why Analysis or correction to eliminate the variation.
9. Under this column enter the specific Action Plan needed as already mentioned above.
10. GUIDELINES FOR USING ANNEXURE – 2
This table can be used for all the causes identified in the Cause and Analysis Table with top
priority for the Causes found to have variation from the Master Cause Analysis Table.
1. Enter the running serial number
2. Enter the cause to be studied
3. Enter Why this cause should vary. There may be more than one reason. Enter all the
reasons one below the other.
4. For each of the Why identified in Column 3, write the possible causes. Note that the cause is
to be identified only for column 3 and not backward.
5. Proceed in the same manner as Column 4. Ensure that each time the focus is only on the
previous column.
6. Proceed in the same manner as Column 4. Ensure that each time the focus is only on the
previous column.
7. Proceed in the same manner as Column 4. Ensure that each time the focus is only on the
previous column.
Continue in this manner, till any of the following happen:
a. No further Why can be answered
b. The system cause has been identified (Ex: No system for checking, verification, control, etc.)
c. The reverse is the solution
Based on the listed why's, develop the action plan for implementation.
Remember:
It is the system, which is at the Root Cause of all problems and not individuals.
11. PREDICTABLE PROCESS :- Process free from Assignable causes.
CAPABILITY :- Measure of inherent variation.
CAPABLE PROCESS : Cp & Cpk > 1.33
1.MEASUREMENT SYSTEM ANALYSIS :
Measurement System Analysis measures the contamination of the variation due to measurement
system in the total variation of characteristic. In this technique both variable and attribute data
measurement systems are verified.
Following types of variations are observed in M.S.A.
1. Equipment Variation :- Variation of measuring instrument.
2. Appraiser Variation :- Variation between measuring persons.
3. Combine Variation :- Variation of both instruments and person.
4. Part to Part Variation :- Variation comes when measuring two different parts.
5. Within Part Variation :- Variation comes when measuring same part at different places.
Resultant of all these variation is called as Total Variation in the measuring system.
Reproducing and Repeatability Study are conducted to evaluate Equipment Variation and
Appraiser Variation.
This R & R value should be less than 10% when it is between 10 to 30%, then measuring system
requires improvement. But if this variation is more than 30% then measurement system required
to be changed.
2. DATA COLLECTION :-
Data is available in two types :
1. Variable data : Data which is available in numerical form.
2. Attribute Data :- Data which is in term of decision and not in numerical terms. e.g. - Data
form Go-No go gauges.
12. 3. CHECKING FOR PROCESS PREDICTION :-
Process is said to be predictable when it is in control and stable i.e. when all Special causes are
removed from the process. The process can be checked from Control Chart and Histogram.
Control Chart: - When all points are within control limits or there is no obvious run or non-
random pattern of points with in the control limits.
Histogram: - When bell shape is observed on Histogram.
REMOVING ASSIGNABLE CAUSES:
When process is fail to satisfy above requirements then existence of special causes may be
there. In this cause find special causes and remove.
4. CALCULATING PROCESS CAPABILITY: -
After removing all special causes from the process calculate the capability indices Cp and Cpk.
If Cp and Cpk is greater than 1.33 then process is said to be within acceptable capability. Based on
the priority make improvement plan for the process.
If Cp and Cpk is less than 1.33, then find out major common causes and remove it.
5. ESTABLISHING CONTROL LIMITS: -
When Cp and Cpk is greater than 1.33 , Then , Establish UCL/LCL and CL marked on control chart
and Issued to Operators for ongoing control.
6. PREPARE REACTION PLAN: -
After deciding control limits, Corrective and disposition actions to be given to the operators for
any special causes expected to occur during the process. These corrective and disposition actions
can be documented in Reaction Plan.
13. FACTORS FOR COMPUTING LIMITS
n d2 A2 D3 D4 E2
2 1.128 1.880 0 3.268 2.66
3 1.693 1.023 0 2.574 1.77
4 2.059 0.729 0 2.282 1.46
5 2.326 0.577 0 2.114 1.29
6 2.534 0.483 0 2.004 1.18
CONTROL CHART INTERPRETATION AND
DISPOSITION ACTION
The MOST RECENT POINT
indicates that the process
ACTIONS ON THE PROCESS OUTPUT
Based on the Ongoing process capability (Cpk)
Is in Control 1.33 - 1.67 Greater than
1.67
Accept product Continue to reduce
product variation
Has gone out of control in an
adverse direction. All
individuals in the sample are
within specification
IDENTIFY & CORRECT SPECIAL CAUSE
Inspet
100%
since
the last
in-
control
point.
Accept
product
Continu
e to
reduce
product
variation
Has gone out of control in an
and one or more individuals
in the sample are outside
specification
IDENTIFY & CORRECT SPECIAL CAUSE
100% inspect product produced since
the last in-control sample.
14. CONTROL CHART METHODOLOGY
INTRODUCTION:
It is a technique, which builds quality into the process. SPC is most effective when problems are
resolved as soon as identified. Control charts are mainly to increase productivity, improve quality
and reduce cost. Process variation can be easily analysed by control charts. Objective of control
chart analysis is to identify any evidence that through process variability or the process averages
are not operating at a constant level.
The goal of the process control chart is not perfection, but a reasonable and economical state of
control.
CONTROL CHARTS FOR VARIABLES
X BAR R chart is developed from measurements of a particular characteristic of a process output.
This chart is pertaining to variables. Control charts for variables are powerful tools that can be
used when measurements from a process are available.
With variable data performance of a process can be analysed and improvement can be qualified
even if all individual values are within the specification limits.
Basically fewer pieces need to be checked before making reliable decisions. So the time gap
between production of parts and corrective action often cab be shortened.
1. DATA COLLECTION
X bar -R CHART:
X bar -R chart is developed from measurements of a particular characteristic of a process output. X bar-R chart
explains process data in terms of both its spread (piece to piece variability) and its location (process average).
DATA COLLECTION:
X Measure of Location
R Measure of Spread
15. To analyze the particular characteristics of a process or process output, data are collected in
small subgroups of constant size (2 to 5 consecutive pieces). Subgroups are taken periodically.
Sample size should remain constant for all subgroups.
SUBGROUP SIZE:
Subgroup size should be chosen so that opportunities for variation among the units within a
subgroup are small. If the variation within the subgroup represents the piece to piece variability
over a very short period of time, then any unusual variation between subgroups would reflect
changes in process that should be investigated for appropriate action.
Pieces within each subgroup would all be produced under very similar production condition over
a very short time. So the variation within each subgroup would primarily reflect common causes.
SUBGROUP FREQUENCY:
Purpose of selecting subgroup is to detect changes in the process over time.
During an initial process study, the subgroups are often taken consecutively or at short intervals,
to detect whether the process can shift to show other instability over brief time periods. As the
process demonstrates stability, the frequency of subgroups can be increased.
NUMBER OF SUBGROUPS:
From a process standpoint, enough subgroups should be gathered to assure that the major
sources of variation have had an opportunity to appear. Generally 25 or more subgroups
containing 100 or more individual readings give a good test for stability.
Plot the averages and Ranges on the Control Charts:
Plot the averages and ranges on their respective charts. This should be done as soon as
possible after scaling has been decided. Connect the points with lines to help visualize patterns
and trends.
16. Scan the plot points, confirm that the calculations and plots are correct. Make sure that the plot points for the
corresponding X and R is vertically in line.
Initial study charts used for first time capability or for studies after process improvements/changes should be the
only process control charts allowed on the production floor which do not have control limits placed on them.
2. CALCULATE CONTROL LIMITS :
R = ( R1 + R2 + ………+ RK ) / K
X = ( X1 + X2 + ………+ XK ) / K
Where
K is the number of subgroups.
R1 is the range of the first subgroup.
X1 is the average of the first subgroup.
Setup control charts :
X and R charts are normally drawn with the X chart above the R chart, and a data block. The values of X
and R will be the vertical scales.
Data block should include spare for each individual reading, average ( X ), Range ( R ) and the date/time or
other identification of the subgroup.
Characteristics to be plotted are the sample average ( X ) and the sample size ( R ) for each subgroup,
collectively these reflect the overall process average and its variability.
Average ( X ) = ( X1 + X2 + ………. +Rn ) / n
Where n subgroup sample size.
Range ( R ) = Highest – Lowest
Select the Scales for control charts :
Some general guidelines for determining the scales may be helpful, although they may have to be modified in
particular circumstances.
For X Chart :
17. The difference between the highest and the lowest values on the scale should be atleast two times the difference
between the highest and the lowest of the subgroup averages
( X ).
For R Chart :
Value extends from zero to an upper value about two times the largest range.
For R Chart :
UCLR = D4 R
LCLR = D3 R
For X Chart :
UCLx = X + A2 R
LCLx = X - A2 R
Where D4, D3, A2 are constants varying by sample size with values from sample sizes from 2 to 10.
Draw the average ( R ) and process average ( X ) as solid horizontal lines.
Control limits ( UCLR , LCLR,UCLx, LCLx ) as dashed horizontal lines. Label the lines.
3.INTERPRETATION FOR PROCESS CONTROL
Since the ability to interpret either the subgroup ranges or subgroup averages depends on the estimate of
piece to piece variability, the R chart is analysed first. The data points are compared with the control
limits, for points out of control or for unusual patterns or trends.
For Range Chart :
(a) Points beyond the control limits are primary evidence of non-control of that point. Any point beyond a
control limit is the signal for immediate analysis of the operation for the special cause.
A point above the control limit is generally due to
(1) Plot point may be miscalculated.
(2) Piece to piece variations has increased.
(3) Measurement system has changed.
18. A point below the control limit is generally due to
(1) Plot point is in error.
(2) Piece to piece variation has decreased.
(3) Measurement system has changed.
(b) Presence of unusual patterns or trends even when all ranges are within
control limits, can be evidence of change of process spread, also indicates
some special causes.
(c) Runs
(1) 7 points in a row on one side of the average indicate that the process is not
normally distributed and there is shift in the process average.
(2) 6 points in a row that are consistently increasing or decreasing.
(d) Presence of cycles in the chart indicates that special causes due to machine
set up, non-uniformity in the material wear of machine.
Find and Address Special Causes
For each indication of special cause in the range data, conduct an analysis
of the operation of the process to determine the cause and to improve the
process.
A process log may also be a helpful source of information in terms of
identifying special causes of variation. Single point out of control is reason
to begin an immediate analysis of the process.
19. SUMMARY OF TYPICAL SPECIAL CAUSE CRITERIA
Recalculate Control Limits
When conducting an initial process study or a reassessment of
process capability, the control limits should be recalculated to exclude the
effects of control periods for which process causes have been clearly
identified and removed.
SL.NO SPECIAL CAUSE CRITERIA
1 1 Point more than 3 standard deviations from centerline
2 7 Points in a row on same side of centerline
3 6 points in a row, all increasing or all decreasing
4 14 points in a row, alternating up or down
5 2 out of 3 points >2 standard deviations from center line
(same side)
6 4 out of 5 points>1 standard deviations from center line
(Same Side)
7 15 points in a row within 1 standard deviations of centerline
(either side)
8 8points in a row >1 standard deviation from centerline
(either side)
20. (1) Measurement system has changed.
A point below the control limit is generally due to
(1) Plot point is in error.
(2) Piece to piece variation has decreased.
(3) Measurement system has changed.
(b) Presence of unusual patterns or trends even when all ranges are within control limits, can be evidence of
change of process spread, also indicates some special causes.
(c) Runs
(1) 7 points in a row on one side of the average indicate that the process is not normally distributed and
there is shift in the process average.
(2) 7 points in a row that are consistently increasing or decreasing.
(d) Presence of cycles in the chart indicates that special causes due to machine set up, non-uniformity in the
material wear of machine.
Find and Address Special Causes
For each indication of special cause in the range data, conduct an analysis of the operation of the process to
determine the cause and to improve the process.
A process log may also be a helpful source of information in terms of identifying special causes of variation.
Single point out of control is reason to begin an immediate analysis of the process.
Recalculate Control Limits
When conducting an initial process study or a reassessment of process capability, the control
limits should be recalculated to exclude the effects of control periods for which process causes have been
clearly identified and removed.
Analyze the data on the AVERAGE CHART
When the ranges are in statistical control, the process spread – the within subgroup variation is
considered to be stable. The averages can then be analysed to see if the process location is changing over
time.
21. Control limits for X Bar are based upon the variation in the ranges. Then if the averages
are in statistical control, their variation is related to the amount of variation seen in the
ranges (common cause variation of the system). If the averages are not in control, some
special causes of variation are making the process location unstable.
Points beyond control limits indicates that there is
(1) shift in process
(2) Plot points are in error.
Find and address the special causes and then recalculate the control limits after
eliminating the special causes.
4. INTERPRET FOR PROCESS CAPABILITY
Interpretation process capability is to be carried out only under the following assumptions:
(1) Process is statistically stable.
(2) Individual measurements from the process conform to normal
distribution.
(3) Design target is in the center of the specification width.
(4) Measurement variation is small.
Having determined that a process is in statistical control, the question still remains whether
the process is capable of meeting customer needs. To understand and improve the capability
of a process, one should understand that capability reflects variation from common causes
and management action on the system is required for capability improvement.
22. Calculate Process Standard Deviation:
Since within subgroup process variability is reflected in the subgroup averages, the estimate of the process standard
deviation “σ“ can be based on the average range (R).
σ= R / d2
Where
R the average of the subgroup ranges.
d2 the constant varying by sample size.
Capability can be described in terms of the distance of the process average from the specification limits in standard deviation units, Z.
For unilateral tolerance
Z = ( USL – Xbar) / σ (or) Z = ( Xbar – LSL ) / σ
For bilateral tolerance
ZUSL =( USL – X ) / σ (or) ZLSL =( X - LSL) / σ
Where
USL Upper specification limit
LSL Lower specification limit
Z Negative value of Z indicates the process average is out of
specification.
ZMIN Minimum of ZUSL and ZLSL
Z values can be used with the table of the standard normal distribution (appendix Fin SPC manual) to estimate the proportion of output
that will be beyond any specification.
The value of ZMIN can also be converted to a capability index, CPK
CPK = ZMIN / 3 = Min [ (USL – Xbar) / 3 σ or (Xbar – LSL) / 3 σ ]
A process of ZMIN = 3 would have a capability index of CPK = 1.00
If ZMIN = 4, the process would have a capability index of CPK = 1.33
23. Evaluate process capability
It is necessary to evaluate the process capability in terms of meeting customer requirements.
Fundamental goal is never ending improvement in process performance.
Improve the process performance by reducing the variation that comes from common causes, or shift the process average
close to the target. This generally means taking management action to improve the system.
Improve Process Capability
To improve process capability, there must be increased attention on reducing the common causes. Accounts must be
directed towards the system namely, the underlying process factors which account for the process variability such as
(1) Machine performance.
(2) Consistency of input materials.
(3) Basic methods by which process operates.
(4) Training methods.
(5) Working environment.
As a general rule these system-related causes for unacceptable process capability may be beyond the abilities of the
operator or their local supervisor to correct. Instead they may require management intervention to make basic changes,
allocate resources and provide the co ordination needed to improve the overall process performance.
24. P chart measures the proportion of non conforming items in a group of items being inspected.
eg: 7 pieces are defective out of 70 pieces.
Before P chart can be used several preparatory steps must be taken :
(1) Establish an environment suitable for action.
(2) Process must be understood in terms of its relationship to other operations/users and in terms of the
process elements (people,equipment,material,methods,environment). Technique such as cause and effect
diagram help make these relationships visible.
Subgroup Size :
Charts for attributes require large subgroup sizes to be able to detect moderate shift in
performance.
eg: nP > 5
Subgroup Frequency :
Subgroup frequency should make sense in terms of production periods.
short time intervals allow faster feedback.
Subgroup Number :
It must vbe large enough to capture all the likely sources of variation affecting the process.
Generally 25 or more subgroups.
Proportion Non Conforming :
Number of items inspected n
Number of non conforming items found nP
Proportion Non Conforming, P = nP / n
Process Average Proportion Non Conforming,
P = ( n1 P1 + n2 P2 + ………………. + nK PK ) / ( n1 + n1 + ……….. + n1 )
P CHART
25. Control Limits :
UCLP = P + 3 { P (1 – P) / n}1/2
LCLP = P - 3 { P (1 – P) / n}1/2
where n is the constant sample size.
Suppose if the sample size varies then take average of sample size ( n ).
Then UCLP = P + 3 { P (1 – P) / n}1/2
LCLP = P - 3 { P (1 – P) / n}1/2
Interpret for Process Control :
. Points above upper and lower control limit is generally sign of higher proportion non conforming.
Average number of non conforming items per subgroup (nP) is large ( 9 or more), the distribution of the subgroup is
nearly normal and trend analysis can be used. When nP becomes small, trend and run analysis is not applicable
Interpret For Process Capability :
For a P chart, process capability is reflected by the process average non conforming p. eg: If P = 0.0312
Process capability currently is 3.12% failures of the functional check (96.88% ok).
Evaluate the Process Capability :
Process capability as just calculated reflects the ongoing level of performance that the process of generating and can
be expected to generate as long as it remains in control.
nP CHART
nP chart measures the number of non conforming items in an inspection. It proves the actual numberof non
conforming items rather than proportion of the sample.
Gather Data :
Sample sizes must be equal.
Samples should large enough to allow several non conformingitems to appear in each subgroup.
Control Limits :
Process Average Non Conforming is nP
UCLnP = nP + 3 {nP (1-P)}1/2
LCLnP = nP - 3 {nP (1-P)}1/2
Process Capability :
Note that the process capability for an nP chart is still P.
26. C – CHART
C-Chart is used when number of defects are found in single unit or product.
Data Collection :
Sample size must be constant. It is applied to
(1) Non conformities are scattered through a continous flow of product.
eg: flaws in a bolt of vinyl, bubbles in glam.
Calculate Control Limits :
Process average number of non conformities
C = (C1 + C2 + ……… CK ) / K
UCLC = C + 3 ( C )1/2
LCLC = C - 3 ( C )1/2
Process Capability :
Process Capability is C.
‘U’ CHART
U – Chart measures the number of non conformities per inspection reporting unit in subgroups which can
have varying sample sizes.
It is similar to C-Chart except that the number of non conformities is expressed on a per unit basis.
Control Limits :
U = C / n
where C number of non conformities found.
n sample size of the subgroup.
Calculate process average non conformities ( U ).
UCLU = U + 3( U / n)1/2
LCLU = U - 3( U / n)1/2
Process capability is U, the average number of non conformities per reporting unit.
