an introduction to x-bar chart
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AN INTRODUCTION TO CHART
ByMRINMOY PRATIM BHARADWAZ
SHUBHANKAR SHARMAM.Sc Biostatistics & Demography
2015-17
WHAT IS SQC ?Statistical quality control is simply a statistical method for determining the extent to which quality goals are being met without necessarily checking every item produced and for indicating whether or not the variations which occur are exceeding normal expectation. S.Q.C. Also enables us to decide whether to reject or accept a particular product. (by Grant)
ATTRIBUTES
TECHNIQUES OF S.Q.C.
PROCESS
CONTROL(BY
control chart)
PRODUCT
CONTROL
(BY sampling inspection
plan)VARIABLE
SATTRIBUT
ESVARIABLE
S
-CHART
R-CHART
σ- CHART
C-CHART
NP-CHART
P-CHART
Why chart ?In any measurable quality characteristics can be
applied.To control the measure of location(i.e. mean) this
type of chart is used.
BASIC COMPONENTS OF-chart
A center line(CL), usually the mathematical average of all the samples plotted;
Lower control limits(LCL) and upper control limits(UCL) defining the constraints of MEAN cause variations;
Sample means are plotted in order to control the mean value of a variable.
CONTROL LIMITS • Case 1 : when mean(µ) & s.d.(σ) are known
UCL = µ+A σ
CL =
LCL = µA σWhere μ =mean of the variable,
σ =standard deviation of the variable. A = ; n=2,3…25
Case 2 : when mean(μ) & s.d.(σ) are not knownUCL = +A2
CL =
LCL = - A2 Where =estimated mean of the variable,
=estimated standard deviation A2 = ;n=2,3…25d2=constant depends on “n”
(A2 & values can be get from table on the basic of “n”)
CRITERION FOR DETECTING LACK OF CONTROL IN
• A point outside of the control limits• A run of seven or more points• Points too close to CL• Presence of trends• Presence of cycle
INTERPRETATIONSL NO
SITUATION INTERPRETATION
1 Points beyond limits only on one side
Level of process has shifted
2 Points beyond limits on both side
Level of process is changing in unpredictable manner i.e. variability has increased
3 Out of control on one side
Both level and variability has changed
4 Run of 7 or more points on one side of
CL
Shift in process level
5 Trend of 7 or more points within the
control limits & no points outside control
limits
Process level is gradually changing
6 Points too close to CL Systematic difference in the sub-groups
EXAMPLE
TREND
CYCLIC
MIXTURE
SHIFT
Reference• Fundamentals of applied statistics; S.C.
Gupta; V.K.Kapoor• Introduction to statistical quality control
6th edition; D.C. Montgomery
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