STATISTICAL QUALITY CONTROL

1. AN
INTRODUCTION
TO
𝑋 −CHART
By
MRINMOY PRATIM BHARADWAZ
SHUBHANKAR SHARMA
M.Sc Biostatistics & Demography
2015-17

2. 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)

3. ATTRIBUTES
TECHNIQUES OF
S.Q.C.
PROCESS
CONTRO
L
(BY control
chart)
PRODUCT
CONTROL
(BY sampling
inspection
plan)
VARIABLES ATTRIBUTES VARIABLES
𝑿-CHART
R-CHART
σ- CHART
C-CHART
NP-CHART
P-CHART

4. Why 𝑋chart ?
In any measurable quality characteristics can be
applied.
To control the measure of location(i.e. mean) this
type of chart is used.

5. BASIC COMPONENTS OF
𝑋-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.

6. CONTROL LIMITS
• Case 1 : when mean(µ) & s.d.(σ) are known
UCL = µ+A σ
CL = µ
LCL = µ−A σ
Where μ =mean of the variable,
σ =standard deviation of the variable.
A = 3 √𝑛 ; n=2,3…25

7. Case 2 : when mean(μ) & s.d.(σ)
are not known
UCL = 𝜇+A2 𝜎
CL = 𝜇
LCL = 𝜇- A2 𝜎
Where 𝜇=estimated mean of the variable,
𝜎 =estimated standard deviation
A2 = 3 𝑑2√𝑛 ; n=2,3…25
d2=constant depends on “n”
(A2 & 𝑑2 values can be get from table on the basic of “n”)

8. CRITERION FOR DETECTING
LACK OF CONTROL IN 𝑋 − 𝐶𝐻𝐴𝑅𝑇
• 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

9. INTERPRETATION
SL
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

10. EXAMPLE
TREND
CYCLIC
MIXTURE
SHIFT

11. Reference
• Fundamentals of applied statistics; S.C. Gupta;
V.K.Kapoor
• Introduction to statistical quality control 6th edition;
D.C. Montgomery