An introduction to x-BAR chart

STATISTICAL QUALITY CONTROL

1. AN INTRODUCTION TO 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 CONTROL (BY control chart) PRODUCT CONTROL (BY sampling inspection plan) VARIABLES ATTRIBUTES VARIABLES -CHART   R-CHART σ - CHART C-CHART NP-CHART P -CHART

4. W hy chart ?   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 -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 = LCL = µ A σ Where μ = mean of the variable, σ = standard deviation of the variable. A = ; n=2,3…25  

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

8. 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

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 6 th edition; D.C. Montgomery