C chart

STATISTICAL QUALITY CONTROL

1. PRESENTED BY RITUPARNA GHOSH APRAJIT JHA M.Sc BIOSTATISTICS AND DEMOGRAPHY C CHART

2. BASIC PRINCIPLES OF CONTROL CHARTS The control chart is a graphical display of a quality characteristic that has been measured or computed from a sample versus the sample number or time. The charts contains a central line,a upper control limit and a lower control limit.

3. TYPES OF CONTROL CHARTS

4. HEALTHCARE & CONTROL CHART Control chart Aid in process understanding Assess process stability Identify changes indicating improvement or deteoriation in quality Used in Hospital process improvement projects Accrediting bodies and governmental agencies Public health surveillance

5. CONTROL CHART FOR NONCONFORMITIES(DEFECT) The nonconfirming item is a unit of product that doesnt satisfy the specifications for that product. Distinction between a defect and defective is clear Defect:-Any instance of the item’s lack of conformity to specification. Defective:-Item that fails to fulfil one or more of the given specifications

6. WHAT IS C-CHART? Originally proposed by Walter A. Shewhart . It is a control chart for nonconformities. Developed for total number of nonconformities in a unit. Underlying distribution-Poisson distribution. Two cases- 1.Standard given. 2.Standard not given.

7. C-CHART:STANDARD GIVEN UCL =c+3√c. Central line= c LCL=c-3√c. NOTE: where c is the parameter of Poisson distribution. If LCL comes negative, take it as 0.

8. C-CHART:STANDARD NOT GIVEN Let c i be the c value for the sample taken from the ith subgroup( i =1(1)n).Then the appropriate estimate of c will be c’=∑ c i /n. UCL= c’+3√c’. CENTRAL LINE= c’. LCL= c’-3√c’.

9. NOTE: c’ is the estimated value of the poisson parameter. c’ may be estimated as the observed average number of nonconformities in a preliminary sample of inspection units. When no standard is given, the control limits in equation should be regarded as trial control limits.

10. 26 Samples -516 total nonconformities c’=516/26=19.85 UCL=c’+3√c’=19.85+3√19.85=33.22 Centre Line=c’=19.85 LCL=c’-3√c’=19.85-3√19.85=6.48 EXAMPLE…

11. After removing the two out of control points , The estimate of c is now computed as c’=472/24=19.67 Revised control limits:- UCL=c’+3√c’=19.67+3√19.67=32.97 Centre Line=c’=19.67 LCL=c’-3√c’= 19.67-3√19.67=6.36

12. Interpretation The process is under control. No lack of control is indicated.

13. USE OF C-CHART IN HEALTH CARE Attribute data involves- -counts( no.of falls per day). --proportions(proportion of patients receiving right antibiotics). -rate(the number of falls per 1000 patient-days). For counts we use c-chart.

14. CONCLUSION Defect or nonconformity data are always more informative than fraction nonconforming, Widely used in transactional and service business applications of statistical process control. The limitation of c chart is that it takes samples of constant size where in reality it might not be so.In case of variable sample size we use the u charts that gives us the no.of defects per unit i.e u= c/n .

15. SOURCES “Introduction to Statistical Quality Control”- Doughlas C.Montgomery “Fundamentals of Statistics Vol-2”- A.M.Gun,M.K.Gupta,B.Dasgupta support.minitab.com/en-us/ minitab /17/topic-library/quality-tools/control-charts/understanding-attributes-control-charts/what-is-a-c-chart/ http://www.coe.neu.edu/healthcare/pdfs/publications/C13-Use_of_Control_C.pdf.

16. THANK YOU