Statistical quality control .pdf
- 2. 2 What is SQC? Statistical quality control (SQC) is the term used to describe the set of statistical tools used by quality professionals. SQC Categories 1. DESCRIPTIVE STATISTICS Descriptive statistics are used to describe quality characteristics and relationships. a. The Mean- measure of central tendency b. The Range- difference between largest/smallest observations in a set of data c. Standard Deviation measures the amount of data dispersion around mean
- 3. 3 a. The Mean To compute the mean we simply sum all the observations and divide by the total no. of observations. b. The Range: Range, which is the difference between the largest and smallest observations
- 4. 4 c. Standard Deviation Standard deviation is a measure of dispersion of a curve. It measures the extent to which these values are scattered around the central mean. 2. STATISTICAL PROCESS CONTROL • Extend the use of descriptive statistics to monitor the quality of the product and process • Statistical process control help to determine the amount of variation • To make sure the process is in a state of control Variation in Quality No two items are exactly alike. Some sort of variations in the two items is bound to be there. In fact it is an integral part of any manufacturing process. This difference in characteristics known as variation. This variation may be due to substandard quality of raw material, carelessness on the part of operator, fault in machinery system etc.
- 5. 5 Types Of Variations A. Variation due to chance causes/common causes Variation occurred due to chance. This variation is NOT due to defect in machine, Raw material or any other factors. Behave in “random manner”. Negligible but Inevitable The process is said to be under the state of statistical control. B. Variation due to assignable causes Non – random causes like: Difference in quality of raw material Difference in machines Difference in operators Difference of time
- 6. 6 Specification and control limits No item in the world can be a true copy of another item. It is not expressed in absolute values but in terms of a range. For Example: The diameter of a tablet punch is expected by its manufacturer not as 7mm but as 7mm ± 0.05. Thus, the diameter of a tablet punch produced by the manufacturer can vary from 6.95 mm to 7.05 mm. Setting Control Limits HOW CONTROL LIMITS ARE USEFUL…..?
- 7. 7 SPC Methods-Control Charts Control Charts show sample data plotted on a graph with CL, UCL, and LCL Control chart for variables are used to monitor characteristics that can be measured, e.g. Hardness, weight, diameter, %age Assay Control charts for attributes are used to monitor characteristics that have discrete values and can be counted e.g. % age of Tables have mottling. Control Charts for Variables a. x-bar charts It is used to monitor the changes in the mean of a process (central tendencies). b. R-bar charts It is used to monitor the dispersion or variability of the process Constructing a X-bar chart ( sigma is not given) A factory produces 50 injections per hour. Samples of 10 injections are taken at random from the production at every hour and the amount of API of injection are measured (Assay). Draw X-bar and R charts and decide whether the process is under control or not.
- 8. 8 Calculation of x-bar and R-bar Now,
- 9. 9 Control limits of X-Bar Chart:
- 10. 10 X-Bar Chart: Control limits of R-Bar Chart R-Bar Chart
- 11. 11 Control Charts for Attributes Attributes are discrete events; yes/no, pass/fail Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions Number of leaking vials in a box of 48 Number of broken syrup bottles in a carton Use C-Charts for discrete defects when there can be more than one defect per unit Number of particulates in a vial sample taken from a production run Number of complaints per customer of pen injection insulin users P-Chart Example A Production manager of a Pharmaceutical company has inspected the number of defective tablets in 20 random samples with 20 tablets in each sample. The table below shows the number of defective tablets in each sample of 20 tablets. Calculate the control limits
- 12. 12 Another Formula (simplified) P- Control Chart
- 13. 13 C - Chart Example The number of weekly customer complaints are monitored of pen injection insulin users using a c-chart. Develop three sigma control limits using the data table below. Number of weekly complaints are monitored. Complaints are recorded over twenty weeks C - Control Chart
- 14. 14 Process Capability Evaluating the ability of a production process to meet or exceed preset specifications. This is called process capability. Product specifications, often called tolerances, are preset ranges of acceptable quality characteristics, such as product dimensions. Two parts of process capability 1) Measure the variability of the output of a process, and 2) Compare that variability with a proposed specification or product tolerance. 1. Measuring Process Capability To produce an acceptable product, the process must be capable and in control before production begins. Example Let’s say that the specification for the acceptable volume of Pharmaceutical liquid filled is preset at 16 ounces ±.2 ounces, which is 15.8 and 16.2 ounces. 6 LSL USL Cp
- 15. 15 Figure (a) The process produces 99.74 percent (three sigma) of the product with volumes between 15.8 and 16.2 ounces. Figure (b) The process produces 99.74 percent (three sigma) of the product with volumes between 15.7 and 16.3 ounces.
- 16. 16 Figure (c) The production process produces 99.74 percent (three sigma) of the product with volumes between 15.9 and 16.1 ounces.