PROCESS CAPABILTY AND CONTROL CHARTS 1

Content Introduction Review of basics Process Capability Types of control Charts Development and maintenance of control charts Interpretation of control charts Practice problem 2

Review of basics Proper strategy for quality control is to Control the process rather than sorting inspection of the product Variability is a norm but it should be minimized Two causes of variation Common causes that are inherent in the process over time Special causes that are not part of the process all the time but arise because of specific circumstances Statistics can help identifying the presences of special causes 3

Process variation Inherent conflict between two points: Variation is inevitable The production is most economical when output is of uniform quality Source of Variation: Man, Material, Machine, Mood, Environment etc. ; 4

Need for process capability study A manager is interested in knowing whether the process is capable of producing the products of desired quality What proportion of the products produced by process are expected to be accepted/rejected What changes are needed to improve the capability of the process or to reduce the rejection rate Process capability study provide answers to all of the above questions 5

Process capability It refers to the performance of the process when it is operating in statistical control. It is a measure of the uniformity of a process that makes a product A common measure of process capability is 6-sigma or spread It makes sense only when the process is in statistical control 6

Process capability Definition It is performance under chronic conditions in which sporadic variation do not exist. 7

Process capability analysis? It is an engineering study to estimate process capability It may involve estimating the process mean and standard deviation It might also involve estimating the proportion of nonconforming items 8

Benefits Help predicting how well the process will hold the tolerances Assist in product and process development Assists in specifying performance requirements for new equipment Assists in vendor selection Help in variability reduction and reduces total cost by lowering internal and internal failure costs 9

Specification and control limits Specification Limits (or tolerance limits Limits that define the conformance boundary for an individual unit Provided by the designer or the customer for the products for its functioning Control Limits (or natural tolerance limits) outcome of the process identifying process variability Does not apply to an individual units No relation between specification and control limits 10

Specifications and control limits LSL USL LCL UCL Process spread= Specifications and control limits 11

Stable and capable process Stable process is whose output is influenced only by chance causes and not by special causes This does not imply that the output will be as per specifications Capable process is one that is expected to produce output conforming to the specifications when the process is in control 12

Capable and incapable process LSL USL Capable Not Capable Capable and incapable process 13

Control Chart General theory first proposed by Walter. A. Shewhart of the Bell Telephone Lab in 1920s A control chart is a graphical tool for monitoring a process It indicates presence/absence of special cause(s) of variation in the process It is an on-line quality control tool 14

Types of control charts (Based of type of data) Attribute control charts p chart c chart Variable control charts X-bar chart R chart 15

Steps Involved in the construction of Control Charts Partition the historical data: two distinctly data set- one for the construction and other for reflecting on the performance Use data to identify 3 sigma limit Draw the control charts axis. Y axis for variable measurement, X axis for sequence of samples Plot the most recent average 16

Steps Involved in the construction of Control Charts Interpret (a) in control (b) out of control ( c ) in control but need caution Update the control charts by discarding the old data and including the recent data 17

Type 1, α risk, or producer’s risk:- Probability of concluding that the process is out of control where actually it is in control. Reduced by 3 sigma limit, Increased by 1 sigma limits Type 2, β risk, or consumer’s risk:- Probability of concluding that the process is in control where as this is out of control. Risk increases as the limits are widened and reduces as limits are reduced.

Comparison of variable and attribute charts Variables provide more information than attributes Cost of inspection for obtaining variable data is normally higher than for attributes Attribute charts more useful at plant level while variable charts at the machine or operator level 21

Benefits of control charts Distinguish special from common causes of variation to guide management action Can be used by operators for on-line control of a process Provides predictability for quality and cost Allow the process to achieve Higher quality Lower unit cost Higher effective capacity 22

Steps involved Analyze the product and the process Define the purpose of using control charts Select the the characteristic/s for control charting Select the type of control chart to be used Analyze the process of measurement Determine subgroup size and frequency of sampling Design the format for data recording and charting 23

Determine the trial control limits Plot the points and identify points indicating out of control process Search for special causes and rectify Calculate final control limits Continue the process 24

Interpretation of control charts Process under control Process whose outcomes are affected by common causes is called stable process or process that is in a state of statistical control It does not imply that the process is producing the desired quality of products relative to specifications Let the process continue Process out of control Process whose outcomes are affected both by common causes and special causes is called un- stable process or out of control process Attention required 25

Out of control process A control chart may indicate an out-of- control condition either when one or more points fall beyond the control limits, or when the plotted points exhibit some nonrandom pattern of behavior 26

Some Rules for identifying out of control process (Developed at Western Electric) If a single point plots outside the control limits Two of three consecutive points outside the warning (2-sigma) on the same side of the center line Four of five consecutive points beyond the 1- sigma limits. Eight or more consecutive points fall to one side of the center line A trend of eight or more points in a row in upward or downward direction 27

Some patterns which may be due to out of control process Change in the level of plotted points Trend in the plotted pattern Cyclic behavior in the plotted pattern Concentration of points near control limits 28

Control charts for variables Used for variable data Separate chart for each quality characteristic Two things – mean and spread – must be in control hence two charts are maintained simultaneously X-bar and R chart Spread chart is analyzed first and then the chart for mean 29

X-bar chart Details 30

Control limits for X-bar and R chart R chart 31

Charts for attributes Used for attribute data p chart and np chart for classification data c chart and u chart for count data Only one chart is plotted instead of two as in case of charts for variables 32

Chart for fraction nonconforming (p Chart) Used when items are inspected for its conformity or nonconformity to the specifications Based on Binomial distribution 33

Control limits for p chart Fraction nonconforming in a sample can be found by Where x in number of nonconforming items and and n is sample size Where is average of over all the samples 34

Chart for number of nonconformities (c chart) Used to track total number of nonconformities in a sample (of constant size) or the area of opportunities Based on Poisson distribution 35

Control limits for c chart Where is the average number of nonconformities per sample unit 36

Summary Control charts are tool for SPC which help identifying the presence of assignable causes in the process Different types of charts for different types of data Different rules are there for detecting out of control process 37

Type of data Continuous data Classification data Count data A measured value of the quality characteristic is recorded e.g. dimension, weight, specific gravity, cost Classification data Quality characteristic is recorded in one of two classes e.g. conforming/nonconforming units, good/bad Count data The number of incidences of a particular characteristic is recoded e.g. number of accidents, number of mistakes 38

Conceptually, 3-sigma limits for X-bar control charts are is standard deviation of the sample means and as per central limit theorem where is the s.d. for the individual units where is a constant depending on the sample size as another constant 39

Value of the characteristic Center line Upper control limit Sample number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Lower Warning limit Upper Warning limit Value of the characteristic One sigma limit One sigma limit Lower control limit 40

Value of the characteristic CL UCL Sample number 1 2 3 4 5 6 7 8 9 10 Value of the characteristic LCL 41

Value of the characteristic CL UCL 1 2 3 4 5 6 7 8 9 10 Value of the characteristic LCL Sample number 42

Value of the characteristic CL UCL 1 2 3 4 5 6 7 8 9 10 Value of the characteristic LCL One sigma limit One sigma limit 43

Value of the characteristic CL UCL 1 2 3 4 5 6 7 8 9 10 Value of the characteristic LCL 44

Value of the characteristic CL UCL 1 2 3 4 5 6 7 8 9 10 Value of the characteristic LCL 45

Thank You 46

Genesis of control charts Walter A. Shewhart of the Bell Telephone Laboratories issued a memorandum on May 16, 1924 that featured a sketch of a modern control chart.  Published a book on statistical quality control, "Economic Control of Quality of Manufactured Product", in 1931, published Van Nostrand in New York. This book set the tone for subsequent applications of statistical methods to process control. 47