Tech 31: Unit 3 Control Charts for Variables Statistical Process Control (SPC)

Control Charts Control charts are tools used to determine whether or not a manufacturing process is in a state of statistical control

Process Variation is Present in Every Process Due to a Combination of Factors: Equipment Materials Environment Operator

Types of Variation Within-piece variation Piece-to-piece variation Time-to-time variation Chance causes Assignable causes

Statistical Process Control A method of quality control using statistical methods. Applied in order to monitor and control a process. Monitoring and controlling the process ensures that it operates at its full potential. At its full potential, the process can make as much conforming products as possible with a minimum waste, rework or scrap. SPC can be applied to any process.

Standard Normal Curve = 99.74% of Quality

Examples of Normal Distribution

Normality & Control Charts: Principles

Sample Control Chart

Elements of the Control Chart . . UCL = CL+ 3s . . . . X . CL = X LCL = CL - 3s 1 2 3 4 5 6 7 Time/Order

Elements of a Control Chart . . . UCL = CL+ 3s . . R . . CL = R LCL = CL - 3s 1 2 3 4 5 6 7 Time/Order

Determining X-Bar and X-Double Bar X-Bar = Mean or Average of sub-groups, usually made up of 4 items per sub-group X-Bar of 4 + 4.2 + 3.9 + 4.1 = 15.3/4 = 3.8 Class projects will involve 25 subgroups X-Double Bar is the mean (grand mean) of all the sub-group means

Determining the Control Limits The control limit is equal to the grand mean CL = Grand mean or X-double bar UCL = Upper control limit = CL + 3ϱ UCL = Upper control limit = CL + A2R-bar LCL = Lower control limit = CL - 3ϱ LCL = Upper control limit = CL - A2R-bar

Objectives of Control Charts For quality improvement To determine process capability For decisions in regard to product specifications For decisions in regard to new and existing production processes

Process Capability Vs Specifications

Process Capability Vs Specifications

Process Capability Vs Specifications

Control Chart Techniques Select the quality characteristic Choose the rational subgroup Collect Data Determine the trial central line (CL) and control limits (UCL & LCL) Establish the revised CL, UCL, & LCL Achieve Objectives

Control Charts Types of Control Charts Control Chart for Variables X-bar charts R charts The sample standard deviation control chart The median and range chart The individual and range chart

Control Charts continued Control Charts for Attributes p & np charts c charts u charts

State of Control Process in control Process out of control

Process in Control

. . . . . . . Process Out of Control X CL = X 1 2 3 4 5 6 7 Time/Order UCL = CL+ 3s . . CL + A2R-bar . . X . CL = X LCL = CL - 3s 1 2 3 4 5 6 7 CL - A2R-bar Time/Order

Analysis of Out-of-Control Condition Change or jump in level Trend or steady change in level Recurring cycles Two populations (mixture) Mistakes

Specifications Individual values compared to averages Central limit theorem Control limits and specifications Process capability and tolerance

Process capability = Six X Sigma UCL A B C CL C B A LCL

Cpk = Min{(USL-X-bar) or (LSL-X-bar)}/3s Process Capability Control Limits & Specification Limits Process Capability = 6s Process Capability Index: CP = (USL-LSL)/ 6s Cpk = Min{(USL-X-bar) or (LSL-X-bar)}/3s

Six sigma If sigma can be reduced to the point that the specifications are at + or – 6 sigma, then 99.9999998% of the product or service will be within specifications

Different Control Charts Charts for better operator understanding Charts for variable subgroup size Charts for trends Charts for moving average and moving range Charts for median and range Charts for individual values Charts with non-acceptance limits