Lecture The management and control of quality - Chapter 14: Statistical process control. This chapter presents the following content: Statistical quality control, statistical process control, types of variations, causes of variation, assignable causes,...
Chapter 14 Statistical Process Control Statistical Quality Control Acceptance sampling Attributes Variables Process Control Attributes Variables Statistical Quality Control for Acceptance Sampling and for Process Control Statistical Process Control Statistical process control is the application of statistical techniques to determine whether a process is delivering what the customer wants Acceptance sampling is the application of statistical techniques to determine whether a quantity of material should be accepted or rejected based on the inspection or test of a sample Types of Variations Common Cause Random Chronic Small System problems Mgt controllable Process improvement Process capability Special Cause Situational Sporadic Large Local problems Locally controllable Process control Process stability Variation from Common Causes Variation from Special Causes Causes of Variation Two basic categories of variation in output include common causes and assignable causes Common causes are the purely random, unidentifiable sources of variation that are unavoidable with the current process – If process variability results solely from common causes of variation, a typical assumption is that the distribution is symmetric, with most observations near the center Assignable Causes The red distribution line below indicates that the process produced a preponderance of the tests in less than average time Such a distribution is skewed, or no longer symmetric to the average value A process is said to be in statistical control when the location, spread, or shape of its distribution does not change over time After the process is in statistical control, managers use SPC procedures to detect the onset of assignable causes so that they can be eliminated Location Spread © 2007 Pearson Education Shape Statistical Process Control (SPC) A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate SPC relies on control charts 10 Spreadsheet Template Special Variables Control Charts xchart for individuals Key Idea Charts for Individuals Control charts for individuals offer the advantage of being able to draw specifications on the chart for direct comparison with the control limits Charts for Attributes Fraction nonconforming (pchart) – Fixed sample size – Variable sample size npchart for number nonconforming Charts for defects – cchart – uchart Key Idea Choosing between C & Ucharts Confusion often exists over which chart is appropriate for a specific application, because the c and ucharts apply to situations in which the quality characteristics inspected do not necessarily come from discrete units Control Chart Formulas Control Chart Selection Quality Characteristic variable attribute defective n>1? no x and MR yes n>=10 or no computer? yes x and s defect x and R constant sample size? yes p or np no p-chart with variable sample size constant sampling unit? 37 yes no c u Control Chart Design Issues Basis for sampling Sample size Frequency of sampling Location of control limits 38 Key Idea In determining the method of sampling, samples should be chosen to be as homogeneous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time Key Idea In practice, samples of about five have been found to work well in detecting process shifts of two standard deviations or larger. To detect smaller shifts in the process mean, larger sample sizes of 15 to 25 must be used Economic Tradeoffs PreControl LTL Red Zone UTL Red Zone Green Zone nominal value Yellow Zones 43 Key Idea Precontrol is not an adequate substitute for control charts and should only be used when process capability is no greater than 88 percent of the tolerance, or equivalently, when Cp is at least 1.14. If the process mean tends to drift, then Cp should be higher .. .Statistical? ? Quality? ?Control Acceptance sampling Attributes Variables Process? ? Control Attributes Variables Statistical? ?Quality? ?Control? ?for Acceptance Sampling? ?and? ? for? ?Process? ?Control Statistical? ?... Statistical? ? Process? ?Control Statistical? ?process? ?control? ?is? ?the? ? application? ?of? ?statistical? ?techniques to determine whether a? ?process? ?is delivering what? ?the? ?customer wants Acceptance sampling is? ?the? ?... Interpreting? ?Control? ?Charts When a? ?process? ?is in? ?statistical? ?control, the? ?points on a? ?control? ?chart fluctuate randomly between? ?the? ?control? ?limits with no recognizable pattern Typical Out? ?of? ?Control? ?