# Statistical Process Costantrol

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Introduction to Inferential Statistics

Statistical Process Control 02/03/20141Statistical Process ControlAmor MessaoudAssistant professor at Tunis Business SchoolUniversity of TunisEmail: [email protected]

IntroductionIt is assumed that the quality charcteristic X is normally distributed with mean and standard deviation In practice, and are usually unknownThey are estimated from preliminary m samples or subgoups taken when the process is thought to be in controlThese estimates should usually be based on at least 20 to 25 samples02/03/2014Statistical Process Control2

Definitions of Quality Quality means fitness for usequality of designquality of conformanceQuality is inversely proportional to variability02/03/2014Statistical Process Control3

Quality ImprovementQuality improvement is the reduction of variability in processes and products

Alternatively, quality improvement is also seen as waste reduction

02/03/2014Statistical Process Control4

Statistical Process ControlStatistical process control (SPC) is a collection of tools that when used together can result in process stability and variance reductionSPC is a powerful collection of problem-solving tools useful in achieving process stability and improving capability through the reduction of variability02/03/2014Statistical Process Control5

The Magnificent sevenThe seven major tools areHistogramPareto ChartCause and Effect DiagramDefect Concentration DiagramControl Chart Scatter Diagram Check Sheet

02/03/2014Statistical Process Control6

Understanding variation

A process that is operating with only chance causes of variation present is said to be in statistical controlA process that is operating in the presence of assignable causes is said to be out of controlimproperly adjusted or controlled machinesoperator errorsdefective raw materialThe eventual goal of SPC is the elimination of variability in the process02/03/2014Statistical Process Control7

Understanding variation02/03/2014Statistical Process Control8

Statistical basis of the control chartA typical control chart has control limits set at values such that if the process is in control, nearly all points will lie within the upper control limit (UCL) and the lower control limit (LCL)02/03/2014Statistical Process Control9

Statistical basis of the control chartThe center line that represents the average value of the quality characteristic corresponding to the in-control state (That is, only chance causes are present)The UCL and LCL are chosen so that if the process is in control, nearly all of the sample points will fall between them02/03/2014Statistical Process Control10

Statistical basis of the control chartAs long as the points plot within the control limits, the process is assumed to be in control, and no action is necessaryHowever, a point that plots outside of the control limits is interpreted as evidence that the process is out of control, and investigation and corrective action are required to find and eliminate the assignable cause or causes responsible for this behavior02/03/2014Statistical Process Control11

General Model for a control chartLet w be a sample statistic that measures some quality characteristic of interest, and suppose that the mean of w is w and the standard deviation of w is w. Then,

L is the distance of the control limits from the center line, expressed in standard deviation units02/03/2014Statistical Process Control12

General Model for a control chartThe control chart is a device for describing in a precise manner exactly what is meant by statistical control; as such, it may be used in a variety of ways In many applications, it is used for on-line process surveillanceWe may be interested here in determining both whether the past data came from a process that was in control and whether future samples from this process indicate statistical control02/03/2014Statistical Process Control13

Most processes do not operate in a state of statistical controlConsequently, the routine and attentive use of control charts will identify assignable causes. If these causes can be eliminated from the process, variability will be reduced and the process will be improvedThe control chart only detects assignable causes. Management, operator, and engineering action will be necessary to eliminate the assignable causes02/03/2014Statistical Process Control14Process Improvement using control charts

Process Improvement using control charts02/03/2014Statistical Process Control15

Out-of-control action plan (OCAP)An OCAP is a flow chart or text-based description of the sequence of activities that must take place following the occurrence of an activating event. These are usually out-of-control signals from the control chartThe OCAP consists of checkpoints, which are potential assignable causes, and terminators, which are actions taken to resolve the out-of-control condition, preferably by eliminating the assignable cause02/03/2014Statistical Process Control16

Types of the control chartVariables Control ChartsThese charts are applied to data that follow a continuous distributionAttributes Control ChartsThese charts are applied to data that follow a discrete distribution02/03/2014Statistical Process Control17

Popularity of control chartsControl charts are a proven technique for improving productivity.Control charts are effective in defect prevention.Control charts prevent unnecessary process adjustment.Control charts provide diagnostic information.Control charts provide information about process capability02/03/2014Statistical Process Control18

Suppose we have a process that we assume the true process mean is = 74 and the process standard deviation is = 0.01. Samples of size 5 are taken giving a standard deviation of the sample average, is

Example: Design of a control chart02/03/201419Statistical Process Control

Control limits can be set at 3 standard deviations from the mean in both directions.3-Sigma Control Limits UCL = 74 + 3(0.0045) = 74.0135 CL= 74 LCL = 74 - 3(0.0045) = 73.9865

Example: Design of a control chart02/03/201420Statistical Process Control

Example: Design of a control chart02/03/201421Statistical Process Control

Choosing the control limits is equivalent to setting up the critical region for hypothesis testing H0: = 74 H1: 74Example: Design of a control chart02/03/201422Statistical Process Control

Choice of control limitsType I error: the risk of a point falling beyond the control limits, indicating an out-of-control condition when no assignable cause is presentType II error: the risk of a point falling between the control limits when the process is really out of control02/03/2014Statistical Process Control23

Choice of control limitsMoving the control limits farther from the center line (widening the control limits), we decrease the risk of a type I error but we increase the risk of type II errorIf we move the control limits closer to the center line, the opposite effect is obtained: The risk of type I error is increased, while the risk of type II error is decreasedWe typically justify the use of three-sigma (L=3) on the basis that they give good results in practice02/03/2014Statistical Process Control24

Subgroups or samples should be selected so that if assignable causes are present, the chance for differences between subgroups will be maximized, while the chance for differences due to these assignable causes within a subgroup will be minimized.Rational subgroups02/03/201425Statistical Process Control

Constructing Rational SubgroupsSelect consecutive units of production.Provides a snapshot of the process.Good at detecting process shifts. Select a random sample over the entire sampling interval.Good at detecting if a mean has shifted out-of-control and then back in-control.Rational subgroups02/03/201426Statistical Process Control

Look for runs - this is a sequence of observations of the same type (all above the center line, or all below the center line)Runs of say 8 observations or more could indicate an out-of-control situation.Run up: a series of observations are increasingRun down: a series of observations are decreasingAnalysis of patterns on control charts02/03/201427Statistical Process Control

Analysis of patterns on control charts02/03/201428Statistical Process Control

Analysis of patterns on control charts02/03/201429Statistical Process Control

Analysis of patterns on control charts02/03/201430Statistical Process Control

Phase I and Phase II of control chart applicationIn phase I, a set of process data is gathered and analyzed all at once in a retrospective analysis, constructing trial control limits to determine if the process has been in control over the period of time where the data were collected, and to see if reliable control limits can be established to monitor future productionThis is typically the first thing that is done when control charts are applied to any process. Control charts in phase I primarily assist operating personnel in bringing the process into a state of statistical control02/03/2014Statistical Process Control31

Phase I and Phase II of control chart applicationPhase II beings after we have a clean set of process data gathered under stable conditions and representative of in-control process performance In phase II, we use the control chart to monitor the process by comparing the sample statistic for each successive sample as it is drawn from the process to the control limits02/03/2014Statistical Process Control32

Phase I and Phase II of control chart applicationGenerally, Shewhart control charts are very effective in phase I because they are easy to construct and interpret, and because they a