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spc tools-histogram

Histogram
Histogram as a  spc tool, is a useful tool to show the distribution of data collected over a time period.  The shape of the distribution provides information on whether the variations in a process is stable (random or natural variation) or unstable (non random or externally influence variation)

Benefit
– Simple graphical display or “Bird’s eyes view” of the variation in a set of data according to their frequency of occurrences.
– Quick estimate of the mean of a distribution
– Information on the behavior of a process on whether its variations are natural or abnormal, and whether it meets specification or not.

Application>>>Histogram

Histogram

Histogram

How to Set-up a Control Chart?

1.Select appropriate type of control chart to be used
2.Gather data to establish the control chart.

  • A minimum of 30 subgroups is required over a time frame as determined by the sampling plan.

3.Plot the data in time order on a Trend Chart.
4.Compute the control limits & plot them on the trend chart
5.Outliers identification & exclusion

  • Exclude the Out-of Control (OOC) points or outliers for which there are verified/confirmed special causes from the chart
  • Re-compute the control limits, excluding the OOC points
  • If there are fewer than 30 points remaining at any time, collect more data.  It’s very important that the control limits are calculated using at least 30 subgroups.

Note:Refer to Appendix A for Control Charts for Limited Production, i.e. < 30 subgroups.

6.Validate the computed control limits against data collected by re-plotting the control chart with data & new control limits

  • Do the limits detect known problems?
  • Are the limits too sensitive?  Would they flag problems you do not know how to react to?

7.Use the control limits established to monitor the critical parameter identified
8.For each parameter, every machine should have a separate control chart with separately computed control limits

X-MR Charts

Applications where sample size for process monitoring is n=1

  • 100% automated inspection and measurement
  • production rate is very slow
  • repeatability of measurement is negligible
  • variation within unit (e.g. roll of paper) is negligible

The X-MR Chart (or I-MR Chart) is a useful control chart if the characteristic is independently and normally distributed.

If Xi is the measurement obtained during sampling i, then the Moving Range MRi is given by
MRi   =   Abs{Xi – Xi-1}   =   | Xi – Xi-1 |

e.g.    MR1   =   |X1 – X0|
MR2   =   |X2 – X1|
MR3   =   |X3 – X2|

X0 may be set at some historical estimate of the process mean.If X0 is omitted, then MR1 is not calculated.

The Center Line and Control Limits of a X Chart are

X-MR Charts1

X-MR Charts1

The Center Line and Control Limits of a MR Chart are

X-MR Charts2

X-MR Charts2

Example

The viscosity of an aircraft primer is an important quality characteristic.  Production is in batches, with a very slow production rate.  Hence, only 1 sampling is performed per batch.The viscosity over 15 batches of primer is reviewed to determine if the process is in-statistical-control.

X-MR Charts3

X-MR Charts3

Smart SPC Analyst’s—Statistic—I-MR Chart

X-MR Charts4

X-MR Charts4

The moving ranges are correlated, i.e. they are dependent on the current and previous data points (X0 and Xi-1).
This correlation may induce a pattern of runs or cycles on the MR Chart.
Avoid or ignore secondary indicators of instability.

Types of Control Charts

The quality of a product or process may be assessed by means of

  • Variables : actual values measured on a continuous scale e.g. length, weight, strength, resistance, etc
  • Attributes : discrete data that come from classifying units (accept/reject) or from counting the number of defects on a unit

If the quality characteristic is measurable

  • monitor its mean value and variability (range or standard deviation)

If the quality characteristic is not measurable

  • monitor the fraction (or number) of defectives
  • monitor the number of defects

Defectives vs Defects
Defective or Nonconforming Unit

  • a unit of product that does not satisfy one or more of the specifications for the product

–e.g. a scratched media, a cracked casing, a failed PCBA

Defect or Nonconformity

  • a specific point at which a specification is not satisfied

–e.g. a scratch, a crack, a defective IC

Shewhart Control Charts – Overview

Shewhart Control Charts - Overview

Shewhart Control Charts – Overview

Shewhart Control Charts for Variables

Shewhart Control Charts for Variables

Shewhart Control Charts for Variables

 

Control Chart Classifications

Classifications of control charts are depending on the type of data:

1.Variables data

  • A characteristic measured on a continuous scale resulting in a numerical value
  • Examples: Void Size, Bond Pull Strength, Coplanarity, Ball Height, etc.

2.Attributes data

  • A characteristic measured by # of conforming & non-conforming to a specification.  Output is classified as pass/fail or accept/reject.
  • E.g. Broken Wire, Lifted Bond, FM, Chipping, Bent Lead,  etc.
  • Can be expressed in terms of fraction, percentage, count or DPM

 

Control Charts For Variables

Control Charts For Variables

Control Charts For Variables

Control Charts For Attributes

Control Charts For Attributes

Control Charts For Attributes

 

What is a Control Chart?

  • A trend chart with control limits
  • Graphical representation of process performance, where data is collected at regular time sequence of production
  • Valuable tool for differentiating between common cause and special cause variation
  • Evaluating whether a process is or is not in a state of statistical control
  • It lets the data ‘talk’ by itself & basis for data-driven decisions

Control Limits
A typical control chart consists of three lines :

control chart

control chart

CL: The average (measure of location) process performance when the process is in-control

UCL & LCL: The range of ‘usual’ process performance when the process is stable.  Lines drawn 3 standard deviations (3 sigma) on each side of the center line.