STATISTICAL PROCESS CONTROL CONTROL CHARTS for VARIABLES Control

STATISTICAL PROCESS CONTROL: CONTROL CHARTS for VARIABLES • Control charts are the tools that are used in SPC to indicate when special-cause variation is present in a process • Control chart means of visualizing variations that occur in the central tendency and dispersion of a set of observations • Variables control charts use actual measurement for charting • To create a control chart, samples, arranged into subgroups, are taken during the process • The centerline (CL) of this chart shows where the process average is centered, the tendency of the data • The upper control limit (UCL) and lower control limit (LCL), calculated based on ± 3 sigma, describe the spread of the process • Once the chart is constructed, it presents the user with a picture of what the process is currently capable of producing • Since control charts show changes in the process measurements, they allow for early detection of process changes

CONTROL CHARTS for VARIABLES

CONTROL CHARTS for VARIABLES • In fact, the variation concept is a law of nature in that no two natural items in any category are the same, the variation exists • Even if variation small and appears same; precision instruments show differences • Ability to measure variation necessary before it can be controlled Source of variation (combination of 4 M and etc. ) • Equipment (tool wear, machine vibration, workholding-device) • Material (tensile strength, moisture content, ductility, porosity) • Environment ( temperature, light, humidity, radiation) • Operator (method, SOP followed, motivation level, training) • Inspection (faulty inspection equipment, incorrect application)

CONTROL CHARTS for VARIABLES Objective of Variable Control Chart • For quality improvement – indicate that there is a quality control program is missing the point • To determine process capability – the true process capability can be achieved only after substantial quality improvement has been achieved • For decisions in product specifications – once the true process capability is obtained, effective specifications can be determined • Make decisions on recently produced items – release next process, customer or other disposition method, sorting, rework, reject

CONTROL CHARTS for VARIABLES The types of variables control charts include the following: 1. Average and range charts (X-Bar and R) - consists of two separate charts on the same sheet of chart paper - one graph tracks the sample mean X-Bar and the other tracks the sample range R - the sample size must be the same for all samples and usually consists of three to seven pieces - the mean and range for each sample are calculated, recorded, and charted - the charts is analyzed as it develops for indications of specialcause variation, and after about 25 samples - it is analyzed again to determine the location, spread, and shape of the distribution of measurements - it is most effective when the sample size is less than 10, range (R) chart is simple to construct

CONTROL CHARTS for VARIABLES 2. Average and standard deviation charts (X-Bar and S) - the X-Bar and S chart tracks X-Bar on one part of the chart and the sample standard deviation, S, on the other - the X-Bar and S chart does everything that the X-Bar and R chart does and is used in the same way - Although it is preferred to the R chart because the standard deviation is a better measure of variation than the range - X-Bar and S charts are not used as much as the other variables charts because the standard deviation is more difficult to calculate than the range - the X-Bar and S chart will be used more extensively in the future and may eventually become the standard control chart in use - when the sample size exceeds 10, the ranges does not truly represent the variation present in the process, the standard deviation S chart is used

CONTROL CHARTS for VARIABLES 3. Median and range charts ( and R) - exactly like the X-Bar and R chart, with one exception - the median is calculated and charted instead of the mean - the and R chart analysis also shows indications of special-cause variation and the location, spread, and shape of the distribution of measurements - some companies prefer the and R chart because the calculation of the median is easier and faster than the calculation of the mean - one reason that the X-Bar and R chart is usually preferred over the and R chart is that the X-Bar and R chart is more sensitive to variation analysis

CONTROL CHARTS for VARIABLES 4. Individual and moving range charts (X and MR) - this chart tracks consecutive individual measurement, X, on one chart and the piece-to-piece variability, MR, on the other - the X and MR chart is less reliable than the X-Bar and R chart because it is based on fewer data values - the X and MR chart is generally used when just a small number of data are available, such as for small or short production runs or for batch processes 5. Run charts - simplest measurement-type control chart - it track individual measurements against a target measurement - there is no measure of variation, and the run chart is very susceptible to over adjustment - the run chart is often misused as a control chart with samples of size one by periodically checking the measurement of just one piece

CONTROL CHARTS for VARIABLES Procedure to establish X-Bar (average) and R (Range) chart: 1 Select quality characteristics - measurable data i. e. numbers - 7 basic units – length, mass, time, temperature, substance, etc. - affecting performance and function of product - Pareto analysis – highest % rejects, high production costs, etc. - impossible to put X-Bar & R on all characteristics selective OR treat as attributes chart 2. Choose rational subgroup - rational subgroup which have variation within the group due only to chance causes - two ways selecting subgroup samples 1. Select subgroup samples at one instant of time or as close as possible 2. Select period of time product produced - lots must be homogeneous: same machine, same operator

CONTROL CHARTS for VARIABLES - decision on size of sample empirical judgment & relates to costs choose n = 4 or 5 use R chart when n ≥ 10 use S chart - frequency of taking subgroup often enough to detect process changes - guideline of sample sizes/frequency using - say, 3000 parts/day, then 50 total inspections are suggested - if n = 4, suggested 19 subgroups would be a good starting point

CONTROL CHARTS for VARIABLES 3. Collect data - use form or standard check sheet - collect a minimum of 25 subgroups - does not matter Vertical or Horizontal (sample & subgroup)

CONTROL CHARTS for VARIABLES 4. Determine trial control limits - central line X-Bar and R-Bar - where A 2, D 4, D 3 are factors – vary according to different n

CONTROL CHARTS for VARIABLES 5. Establish revised control limits - first plot preliminary data collected using control limits & center lines establish in step 4 - next step adopt standard values. If good control i. e. no out-ofcontrol points - if there are points out-of-control discard from data Look at record – show an assignable cause – don’t use

CONTROL CHARTS for VARIABLES - limits for both charts become narrower after revised - revised limits used to report/plot future sub-group - for effective use – chart must be displayed and easily seen

X-bar and S

CONTROL CHARTS for VARIABLES

CONTROL CHARTS SELECTION GUIDELINE

CHARTS AND TABLES FORMULA AND CONSTANT FOR CONTROL CHARTS

CONTROL CHARTS for VARIABLES STATE OF CONTROL • When assignable causes eliminated and points plotted are new within CL process state of control • Further improvement through changing basic process, system • What are the characteristics of process in control? (natural pattern variation) - 34% within - 13% between - 2. 5% of plotted points, - points located back & forth across center line random way - no points out of control - subgroup averages forms frequency dist which is normal distribution • Control limits – establish at from center line • Choice of is economic decision with respect to 2 types of error

CONTROL CHARTS for VARIABLES Process in control • Individual parts will be more uniform – less variation and fewer rejects • Cost of inspection will decrease • Process capability easily attained • Trouble can be anticipated before it occurs • Percentage of parts fall between two values can be predicted with highest degree of accuracy, e. g. filling machines • X-Bar & R charts can be used as statistical evidence for process control • Predictable and stable process only chance causes present

CONTROL CHARTS for VARIABLES

CONTROL CHARTS for VARIABLES Analysis for out-of-control 1. Freaks - is a single point that is beyond a control limit - it signifies that something changed dramatically in the process for a short time or that a mistake was made - out-of-control points marked with X’s • Causes - sudden change material, mistake measurement, error in recording, omitted operation, damage in handling, etc.

CONTROL CHARTS for VARIABLES 2. Shifts - sets of seven or more consecutive points that are all on one side of the center line - something was introduced to the process that changed the whole process - usually temporary • Causes - poorly trained operator, maintenance problem, change material, change method, new setup, change machine, etc.

CONTROL CHARTS for VARIABLES 3. Runs and Trends - points that are steadily climbing or steadily falling is called run - another pattern that is closely associated with a run is a trend - which 7 consecutive points are climbing or 7 points are steadily falling is classified as a run - trends are usually more gradual with more fluctuations and often indicate a slower process change • Causes - material variability, loosening fixtures, operator fatigue, machine wear, better training & maintenance, etc.

CONTROL CHARTS for VARIABLES 4. Cycles - pattern that repeat on a regular basis - concentration on the factors that change the process periodically • Causes - operator fatigue, shift changes, periodic speed changes, power fluctuations, reliance on different suppliers, etc.

CONTROL CHARTS for VARIABLES 5. Grouping - this is another case in which one trouble classification may be embedded in another - grouping, or bunching, occurs when the points on a chart occur in clusters • Causes - inconsistent materials & method, several upstream problems, shifting fixtures, differences in work quality, etc.

CONTROL CHARTS for VARIABLES 6. Instability - an erratic pattern that has large fluctuations on a control chart is classified as instability, or unstable mixture - more than one-third of the points lie outside the center ± band or more than 4% of the points fall in or beyond the outer bands - the chart has a steep, zigzag pattern • Causes - frequent breakdowns and startups, overadjustment, poor sampling procedures, inconsistent materials, faulty gauge, etc.

CONTROL CHARTS for VARIABLES 7. Stable mixtures - a mixture pattern that has erratic ups and downs similar to the instability pattern but has very few points in the middle of the chart - usually indicates a mixing of two different stable distribution: one for the upper set of points and one for the lower set - five or more consecutive points outside the C zones or either side of the center line signal a stable mixture pattern • Causes - different (suppliers, inspectors, operators, lines, gauges, etc. )

CONTROL CHARTS for VARIABLES 8. Stratification - the points hug the averages line on a control chart - this pattern is 14 or more consecutive points in the two C zones, within ± of the average value • Causes - falsification of data, gauge scale too crude for the job, nonrandom, representative sampling, etc.