# LC Technology Manufacturing Systems. Quality Management – Pareto Analysis Pinpoints problems through the identification and separation of the ‘vital few’

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LC Technology Manufacturing Systems

Quality Management – Pareto Analysis Pinpoints problems through the identification and separation of the ‘vital few’ problems from the trivial many. Vilifredo Pareto: concluded that 80% of the problems with any process are due to 20% of the causes.

Quality Management – Pareto Analysis Causes of poor soldering

Causes of poor soldering – descending order Quality Management – Pareto Analysis

Cumulative plot is made of all of the causes 80% caused by two problems Quality Management – Pareto Analysis

Statistical Process Control Statistical procedure to verify quality Check manufacturing process is working correctly →Inspect and measure manufacturing process →Varying from target – corrective action taken Prevents poor quality before it occurs

Statistical Process Control When? Manufacturing large quantities of items Euro coins Computers Cars etc. Why? Impractical to measure each item made Machine/equipment/human error How? Measure a small proportion of the produced items (sample) Use X-bar and R Charts to see if process is in control Conclude the quality characteristics of the whole process

Laser machine A – cutting 20mm hole Normal Distribution Some measurement < 20mm Some measurements > 20mm Natural occurrence

Normal Distribution Machine B making same part as machine A Same distribution Skewed to right

Normal Distribution Histogram: Statistical information Column width represents a range of sizes Shape of histogram is proportional to spread of data Results of a survey on the heights of a group of pupils in a large school Column width = 25mm

Normal Distribution Larger survey – population of a town Column width = 10mm Centered about mean Characteristic ‘Bell’ shape curve Number of occurrences reduce as they deviate from the mean

Normal Distribution A very small sample interval approximates a curve as shown

Normal Distribution 0 10 20 30 40 50 60 All measurable attributes show a variation Spread of Sizes = Normal Distribution

Normal Distribution The spread or ‘width’ of the curve has a precise mathematical meaning - Variance The greater the variance the wider the curve Defined by a parameter called the standard deviation

Normal Distribution Calculation of standard distribution (sigma) -measured sizes of a sample of parts y1,y2…etc are the measured values of the sample is the average value N is the number of samples taken

Normal Distribution Sharpen 5 pencils to a length of 8 mm Mean average = 7.54 Sigma = (each value – mean average)² + number of values (6.5 - 7.54)² + (8.2 – 7.54)² + (8.5 – 7.54)² + (7.5 – 7.54)² + (7 – 7.54)² 5 SIGMA = 0.73 6.5mm8.2mm8.5mm7.5mm7.0mm

Normal Distribution If sigma is known then we know that: 95% of parts will lie within +/- 2σ of the mean 99.74% of parts will lie within +/- 3σ of the mean

Control Charts Used to establish the control limits for a process Used to monitor the process to show when it is out of control 1.X-bar Chart (Mean Charts) 2.R Charts (Range Charts)

Control Charts Process Mean = Mean of Sample Means Upper control limit (UCL) = Process mean+3 sigma Lower control limit (LCL) = Process mean-3 sigma

Control Charts – X-bar Charts 1. Record measurements from a number of samples sets (4 or 5)

Control Charts – X-bar Charts Oven temperature data MorningMiddayEvening Daily Means Monday 210208200206 Tuesday 212200210207 Wednesday 215209220215 Thursday 216207219214 Friday 220208215214 Saturday 210219200210 2. Calculate the mean of each sample set

3. Calculate the process mean (mean of sample means) Daily Means 206 207 215 214 210 Control Charts – X-bar Charts

4. Calculate UCL and LCL UCL = process mean + 3σ sample LCL = process mean - 3σ sample The standard deviation σ sample of the sample means where n is the sample size (3 temperature readings) σ = process standard deviation (4.2 degrees) σ sample = Control Charts – X-bar Charts

4. Calculate UCL and LCL UCL = process mean + 3σ sample LCL = process mean - 3σ sample σ sample UCL = 211 + 3(2.42) = 218.27 degrees LCL = 211 – 3(2.42) = 203.72 degrees Control Charts – X-bar Charts

UCL = 218.27 LCL = 203.72

Control Charts – X-bar Charts Interpreting control charts: Process out of control Last data point is out of control – indicates definite problem to be addressed immediately as defective products are being made.

Control Charts – X-bar Charts Interpreting control charts: Process in control Process still in control but there is a steady increase toward the UCL. There may be a possible problem and it should be investigated.

Control Charts – X-bar Charts Interpreting control charts: Process in control All data points are all above the process mean. This suggests some non-random influence on the process that should be investigated.

Control Charts – Range Charts The range is the difference between the largest and smallest values in a sample. Range is used to measure the process variation 1. Record measurements from a set of samples Oven temperature data MorningMiddayEvening 210208200 212200210 215209220 216207219 220208215 210219200

Control Charts – Range Charts 2. Calculate the range = highest – lowest reading Oven temperature data MorningMiddayEveningRange 21020820010 21220021012 21520922011 21620721912 22020821512 21021920019

Control Charts – Range Charts 3. Calculate UCL and LCL UCL = D4 x R average LCL = D3 x R average Sample size (n)D3D3 D4D4 203.27 302.57 402.28 502.11 602.00 70.081.92 80.141.86 90.181.82 100.221.78 110.261.74 UCL = 2.57 x 13 = 33.41 degrees LCL = 0 x 13 = 0 degrees

Control Charts – Range Charts UCL LCL R average

Matches the natural variation in a process to the size requirements (tolerance) imposed by the design Filling a box with washers: exact number not in all boxes upper limit set lower limit set Process Capability

Process not capable: a lot of boxes will be over and under filled Process Not Capable Normal distribution > specifications Cannot achieve tolerances all of the time

Process capable: However there will still be a small number of defective parts Process Capable Normal distribution is similar to specifications Tolerances will be met most of the time

Process capable: No defective parts Process Capable Normal distribution < specifications Tolerances will be met all the time

If C p =1 Process is capable i.e. 99.97% of the natural variation of the process will be within the acceptable limits Process Capability Index

If C p > 1 Process is capable. i.e. very few defects will be found – less than three per thousand, often much less Process Capability Index

If C p <1 Process is NOT capable i.e. the natural variation in the process will cause outputs that are outside the acceptable limits. Process Capability Index

Statistical Process Control Is doing things right 99% of the time good enough? 13 major accidents at Heathrow Airport every 2 days 5000 incorrect surgical procedures per week ……………… Pharmaceutical company producing 1 000 000 tablets a week, 99% quality would mean tablets would be defective! 10 000 Process of maintaining high quality standards is called : Quality Assurance Modern manufacturing companies often aim for a target of only 3 in a million defective parts. The term six sigma is used to describe quality at this level

Sampling Size of Sample? Sufficient to allow accurate assessment of process More – does not improve accuracy Less – reduced confidence in result

Size of Sample S = sample size e = acceptable error - as a proportion of std. deviation z = number relating to degree of confidence in the result ConfidenceValue for z 99%2.58 95%1.96 90%1.64 80%1.28 Sampling

Example – find mean value for weight of a packet of sugar with a confidence of 95% acceptable error of 10% Weight of packet of sugar = 1000g Process standard deviation = 10g Sampling

z = 1.96 from the table e = 0.1 (i.e.10%) Therefore the sample size s = (1.96 / 0.1)2 Therefore s = 384.16 Sample size = 385 Sampling

Assume mean weight = 1005g Sigma = 10g Therefore error = 10g + 10% = 11g Result: 95% confident average weight of all packets of sugar Sampling

QC, QA and TQM Quality Control: emerged during the 1940s and 1950s increase profit and reduce cost by the inspection of product quality. inspect components after manufacture reject or rework any defective components Disadvantages: just detects non-conforming products does not prevent defects happening wastage of material and time on scrapped and reworked parts inspection process not foolproof possibility of non-conforming parts being shipped by mistake

QC, QA and TQM Quality Assurance Set up a quality system documented approach to all procedures and processes that affect quality prevention and inspection is a large part of the process all aspects of the production process are involved system accredited using international standards

QC, QA and TQM Total Quality Management International competition during the 1980s and 1990s Everybody in the organisation is involved Focussed on needs of the customer through teamwork The aim is ‘zero defect’ production

Just-In-Time Manufacture Modern products – shortened life cycle Manufacturer – pressure for quick response Quick turnaround - hold inventory of stock Holding inventory costs money for storage Inventory items obsolete before use New approach: Just-In-Time Manufacture

Just-In-Time Manufacture Underlying concept: Eliminate waste. Minimum amount: Materials Parts Space Tools Time Suppliers are coordinated with manufacturing company.

Delivery address Return Container to Previous process Next process Number of components Just-In-Time Manufacture Kanbans – Japanese word for card Order form for components Passed from one station to another Initiates the production or movement of parts

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