Operations CH 3: Statistical Process Control

Types of Control Charts

- Attributes • p-chart • c-chart - Variables • mean (x bar - chart) • range (R-chart)

Control Charts for Attributes

- p-chart (proportion defective chart) - c-charts (# of defects chart)

X-Bar Chart

• x= Avg. of sample means = process avg. •R = Avg. Range value •Range = Difference betn. Smallest and largest values in sample

SPC in TQM SPC (continuous process improvement)

-Tool for identifying problems (undesired process variability) (Further tools used to identify the causes of the problem: Pareto Charts, quality circles, controlled experiments, fishbone diagram, flow chart, check sheets, brainstorming) and make improvements -Employee contributes to the TQM goal of continuous improvement (by continually monitoring the production process and making improvements)

Using x- bar and R-Charts Together

-Use of BOTH control charts together provide more complete picture of the overall process variability -BOTH process average and process variability must be in control -It is possible for samples to have very narrow ranges, but their averages beyond control limits -It is possible for sample averages to be in control, but ranges might be very large (Read solved example 3.4 and 3.5, pp. 120-123)

c-charts (# of defects chart)

-Uses actual number of defects in an item Ex: # of blemishes on roll of upholstery (Read c-chart example. pp. 116-118)

Where to Use Control Charts:

-Where the process has a tendency to go out of control (i.e. critical points, where historically the process has shown a tendency to go out of control) -Where if the process goes out of control it is particularly harmful and costly Examples -at the beginning of a process because it is a waste of time and money to begin production process with bad supplies -before a costly or irreversible point, after which product is difficult to rework or correct -before and after assembly or painting operations that might cover defects -before the outgoing final product or service is delivered (ex : QC check sticker)

Quality Measures

1. Attribute (Qualitative) Measure 2. Variable (Quantitative) Measure

Steps for Constructing a P-chart

1. Calculate Proportion defective column 2. Calculate = 3.Calculate UCL, LCL UCL = LCL = 4.Plot Chart - Proportion Defective vs. Sample# (with centre line, UCL, LCL, and individual sample points) 5.Comment on points outside LCL and UCL 6.Suggestions/Recommendations based on control chart

Steps for constructing any control chart

1. Calculate the "statistic" 2. Calculate centre line (using appropriate formula) 3. Calculate UCL & LCL (------"----"-------) • May have to calculate "standard deviation" 4. Plot Control Chart: (a) X-axis: Sample # (b) Y-axis: Statistic (c) Select appropriate scale (d) Centre Line (e) UCL, LCL (f) plot points (sample, statistic) (g) join points 5. Comment on Chart: In Control or Out of control (a) Points outside control limits (investigate the cause + correct the process + discard samples, devp. new center line and ctrl. limits from a diff. set of samples) (b) Patterns (--"—"—") (c) If a and b absent, process in control (estb. solely on random variation in the process, use chart to monitor the process)

Control Charts

Tool (Graph) to ensure that the process is within statistical control limits

Control Limits (Control Charts)

Upper and lower bands of a control chart

p-chart (proportion defective chart)

- Uses proportion of defective items in a sample as sample statistic - Sample of 'n' items taken periodically from the process - Plot proportion defective items in sample (to check if it falls within control limits on control chart) -Uses 'proportion of defective items' in a sample as sample statistic UCL = LCL = z= number of standard deviations from process average p= avg. proportion defective (process avg. / center line) Qp= standard deviation of sample proportion Qp =

When Control Chart is first Developed and Process found to be out of control, Then:

- examine process and investigate the causes of "out of control" - make corrections - determine new center line and control limits from a new set of sample observations - Use this "corrected" control chart to monitor the process

Attribute (Qualitative) Measure

-A product / service characteristic that can be evaluated with a discrete response such as good or bad, yes or no -ex: color, taste, smell, surface texture, cleanliness -ex: light bulb

Variable (Quantitative) Measure

-A product / service characteristic that is measured on a continuous scale -ex: height, weight, length, temperature, time

Sample Size

-Attribute charts require larger sample sizes • 50 to 100 parts in a sample -Variable charts require smaller samples • 2 to 10 parts in a sample

Statistical Process Control (SPC)

-Continual monitoring the production process to detect and prevent poor quality -If undesired variability, process corrected to avoid defects from occurring -Prevents quality problems by correcting the process before it starts producing defects -Extensive training (companies failing to achieve high quality)

Applying SPC to Service

-Nature of defect is different in services -Service defect is a failure to meet customer requirements -Control Charts use time and customer satisfaction (Read different services: pp. 111) -Hospitals •Timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts -Grocery stores •Waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors -Airlines •Flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance -Fast-food restaurants •waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy -Catalogue-order companies •order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time -Insurance companies •billing accuracy, timeliness of claims processing, agent availability and response time

Range chart ( R-Chart )

-Reflects amount of dispersion (variability) in a sample -Reflects process variability instead of tendency toward a mean value R= Avg. Range value k= number of samples

*(3)* Basics of Statistical Process Control

-Statistical Process Control (SPC) -Sample -Control Charts

Variability "No Process Produces Exactly Identical Items. All Processes Contain Certain Amount of Variability that Makes Some Variation between Units Inevitable"

1. Random Cause -Common/natural causes •inherent in a process •Result of natural occurrences -Causes process to vary between control limits •can be eliminated only through improvements in the system •Depends on: equipment and m/c, operator, system used for measurement 2. Special/Assignable/Non-random cause -Special causes •due to identifiable factors / non random (can be corrected) -If left unattended, will cause poor quality -Causes process to fall outside control limits (or causes patterns) •can be modified through operator or management action •Includes: equipment that is out of adjustment, broken m/c or equipment, defective materials, changes in parts or materials, operator fatigue, errors due to lack of training, poor work methods

Basics of Statistical Process Control (STEPS)

1. Take periodic samples from the process 2. Plot these sample points (attributes) on chart 3. To check if process is within statistical control limits If sample point/s out of control limits, find cause and correct problem (using other Quality tools) 4. Else / And process continues without interference with continued monitoring 5. Thus SPC (also called SQC) prevents quality problems by correcting process before it starts producing defects on a large scale

2 functions of ctrl charts:

1. establishes control limits of a process 2. process monitoring (visually indicates if a sample is within statistical control limits)

A Process Is in Control If:

1. no sample points outside limits 2. most points near process average (i.e. centre line) without too many close to control limits 3. about equal number of points above and below centerline 4. points appear randomly distributed (If any of these conditions are violated, process may be out of control)

Sample

Subset of items produced to use for inspection

Control Charts for Variables

• Sample size is small (around 4/5) (each sample observation provides usable info. Vs Attribute control charts - more obs. reqd. to devp. a usable qlty. measure) • Mean chart ( x - Chart ) Sample of a group of items taken from the process -The mean of the sample computed and plotted on chart • Each sample mean is a point on the control chart • Centre line of control chart = overall process avg. (i.e. mean of sample means)