Statistical Process Control (SPC)

• The chapter focuses on Statistical Process Control (SPC) to ensure product and service quality.
• It details when and how to utilize SPC, including constructing control charts, assessing process capability, and identifying control chart patterns.

Quality Control in Smartphone Manufacturing

• Smartphone manufacturers employ Process Control techniques because quality is often more important to consumers than price.
• Samsung and Apple have extensive quality management systems using SPC to monitor and improve manufacturing processes to remove and prevent defects.
• SPC is a statistical procedure that uses control charts to determine whether a production process is functioning correctly and to prevent poor quality.

Basics of Statistical Process Control

• Samples are periodically taken from the production process and plotting these sample points on a chart to know if the process is within statistical control limits.
• A sample can be a single item or a group of items.
• If a sample point falls outside the control limits, the process might be out of control, and the cause is sorted to correct the problem.
• With continued monitoring and if the sample is within the control limits, the process is allowed to continue without interference.
• SPC prevents quality problems by correcting the process before it starts producing defects.

SPC in Quality Management

• Companies use SPC to determine if their processes are in control.
• SPC requires companies to train individuals to use it as a tool for monitoring production or service processes to make continuous improvements.
• Through SPC, employees can identify and rectify problems in their area to maintain quality.
• Statistical control charts is a graph to monitor a production process.
• By using control charts, employees and management can quickly identify problems and prevent low-quality items, saving resources.

Quality Measures: Attributes and Variables

• Attribute refers to a product characteristic like color, texture, cleanliness, or smell, evaluated quickly with responses like good/bad or yes/no.
• Variable measure refers to a product characteristic measured on a continuous scale, such as length, weight, temperature, or time.

SPC Applied to Services

• Control charts are useful for monitoring quality in services.
• Defect in services means a failure to meet customer requirements in any product or service.
• The defect can be an empty soap dispenser, a phone catalog order error, a blemish on cloth, or a faulty tray.
• Control charts for service processes use quality characteristics and measurements like time and customer satisfaction.

Examples of services that can be measured with control charts:

• Hospitals focus on timeliness of care, staff response, lab test and paperwork accuracy, and speed of admittance.
• Grocery stores looks at waiting time, out-of-stock items, food quality, cleanliness, customer complaints, and register errors.
• Airlines consider flight delays, lost luggage handling, waiting time at counters, agent courtesy, flight information accuracy, and cabin cleanliness.
• Fast-food restaurants monitor waiting time, customer complaints, cleanliness, food quality, order accuracy, and employee courtesy.
• Catalog-order companies focus on order accuracy, operator knowledge, packaging, delivery time, and phone order waiting time.
• Insurance companies observe for billing accuracy, claims processing, agent availability and response time.

Where to Use Control Charts

• Most companies don't use control charts for every step, because it is costly and time-consuming.
• Control charts should be used at critical points that have historically shown a tendency to go out of control.
• Critical points are where the process going out of control would be harmful and too costly.

Control Charts

• They are graphs that visually show if a sample is within statistical control limits.
• Two main purposes of a control chart:
  • Establish control limits.
  • Monitor to indicate when a process is out of control.
• Control charts exist for both attributes and variables.

Control Charts for Attributes

• Attribute control charts use discrete values reflecting a simple decision criterion such as good or bad.
• A p-chart is used to show the defective items in a sample as the sample statistic
• A c-chart is used to show the actual number of defects per item in a sample.
• A p-chart suits situations where defective vs. non-defective items can be distinguished and the number of defectives presented as a percentage of the whole.
• When the proportion defective cannot be determined, a c-chart is required.

P Chart

• A sample of n items is periodically drawn from the production process when using a p-chart, and the proportion of defective items in the sample is determined to know if the control limits on the chart.
• Normal distribution approximates the proportion defective as the sample size (n) increases for p-charts employing a discrete attribute measure.
• Upper Control Limit (UCL) and Lower Control Limit (LCL) are computed based on equations.

C Chart

• c-charts are used when it is impossible to compute a proportion defective and the actual number of defects must be used.
• A c-chart can be used when the number of blemishes can be counted on automobiles.
• The normal distribution approximates the distribution of defects.

Control Charts for Variables

• When a sample of items is taken from a process the mean of the sample is computed and plotted on the chart (in a mean or x chart).
• Sample taken tend to be around 4 or 5.
• The center line of the control chart is the overall process average, which is the mean of the sample means.
• The x chart is based on normal distribution and can be constructed in 2 ways depending on the information available.

Mean (x¯-) Chart Formulas

• Computation of the UCL and LCL:
  • UCL = x + zσx
  • LCL = x − zσx
• where:
  • x = process average =Σ(x1 to xn)/k
  • σ = process standard deviation
  • σx = standard deviation of sample means = σ/√n
  • k = number of samples
  • n = sample size
• The UCL and LCL are computed using formulas like:
  • UCL = x + A2R
  • LCL = x – A2R

Range (R-) Chart

• The difference between the smallest and largest values in a sample is the range in an R-chart.
• This range reflects the process variability.
• UCL = D4R
• LCL = D3R
• R is the average range for the samples.

Using the X and R Charts Together

• The x-chart is used with the R-chart because process average and variability must be in control.
• Two charts measure distinctly process
• It is possible for there to have narrow ranges, suggesting little process variability, but the sample averages might be beyond the control limits.

Control Chart Patterns

• Even with the control chart the variations can still be random.
• If the values display a pattern, it can mean that this isn't naturally random and needs investigation.
• Natural variation in the process will see bouncing around above and below the centerline.
• Values are consistently above or below the centerline or moving consistently in a direction, it usually means it isn't random or has a cause.

3 Control Chart Patterns

• A pattern is characterized by a sequence of observations.
• Also known as a run
• A sequence has observations above or below the centerline
• Several tests are available to determine if a pattern is random or not.
• One type of pattern test divides the control chart into three zones on each side of the center line.

Five guidelines that identify patterns (none of the observations are beyond control limits):

• Eight consecutive points on one side of the center line.
• Eight consecutive points up or down.
• Fourteen points alternating up or down.
• Two out of three consecutive points in zone A on one side of the center line.
• Four out of five consecutive points in zone A or B on one side of the center line.

Sample Size Determination

• Attribute charts require larger sample sizes for quality measurement because more observations are required.
• Variable control charts require smaller sample sizes.
• Only 5% defective requires a sample size of 100, but samples of 10 does not permit a result with percent defective items
• Size may not be the only consideration in sampling. It may be important that the samples come from a homogeneous source so the cause can be determined.

SPC with Excel and OM Tools and Process Capability

• Process control charts can be developed with statistical computer software and spreadsheet packages, such as Excel.
• Can use excel and OM tools to develop a statistical process control chart on the computer.

Process Capability

• Control limits determine natural variation. Tolerances are design specifications reflecting product requirements.
• Process capability is the process's natural variation relative to design specifications.
• The natural range of variation, the process center/ mean and the design specifications are the three keys associated with process capability.

Process Capability Measures

• A measure of the capability of a process to meet design specifications is the process capability ratio Cp. Cp = tolerance range/ process range
  • = upper specification limit- lower specification limit/6σ -If Cp is less than 1.0, the process can't produce within specification all the time.
  • If Cp equals 1.0, tolerance equals process range.
  • If Cp is greater than 1.0, tolerance is greater than process range.
• Process capability index Cpk:
  • indicates if the process mean has shifted. -equals to process capability for both high and low values. -Cpk =minimum-lower specification/3 sigma ,upper specification/- 3
  • If the Cpk index is greater than 1.00, the process is capable of meeting design specifications.
  • Process is off center when Cpk is less than 1.00 -Process is centered when Cpk equals to Cp