Statistical Process Control (SPC)

Statistical Process Control (SPC) Chapter 6

MGMT 326 Capacity, Facilities, & Work Design Products & Processes Quality Assurance Planning & Control Foundations of Operations Project Manage- ment Managing Quality Introduction Strategy Statistical Process Control Product Design Process Design

Capable Processes  = target  = target Statistical Process Control (SPC) SPC for Variables Basic SPC Concepts Types of Measures Variation Attributes Mean charts Range charts Objectives Variables  and  known First steps ,  unknown

Outputs Goods & Services Transformation Process Variation in a Transformation Process Variation Variation • Inputs • Facilities • Equipment • Materials • Energy Variation • Variation in inputs create variation in outputs • Variations in the transformation process • create variation in outputs

Variation • All processes have variation. • Common cause variation is random variation that is always present in a process. • Assignable cause variation results from changes in the inputs or the process. The cause can and should be identified. • Assignable cause variation shows that the process or the inputs have changed, at least temporarily.

Objectives of Statistical Process Control (SPC) • Find out how much common cause variation the process has • Find out if there is assignable cause variation. • A process is in control if it has no assignable cause variation • Being in control means that the process is stable and behaving as it usually does. • It does not mean that we have conformance quality and meet customer requirements.

First Steps in Statistical Process Control (SPC) • Measure characteristics of goods or services that are important to customers • Make a control chart for each characteristic • The chart is used to determine whether the process is in control

Variable Measures • Continuous random variables • Measure does not have to be a whole number. • Examples: time, weight, miles per gallon, length, diameter

Attribute Measures • Good/bad evaluations • Good or defective • Correct or incorrect • Number of defects per unit – always a whole number • Number of scratches on a table • Opinion surveys of quality • Customer satisfaction surveys • Teacher evaluations

SPC for VariablesThe Normal Distribution  = the population mean • = the standard deviation for the population 99.74% of the area under the normal curve is between  - 3 and  + 3

SPC for Variables The Central Limit Theorem • Samples are taken from a distribution with mean  and standard deviation . k = the number of samples n = the number of units in each sample • The sample means are normally distributed with mean  and standard deviation when k is large.

Control Limits for the Sample Mean when  and  are known • x is a variable, and samples of size n are taken from the population containing x. Given:  = 10,  = 1, n = 4 Then A 99.7% confidence interval for is

Control Limits for the Sample Mean when  and  are known (2) The lower control limit for is

Control Limits for the Sample Mean when  and  are known (3) The upper control limit for is

Control Limits for the Sample Mean when  and  are unknown • If the process is new or has been changed recently, we do not know  and  • Excel table, page 180 • Given: 25 samples, 4 units in each sample •  and  are not given • k = 25, n = 4

Control Limits for the Sample Mean when  and  are unknown (2) • Compute the mean for each sample. For example, • Compute

Control Limits for the Sample Mean when  and  are unknown (3) • For the ith sample, the sample range is Ri =(largest value in sample i ) - (smallest value in sample i ) • Compute Ri for every sample. For example, R1 = 16.02 – 15.83 = 0.19

Control Limits for the Sample Mean when  and  are unknown (4) • Compute , the average range • We will approximate by , where A2is a number that depends on the sample size n. We get A2from Table 6.1, page 182

Factor for x-Chart Factors for R-Chart Sample Size (n) A2 D3 D4 2 1.88 0.00 3.27 3 1.02 0.00 2.57 4 0.73 0.00 2.28 5 0.58 0.00 2.11 6 0.48 0.00 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 Control Limits for the Sample Mean when  and  are unknown (5) • n = the number of units in each sample = 4. From Table 6.1, A2= 0.73. The same A2is used for every problem with n = 4.

Control Limits for the Sample Mean when  and  are unknown (6) • The formula for the lower control limit is • The formula for the upper control limit is

Control Chart for The variation between LCL = 15.74 and UCL = 16.16 is the common cause variation.

Factor for x-Chart Factors for R-Chart Sample Size (n) A2 D3 D4 2 1.88 0.00 3.27 3 1.02 0.00 2.57 4 0.73 0.00 2.28 5 0.58 0.00 2.11 6 0.48 0.00 2.00 7 0.42 0.08 1.92 8 0.37 0.14 1.86 9 0.34 0.18 1.82 10 0.31 0.22 1.78 11 0.29 0.26 1.74 12 0.27 0.28 1.72 13 0.25 0.31 1.69 14 0.24 0.33 1.67 15 0.22 0.35 1.65 Control Limits for R • From the table, get D3 and D4 for n = 4. D3 = 0 D4= 2.28

Control Limits for R (2) • The formula for the lower control limit is • The formula for the upper control limit is

fig_ex06_03 fig_ex06_03

Capable Transformation Process • Inputs • Facilities • Equipment • Materials • Energy Outputs Goods & Services that meet specifications CapableTransformation Process a specification that meets customer requirements + acapable process (meets specifications) = Satisfied customers and repeat business

Review of Specification Limits • The target for a process is the ideal value • Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces • Specification limits are the acceptable range of values for a variable • Example: the amount of beverage in a bottle must be at least 15.8 ounces and no more than 16.2 ounces. • The allowable range is 15.8 – 16.2 ounces. • Lower specification limit = 15.8 ounces or LSL = 15.8 ounces • Upper specification limit = 16.2 ounces or USL = 16.2 ounces

Control Limits vs. Specification Limits • Control limits show the actual range of variation within a process • What the process is doing • Specification limits show the acceptable common cause variation that will meet customer requirements. • Specification limits show what the process should do to meet customer requirements

Process is Capable: Control Limits arewithin or on Specification Limits Upper specification limit UCL X LCL Lower specification limit

Process is Not Capable: One or BothControl Limits are Outside Specification Limits UCL Upper specification limit X LCL Lower specification limit

Capability and Conformance Quality • A process is capable if • It is in control and • It consistently produces outputs that meet specifications. • This means that both control limits for the mean must be within the specification limits • A capable process produces outputs that have conformance quality (outputs that meet specifications).

Process Capability Ratio • Use to determine whether the process is capable when  = target. • If , the process is capable, • If , the process is not capable.

Example • Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 16. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.

Example (2) • Given:  = 16,  = 0.06, target = 16 LSL = 15.8, USL = 16.2 The process is capable.

Process Capability Index Cpk • If Cpk > 1, the process is capable. • If Cpk < 1, the process is not capable. • We must use Cpk when  does not equal the target.

CpkExample • Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 15.9. The allowable range is 15.8 – 16.2. The standard deviation is 0.06. Find and determine whether the process is capable.

CpkExample (2) • Given:  = 15.9,  = 0.06, target = 16 LSL = 15.8, USL = 16.2 Cpk < 1. Process is not capable.

Statistical Process Control (SPC)