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## Chapter 9A

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**Chapter 9A**Process Capability and Statistical Process Control**Learning Objectives**• Explain what statistical quality control is. • Calculate the capability of a process. • Understand how processes are monitored with control charts for both attribute and variable data**Types of Situations where SPC can be Applied**• How many paint defects are there in the finish of a car? • How long does it take to execute market orders? • How well are we able to maintain the dimensional tolerance on our ball bearing assembly? • How long do customers wait to be served from our drive-through window? LO 1**Basic Forms of Variation**• Assignable variation: caused by factors that can be clearly identified and possibly managed • Example: a poorly trained employee that creates variation in finished product output • Common variation: variation that is inherent in the production process • Example: a molding process that always leaves “burrs” or flaws on a molded item LO 1**Variation Around Us**• When variation is reduced, quality is improved • However, it is impossible to have zero variation • Engineers assign acceptable limits for variation • The limits are know as the upper and lower specification limits • Also know as upper and lower tolerance limits LO 1**Taguchi’s View of Variation**• Traditional view is that quality within the range is good and that the cost of quality outside this range is constant • Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs LO 1**Process Capability**• Taguchi argues that tolerance is not a yes/no decision, but a continuous function • Other experts argue that the process should be so good the probability of generating a defect should be very low LO 2**Process Capability**• Process limits • Specification limits • How do the limits relate to one another? LO 2**Process Capability**LO 2**Capability Index (Cpk)**• Capability index (Cpk) shows how well parts being produced fit into design limit specifications • Also useful to calculate probabilities LO 2**Example: Capability**• Data • Designed for an average of 60 psi • Lower limit of 55 psi, upper limit of 65 psi • Sample mean of 61 psi, standard deviation of 2 psi • Calculate Cpk LO 2**The Cereal Box Example**• We are the maker of this cereal. Consumer Reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box. • Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box. • Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces • Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces • We go out and buy 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of .529 ounces. LO 2**Cereal Box Process Capability**• Specification or Tolerance Limits • Upper Spec = 16.8 oz • Lower Spec = 15.2 oz • Observed Weight • Mean = 15.875 oz • Std Dev = .529 oz LO 2**What does a Cpk of .4253 mean?**• An index that shows how well the units being produced fit within the specification limits. • This is a process that will produce a relatively high number of defects. • Many companies look for a Cpk of 1.3 or better… 6-Sigma company wants 2.0! LO 2**Process Control Procedures**• Attribute (Go or no-go information) • Defectives refers to the acceptability of product across a range of characteristics. • Defects refers to the number of defects per unit which may be higher than the number of defectives. • p-chart application • Variable (Continuous) • Usually measured by the mean and the standard deviation. • X-bar and R chart applications LO 3**Statistical**Process Control (SPC) Charts UCL Normal Behavior LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time LO 3**Control Limits are based on the Normal Curve**x m z -3 -2 -1 0 1 2 3 Standard deviation units or “z” units. LO 3**x**Control Limits We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.73% of our sample observations to fall within these limits. 99.73% LCL UCL LO 3**Process Control with Attribute Measurement: Using ρ Charts**• Created for good/bad attributes • Use simple statistics to create the control limits LO 3**Interpreting Control Charts**1 – 2- 5- 7 Rule • 1 point above UCL or 1 point below LCL • 2 consecutive points near the UCL or 2 consecutive points near the LCL • 5 consecutive decreasing points or 5 consecutive increasing points • 7 consecutive points above the center line or 7 consecutive points below the center line LO 3**Process Control with Variable Measurements: Using x and R**Charts • In variable sampling, we measure actual values rather than sampling attributes • Generally want small sample size • Quicker • Cheaper • Samples of 4-5 are typical • Want 25 or so samples to set up chart LO 3**Example: The Data**LO 3