Chapter 7 Statistical Quality Control Quality Control Approaches

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Chapter 7 Statistical Quality Control

Chapter 7 Statistical Quality Control

Quality Control Approaches l Statistical process control (SPC) Monitors the production process to prevent

Quality Control Approaches l Statistical process control (SPC) Monitors the production process to prevent poor quality

Statistical Process Control l Take periodic samples from a process l Plot the sample

Statistical Process Control l Take periodic samples from a process l Plot the sample points on a control chart l Determine if the process is within limits l Correct the process before defects occur

Types Of Data l Attribute data l Product characteristic evaluated with a discrete choice

Types Of Data l Attribute data l Product characteristic evaluated with a discrete choice – l Good/bad, yes/no Variable data l Product – characteristic that can be measured Length, size, weight, height, time, velocity

SPC Applied To Services l Nature of defect is different in services l Service

SPC Applied To Services l Nature of defect is different in services l Service defect is a failure to meet customer requirements l Monitor times, customer satisfaction

Service Quality Examples l Hospitals timeliness, responsiveness, accuracy l Grocery Stores Check-out time, stocking,

Service Quality Examples l Hospitals timeliness, responsiveness, accuracy l Grocery Stores Check-out time, stocking, cleanliness l Airlines luggage handling, waiting times, courtesy l Fast food restaurants waiting times, food quality, cleanliness

Process Control Chart Upper control limit Process average Lower control limit 1 2 3

Process Control Chart Upper control limit Process average Lower control limit 1 2 3 4 5 6 Sample number 7 8 9 10

Constructing a Control Chart l l l Decide what to measure or count Collect

Constructing a Control Chart l l l Decide what to measure or count Collect the sample data Plot the samples on a control chart Calculate and plot the control limits on the control chart Determine if the data is in-control l If non-random variation is present, discard the data (fix the problem) and recalculate the control limits

A Process Is In Control If l No sample points are outside control limits

A Process Is In Control If l No sample points are outside control limits l Most points are near the process average l About an equal # points are above & below the centerline l Points appear randomly distributed

The Normal Distribution 95 % 99. 74 % -3 s -2 s -1 s

The Normal Distribution 95 % 99. 74 % -3 s -2 s -1 s m = 0 1 s 2 s 3 s Area under the curve = 1. 0

Control Charts and the Normal Distribution UCL +3 s Mean -3 s LCL

Control Charts and the Normal Distribution UCL +3 s Mean -3 s LCL

Types Of Data l Attribute data (p-charts, c-charts) Product characteristics evaluated with a discrete

Types Of Data l Attribute data (p-charts, c-charts) Product characteristics evaluated with a discrete choice (Good/bad, yes/no, count) l Variable data (X-bar and R charts) Product characteristics that can be measured (Length, size, weight, height, time, velocity)

Control Charts For Attributes l p Charts Calculate percent defectives in a sample; an

Control Charts For Attributes l p Charts Calculate percent defectives in a sample; an item is either good or bad l c Charts Count number of defects in an item

p - Charts Based on the binomial distribution p = number defective / sample

p - Charts Based on the binomial distribution p = number defective / sample size, n p = total no. of defectives total no. of sample observations UCL = p + 3 p(1 -p)/n LCL = p - 3 p(1 -p)/n

p-Chart Example The Western Jean Company produced denim jean. The company wants to establish

p-Chart Example The Western Jean Company produced denim jean. The company wants to establish a p-chart to monitor the production process and main high quality. Western beliefs that approximately 99. 74 percent of the variability in the production process (corresponding to 3 -sigma limits, or z = 3. 00) is random and thus should be within control limits, whereas 0. 26 percent of the process variability is not random and suggest that the process is out of control.

p-Chart Example The company has taken 20 sample (one per day for 20 days),

p-Chart Example The company has taken 20 sample (one per day for 20 days), each containing 100 pairs of jeans (n = 100), and inspected them for defects, the results of which are as follow.

Sample 1 2 3 4 5 6 7 8 9 10 # Defects 6

Sample 1 2 3 4 5 6 7 8 9 10 # Defects 6 0 4 10 6 4 12 10 8 10 Sample 11 12 13 14 15 16 17 18 19 20 # Defects 12 10 14 8 6 16 12 14 20 18

p-Chart Calculations Proportion Sample Defective 1 6. 06 2 0. 00 3 4. 04

p-Chart Calculations Proportion Sample Defective 1 6. 06 2 0. 00 3 4. 04 . . 20 . . 18 200 UCL = p + 3 p(1 -p) /n . . = = 0. 190 . 18 100 jeans in each sample p = = 0. 10 + 3 0. 10 (1 -0. 10) /100 total defectives total sample observations 200 = 0. 10 20 (100) LCL = p - 3 p(1 -p) /n = 0. 10 + 3 0. 10 (1 -0. 10) /100 = 0. 010

Sample number

Sample number

c - Charts l Count the number of defects in an item l Based

c - Charts l Count the number of defects in an item l Based on the Poisson distribution c = number of defects in an item c= total number of defects number of samples UCL = c + 3 c LCL = c - 3 c

c-Chart Example The Ritz Hotel has 240 rooms. The hotel’s housekeeping department is responsible

c-Chart Example The Ritz Hotel has 240 rooms. The hotel’s housekeeping department is responsible for maintaining the quality of the room’s appearance and cleanliness. Each individual housekeeper is responsible for an area encompassing 20 rooms. Every room in use is thoroughly clean and its supplies, toiletries, and so on are restocked each day. Any defects that the housekeeping staff notice that are not part the normal housekeeping service are supposed to be reported hotel maintenance.

c-Chart Example Every room is briefly inspected each day by a housekeeping supervisor. However,

c-Chart Example Every room is briefly inspected each day by a housekeeping supervisor. However, hotel management also conducts inspection for qualitycontrol purposes. The management inspector not only check for normal housekeeping defects like clean sheets, dust, room supplies, room literature, or towels, but also for defects like an inoperative or missing TV remote, poor TV picture quality or reception, defective lamps, a malfunctioning clock, tears or stains in bedcovers or curtain, or a malfunctioning curtain pull.

c-Chart Example An inspection sample include 12 rooms, i. e. , one room selected

c-Chart Example An inspection sample include 12 rooms, i. e. , one room selected at random from each of the twelve 20 -room blocks served by a housekeeper. Following are the results from 15 inspection samples conducted at random during a 1 -month period.

Sample 1 2 3 4 5 6 7 8 9 10 # Defects 12

Sample 1 2 3 4 5 6 7 8 9 10 # Defects 12 8 16 14 10 11 9 14 13 15 Sample # Defects 11 12 12 10 13 14 14 17 15 15

c - Chart Calculations Count # of defects per roll in 15 rolls of

c - Chart Calculations Count # of defects per roll in 15 rolls of denim fabric Sample Defects 1 12 2 8 3 16. . . 15 190 c = 190/15 = 12. 67 UCL = c + 3 c = 12. 67 + 3 12. 67 = 23. 35 LCL = c - 3 c = 12. 67 - 3 12. 67 = 1. 99

Example c - Chart

Example c - Chart

Control Charts For Variables l Mean chart (X-Bar Chart) Measures central tendency of a

Control Charts For Variables l Mean chart (X-Bar Chart) Measures central tendency of a sample l Range chart (R-Chart) Measures amount of dispersion in a sample l Each chart measures the process differently. Both the process average and process variability must be in control for the process to be in control.

Example: Control harts for Variable Data The Goliath Tool Company produces slip-ring bearings, which

Example: Control harts for Variable Data The Goliath Tool Company produces slip-ring bearings, which look like flat doughnut or washer, they fit around shafts or rods, such as drive shaft in machinery or motor. In the production process for a particular slip-ring bearing the employees has taken 10 samples (during a 10 day period) of 5 slip-ring bearing (i. e. , n = 5). The individual observation from each sample are shown as followed:

Example: Control Charts for Variable Data Sample 1 2 3 4 5 6 7

Example: Control Charts for Variable Data Sample 1 2 3 4 5 6 7 8 9 10 Slip Ring Diameter (cm) 1 2 3 4 5 5. 02 5. 01 4. 94 4. 99 4. 96 5. 01 5. 03 5. 07 4. 95 4. 96 4. 99 5. 00 4. 93 4. 92 4. 99 5. 03 4. 91 5. 01 4. 98 4. 89 4. 95 4. 92 5. 03 5. 05 5. 01 4. 97 5. 06 4. 96 5. 03 5. 05 5. 01 5. 10 4. 96 4. 99 5. 09 5. 10 5. 00 4. 99 5. 08 5. 14 5. 10 4. 99 5. 08 5. 09 5. 01 4. 98 5. 07 4. 99 X 4. 98 5. 00 4. 97 4. 96 4. 99 5. 01 5. 02 5. 05 5. 08 5. 03 50. 09 R 0. 08 0. 12 0. 08 0. 14 0. 13 0. 10 0. 14 0. 11 0. 15 0. 10 1. 15

Constructing an Range Chart UCLR = D 4 R = (2. 11) (. 115)

Constructing an Range Chart UCLR = D 4 R = (2. 11) (. 115) = 0. 24 LCLR = D 3 R = (0) (. 115) = 0 where R = S R / k = 1. 15 / 10 =. 115 k = number of samples = 10 R = range = (largest - smallest)

Example R-Chart UCL R LCL

Example R-Chart UCL R LCL

Constructing A Mean Chart UCLX = X + A 2 R = 5. 01

Constructing A Mean Chart UCLX = X + A 2 R = 5. 01 + (0. 58) (. 115) = 5. 08 LCLX = X - A 2 R = 5. 01 - (0. 58) (. 115) = 4. 94 where X = average of sample means = S X / n = 50. 09 / 10 = 5. 01 R = average range = S R / k = 1. 15 / 10 =. 115

Example X-bar Chart UCL X LCL

Example X-bar Chart UCL X LCL

Variation l Common Causes Variation inherent in a process Can be eliminated only through

Variation l Common Causes Variation inherent in a process Can be eliminated only through improvements in the system l Special Causes Variation due to identifiable factors Can be modified through operator or management action

Control Chart Patterns UCL LCL Sample observations consistently below the center line Sample observations

Control Chart Patterns UCL LCL Sample observations consistently below the center line Sample observations consistently above the center line

Control Chart Patterns UCL LCL Sample observations consistently increasing Sample observations consistently decreasing

Control Chart Patterns UCL LCL Sample observations consistently increasing Sample observations consistently decreasing

Sample Size Determination l Attribute control charts 50 to 100 parts in a sample

Sample Size Determination l Attribute control charts 50 to 100 parts in a sample l Variable control charts 2 to 10 parts in a sample