Process Capability (cont’d)Homework Problems

COB 300C

The Operations Dimension

Busing – Fall ‘03

Homework Solutions

SP1. A process that produces computer chips has a mean of .03 defective chips and a standard deviation of .003 chips. The allowable variation is from .02 to .04 defectives.

A. Compute the capability ratio for the process.

B. Is the process capable?

Problem SP1

11.1003.6

02.04.

pC

Yes, the process capability index indicates that the process will produce virtually 100 percent conforming output (the range of the process output permitted by specifications is larger than the actual range of the process).

Problem SP1 (cont’d)

Additional Question: What proportion of chips currently meet specifications?

.9991 proportion

.49957 Table Normal fromy Probabilit

333.3003./01.

01.2

02.04.

Problem SP2

Given the following list of machines, the standard deviation for each, and specifications for a job that may be processed on that machine, determine which machines are capable of performing the given jobs.

MachineStandard Deviation (gr) Job Specification (+/- gr)

001 0.02 0.05

002 0.04 0.07

003 0.10 0.18

004 0.05 0.15

005 0.01 0.04

Problem SP2

Given the following list of machines, the standard deviation for each, and specifications for a job that may be processed on that machine, determine which machines are capable of performing the given jobs.

STD. JOB

MACH DEV’N (in) SPEC. (+/- in.) Cp

001 0.02 0.05 .10/6*.02 = .833

002 0.04 0.07 .14/6*.04 = .583

003 0.10 0.18 .36/6*.10 = .600

004 0.05 0.15 .30/6*.05 = 1.000

005 0.01 0.04 .08/6*.01 = 1.333

Problem SP3

Suppose your manager presents you with the following information that could be used for a job, and wants your recommendation on which one to choose. The specification width is 0.48 mm. In this instance, you can narrow the set of choices, but you probably wouldn’t make a recommendation without an additional piece of information. Explain.

Cost per Standard

MachineUnit ($) Deviation (mm) Cp

A 20 0.079 1.01

B 12 0.080 1.00

C 11 0.084 0.95

D 10 0.081 0.99

Problem SP4

Customers of a pizza maker have specified that pizza crusts they order should be between 28 and 32 centimeters in diameter. Sample data indicates that the crusts actually have a mean diameter of 30 centimeters with standard deviation 1.1 centimeters. Can the company deliver pizza crusts to customer specifications? Of every 1000 crusts, how many crusts will fail to meet specifications?

Solution to Problem SP4

68.8.06881000

.0688 .9312-1 ionsspecificatmeet tofailing ofy Probabilit

.93122*.4656

.4656 Table Normal Std. fromy Probabilit

value)(lookup 82.11.1/2

22

2832

606.1.16

2832

pC

Problem SP5

A customer has specified that they expect a process capability of 2.0 from a supplier’s process. If the process has specifications of 5.2 and 5.6, what is the maximum process variability that will allow the process to meet the customer’s expectations?

Solution to Problem SP5

A customer has specified that they expect a process capability of 2.0 from a supplier’s process. If the process has specifications of 5.2 and 5.6, what is the maximum process variability that will allow the process to meet the customer’s expectations?

.033 12

5.2-5.6

6

2.56.500.2

Problem SP5 (cont’d)

If sigma in fact equals 0.1, what is the process capability and what percentage of items supplied will meet specifications?

Problem SP5 (cont’d)

If sigma in fact equals 0.1, what is the process capability and what percentage of items supplied will meet specifications?

– Cp = 0.4 / 6 (.1) = 0.66

ions.specificatmeet willitems of 95.44%

0.95442.4772 area

side)each (on mean from deviations standard 00.21.

2.

2.2

2.56.5

EXAM 1 Topics

• Introductory Material

• Operations Strategy

• Product Design

• Process Design (cost, volume, profit)

(breakeven analysis)

• Process Capability