A manufacturer of programmable calculators is attempting to determine a reasonable free-service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 30 months. Assume product life can be described by an exponential distribution. T / MTBF e-T /MTBF T / MTBF e-T /MTBF T / MTBF e-T /MTBF 0.10 0.9048 2.60 0.0743 5.10 0.0061 0.20 0.8187 2.70 0.0672 5.20 0.0055 0.30 0.7408 2.80 0.0608 5.30 0.0050 0.40 0.6703 2.90 0.0550 5.40 0.0045 0.50 0.6065 3.00 0.0498 5.50 0.0041 0.60 0.5488 3.10 0.0450 5.60 0.0037 0.70 0.4966 3.20 0.0408 5.70 0.0033 0.80 0.4493 3.30 0.0369 5.80 0.0030 0.90 0.4066 3.40 0.0334 5.90 0.0027 1.00 0.3679 3.50 0.0302 6.00 0.0025 1.10 0.3329 3.60 0.0273 6.10 0.0022 1.20 0.3012 3.70 0.0247 6.20 0.0020 1.30 0.2725 3.80 0.0224 6.30 0.0018 1.40 0.2466 3.90 0.0202 6.40 0.0017 1.50 0.2231 4.00 0.0183 6.50 0.0015 1.60 0.2019 4.10 0.0166 6.60 0.0014 1.70 0.1827 4.20 0.0150 6.70 0.0012 1.80 0.1653 4.30 0.0136 6.80 0.0011 1.90 0.1496 4.40 0.0123 6.90 0.0010 2.00 0.1353 4.50 0.0111 7.00 0.0009 2.10 0.1255 4.60 0.0101 2.20 0.1108 4.70 0.0091 2.30 0.1003 4.80 0.0082 2.40 0.0907 4.90 0.0074 2.50 0.0821 5.00 0.0067 a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fail during the service period? (Enter your answer to 4 decimal places using probabilities shown in the above table.) 1 – e–T/MTBF b. What service period would result in a failure rate of approximately 10 percent? (Enter your answer to the nearest whole month using the closest appropriate table value.) T months

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 52P

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A manufacturer of programmable calculators is attempting to determine a reasonable free-service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 30 months. Assume product life can be described by an exponential distribution.

T / MTBF	e^{-T /}^MTBF	T / MTBF	e^{-T /}^MTBF	T / MTBF	e^{-T /}^MTBF
0.10	0.9048	2.60	0.0743	5.10	0.0061
0.20	0.8187	2.70	0.0672	5.20	0.0055
0.30	0.7408	2.80	0.0608	5.30	0.0050
0.40	0.6703	2.90	0.0550	5.40	0.0045
0.50	0.6065	3.00	0.0498	5.50	0.0041
0.60	0.5488	3.10	0.0450	5.60	0.0037
0.70	0.4966	3.20	0.0408	5.70	0.0033
0.80	0.4493	3.30	0.0369	5.80	0.0030
0.90	0.4066	3.40	0.0334	5.90	0.0027
1.00	0.3679	3.50	0.0302	6.00	0.0025
1.10	0.3329	3.60	0.0273	6.10	0.0022
1.20	0.3012	3.70	0.0247	6.20	0.0020
1.30	0.2725	3.80	0.0224	6.30	0.0018
1.40	0.2466	3.90	0.0202	6.40	0.0017
1.50	0.2231	4.00	0.0183	6.50	0.0015
1.60	0.2019	4.10	0.0166	6.60	0.0014
1.70	0.1827	4.20	0.0150	6.70	0.0012
1.80	0.1653	4.30	0.0136	6.80	0.0011
1.90	0.1496	4.40	0.0123	6.90	0.0010
2.00	0.1353	4.50	0.0111	7.00	0.0009
2.10	0.1255	4.60	0.0101
2.20	0.1108	4.70	0.0091
2.30	0.1003	4.80	0.0082
2.40	0.0907	4.90	0.0074
2.50	0.0821	5.00	0.0067

a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fail during the service period? (Enter your answer to 4 decimal places using probabilities shown in the above table.)

1 – e^–T/MTBF

b. What service period would result in a failure rate of approximately 10 percent? (Enter your answer to the nearest whole month using the closest appropriate table value.)

T months

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